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All questions of Data Sufficiency: 500 Level for GMAT Exam
Of the 58 drinks sold at Darlene’s Beverage Shop, 21 are carbonated. How many of the carbonated drinks sold in Darlene’s Beverage Shop are caffeinated?(1) There are 30 caffeinated drinks sold in Darlene’s Beverage Shop.
(2) Twenty-two of the non-carbonated drinks sold in Darlene’s Beverage Shop are not caffeinated.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
Of the 58 drinks sold at Darlene’s Beverage Shop, 21 are carbonated. How many of the carbonated drinks sold in Darlene’s Beverage Shop are caffeinated?
(1) There are 30 caffeinated drinks sold in Darlene’s Beverage Shop.
(2) Twenty-two of the non-carbonated drinks sold in Darlene’s Beverage Shop are not caffeinated.
(2) Twenty-two of the non-carbonated drinks sold in Darlene’s Beverage Shop are not caffeinated.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
BT Educators answered |
Step 1: Analyse Question Stem
Total drinks sold at Darlene’s Beverage Shop = 58
Total drinks sold at Darlene’s Beverage Shop = 58
- Total Carbonated drinks sold =21
- So, total non – carbonated drinks sold =58 – 21 = 37
We need to find out the number of carbonated drinks sold which were caffeinated too.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: There are 30 caffeinated drinks sold in Darlene’s Beverage Shop.
According to this statement:
(The number of carbonated drinks sold which were caffeinated) + (the number of non-carbonated drinks sold which were caffeinated)
However, we don’t know the number of non – carbonated drinks sold which were caffeinated.
= 30
Hence, we cannot find out the number of carbonated drinks sold which were caffeinated.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
Statement 2: Twenty-two of the non-carbonated drinks sold in Darlene’s Beverage Shop are not caffeinated.
Statement 1: There are 30 caffeinated drinks sold in Darlene’s Beverage Shop.
According to this statement:
(The number of carbonated drinks sold which were caffeinated) + (the number of non-carbonated drinks sold which were caffeinated)
However, we don’t know the number of non – carbonated drinks sold which were caffeinated.
= 30
Hence, we cannot find out the number of carbonated drinks sold which were caffeinated.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
Statement 2: Twenty-two of the non-carbonated drinks sold in Darlene’s Beverage Shop are not caffeinated.
According to this statement:
- Non -carbonated drinks sold which were non -caffeinated = 22
- So, (Non -carbonated drinks sold which were caffeinated) = (total non – carbonated drinks sold) - (Non -carbonated drinks sold which were non -caffeinated) = 37 – 22 = 15
However, with the above information we cannot find the number of carbonated drinks sold which were caffeinated.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.
Step 3: Analyse Statements by combining.
From statement 1:
From statement 1:
- (The number of carbonated drinks sold which were caffeinated) + (the number of non-carbonated drinks sold which were caffeinated) = 30
From statement 2:
- Non -carbonated drinks sold which were caffeinated = 15
On Combining both statements:
- We get, the number of carbonated drinks which were caffeinated = 30 – 15 = 15
Thus, the correct answer is Option C.
A and B are two integers. Is A-7B Even?(1) A and B both have the same Even/Odd nature.
(2) A and B are Both divisible by 100.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
A and B are two integers. Is A-7B Even?
(1) A and B both have the same Even/Odd nature.
(2) A and B are Both divisible by 100.
(2) A and B are Both divisible by 100.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
Rahul Kapoor answered |
Statement (1): A and B both have the same Even/Odd nature.
This statement tells us that A and B have the same parity, meaning they are both either even or odd. If A and B have the same parity, subtracting 7B from A will not change their parity. For example, if A and B are both even, then 7B will also be even, and subtracting an even number from an even number results in an even number. The same holds true if A and B are both odd. Therefore, statement (1) alone is sufficient to determine if A - 7B is even.
This statement tells us that A and B have the same parity, meaning they are both either even or odd. If A and B have the same parity, subtracting 7B from A will not change their parity. For example, if A and B are both even, then 7B will also be even, and subtracting an even number from an even number results in an even number. The same holds true if A and B are both odd. Therefore, statement (1) alone is sufficient to determine if A - 7B is even.
Statement (2): A and B are both divisible by 100.
This statement tells us that both A and B are multiples of 100. However, being divisible by 100 does not provide any specific information about the parity of A or B. For example, A could be an even multiple of 100 and B could be an odd multiple of 100, or vice versa. Without knowing the parity of A and B, we cannot determine the parity of A - 7B. Therefore, statement (2) alone is not sufficient to answer the question.
This statement tells us that both A and B are multiples of 100. However, being divisible by 100 does not provide any specific information about the parity of A or B. For example, A could be an even multiple of 100 and B could be an odd multiple of 100, or vice versa. Without knowing the parity of A and B, we cannot determine the parity of A - 7B. Therefore, statement (2) alone is not sufficient to answer the question.
When we consider both statements together, we know that A and B have the same parity (statement 1) and both are divisible by 100 (statement 2). This means that A and B are both even numbers. Subtracting an even number (7B) from another even number (A) will result in an even number. Therefore, when considering both statements together, we can conclude that A - 7B is even.
Hence, the answer is D: EACH statement ALONE is sufficient to answer the question asked.
A certain aquarium contains only goldfish and angelfish. If the aquarium contains a total of 75 male fish (of either species,) and 60 goldfish (of either sex,) then how many male goldfish are there in that aquarium?(1) There are 40 angelfish in that aquarium.
(2) There are 25 female fish in that aquarium.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
A certain aquarium contains only goldfish and angelfish. If the aquarium contains a total of 75 male fish (of either species,) and 60 goldfish (of either sex,) then how many male goldfish are there in that aquarium?
(1) There are 40 angelfish in that aquarium.
(2) There are 25 female fish in that aquarium.
(2) There are 25 female fish in that aquarium.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
Athira Choudhury answered |
Understanding the Problem
We have an aquarium with goldfish and angelfish. The key data points are:
- Total male fish: 75
- Total goldfish: 60
We need to find the number of male goldfish.
Analyzing Statement (1)
- There are 40 angelfish in the aquarium.
From this, we can deduce the number of goldfish:
- Total fish (goldfish + angelfish) = 75 male + female fish
- Since there are 40 angelfish, the total number of fish = 60 goldfish + 40 angelfish = 100 fish.
However, this does not provide the breakdown of male vs female goldfish or angelfish. Thus, we cannot determine the number of male goldfish from this statement alone.
Analyzing Statement (2)
- There are 25 female fish in the aquarium.
From this, we can also deduce:
- Total fish = 75 male + 25 female = 100 fish.
- Since there are 60 goldfish, we know that the number of female goldfish can be calculated, but we still don't know how many of the remaining male fish are goldfish or angelfish.
Again, this statement alone does not provide sufficient information to determine the number of male goldfish.
Combining Statements (1) and (2)
Even when combining the two statements:
- We know there are 40 angelfish and 25 female fish.
- This gives us 75 total male fish, but we still lack the specific breakdown of males and females among goldfish and angelfish.
Conclusion
Since neither statement alone nor the combination of both provides sufficient information to determine the number of male goldfish, the correct answer is:
Option E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
We have an aquarium with goldfish and angelfish. The key data points are:
- Total male fish: 75
- Total goldfish: 60
We need to find the number of male goldfish.
Analyzing Statement (1)
- There are 40 angelfish in the aquarium.
From this, we can deduce the number of goldfish:
- Total fish (goldfish + angelfish) = 75 male + female fish
- Since there are 40 angelfish, the total number of fish = 60 goldfish + 40 angelfish = 100 fish.
However, this does not provide the breakdown of male vs female goldfish or angelfish. Thus, we cannot determine the number of male goldfish from this statement alone.
Analyzing Statement (2)
- There are 25 female fish in the aquarium.
From this, we can also deduce:
- Total fish = 75 male + 25 female = 100 fish.
- Since there are 60 goldfish, we know that the number of female goldfish can be calculated, but we still don't know how many of the remaining male fish are goldfish or angelfish.
Again, this statement alone does not provide sufficient information to determine the number of male goldfish.
Combining Statements (1) and (2)
Even when combining the two statements:
- We know there are 40 angelfish and 25 female fish.
- This gives us 75 total male fish, but we still lack the specific breakdown of males and females among goldfish and angelfish.
Conclusion
Since neither statement alone nor the combination of both provides sufficient information to determine the number of male goldfish, the correct answer is:
Option E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
If x and y are consecutive even integers, what is the value of xy?(1) x + y = 98
(2) y - x = 2- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
If x and y are consecutive even integers, what is the value of xy?
(1) x + y = 98
(2) y - x = 2
(2) y - x = 2
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
Devansh Shah answered |
Understanding the Problem
To solve for the product of two consecutive even integers \(x\) and \(y\), we need to establish their values based on the information provided in the statements.
Defining Consecutive Even Integers
- Let \(x\) be the first even integer.
- Since \(x\) and \(y\) are consecutive even integers, we can express \(y\) as \(y = x + 2\).
Analyzing Statement (1)
- Statement (1): \(x + y = 98\)
Using the definition of \(y\):
\[
x + (x + 2) = 98 \implies 2x + 2 = 98 \implies 2x = 96 \implies x = 48
\]
Now, substituting \(x\) back to find \(y\):
\[
y = 48 + 2 = 50
\]
The product \(xy\) can now be calculated:
\[
xy = 48 \times 50 = 2400
\]
Thus, Statement (1) is sufficient.
Analyzing Statement (2)
- Statement (2): \(y - x = 2\)
From the definition of consecutive even integers:
\[
y - x = (x + 2) - x = 2
\]
This is a tautology. It does not provide specific values for \(x\) or \(y\), meaning we cannot determine \(xy\) from this statement alone.
Conclusion
- Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question.
- Therefore, the correct answer is option A.
To solve for the product of two consecutive even integers \(x\) and \(y\), we need to establish their values based on the information provided in the statements.
Defining Consecutive Even Integers
- Let \(x\) be the first even integer.
- Since \(x\) and \(y\) are consecutive even integers, we can express \(y\) as \(y = x + 2\).
Analyzing Statement (1)
- Statement (1): \(x + y = 98\)
Using the definition of \(y\):
\[
x + (x + 2) = 98 \implies 2x + 2 = 98 \implies 2x = 96 \implies x = 48
\]
Now, substituting \(x\) back to find \(y\):
\[
y = 48 + 2 = 50
\]
The product \(xy\) can now be calculated:
\[
xy = 48 \times 50 = 2400
\]
Thus, Statement (1) is sufficient.
Analyzing Statement (2)
- Statement (2): \(y - x = 2\)
From the definition of consecutive even integers:
\[
y - x = (x + 2) - x = 2
\]
This is a tautology. It does not provide specific values for \(x\) or \(y\), meaning we cannot determine \(xy\) from this statement alone.
Conclusion
- Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question.
- Therefore, the correct answer is option A.
What is the maximum number of arrangements in which N students can be seated in a row of N seats at a movie theater, if all students from the same college are to sit next to each other?(1) All students come from three colleges, X, Y, and Z that sent 12, 10, and 9 students, respectively.
(2) N is a prime number between 30 and 40.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
What is the maximum number of arrangements in which N students can be seated in a row of N seats at a movie theater, if all students from the same college are to sit next to each other?
(1) All students come from three colleges, X, Y, and Z that sent 12, 10, and 9 students, respectively.
(2) N is a prime number between 30 and 40.
(2) N is a prime number between 30 and 40.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Sinjini Mukherjee answered |
Understanding the Problem
To find the maximum arrangements of N students from different colleges seated together, we must calculate how to treat students from the same college as a single unit.
Statement (1) Analysis
- Total Students:
- College X: 12 students
- College Y: 10 students
- College Z: 9 students
- Total N = 12 + 10 + 9 = 31 students
- Group Arrangement:
- Treat students from the same college as a block:
- 3 blocks (X, Y, Z)
- Arrangements of Blocks:
- 3! ways to arrange the blocks.
- Arrangements within Blocks:
- College X: 12!
- College Y: 10!
- College Z: 9!
- Total Arrangements Calculation:
Total arrangements = 3! * 12! * 10! * 9!
This statement provides a specific number of students, allowing calculation of arrangements.
Statement (2) Analysis
- N as a Prime Number:
- N can be 31, 37, or 29 (only primes between 30 and 40).
- Insufficient Information:
- Without the distribution of students among colleges, we cannot determine the number of arrangements.
- Conclusion:
This statement alone does not provide sufficient data regarding how students are grouped.
Final Conclusion
- Statement (1) sufficiency: Yes, it provides exact data needed for calculations.
- Statement (2) sufficiency: No, it lacks specifics about student distribution.
Thus, the correct answer is (A): Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
To find the maximum arrangements of N students from different colleges seated together, we must calculate how to treat students from the same college as a single unit.
Statement (1) Analysis
- Total Students:
- College X: 12 students
- College Y: 10 students
- College Z: 9 students
- Total N = 12 + 10 + 9 = 31 students
- Group Arrangement:
- Treat students from the same college as a block:
- 3 blocks (X, Y, Z)
- Arrangements of Blocks:
- 3! ways to arrange the blocks.
- Arrangements within Blocks:
- College X: 12!
- College Y: 10!
- College Z: 9!
- Total Arrangements Calculation:
Total arrangements = 3! * 12! * 10! * 9!
This statement provides a specific number of students, allowing calculation of arrangements.
Statement (2) Analysis
- N as a Prime Number:
- N can be 31, 37, or 29 (only primes between 30 and 40).
- Insufficient Information:
- Without the distribution of students among colleges, we cannot determine the number of arrangements.
- Conclusion:
This statement alone does not provide sufficient data regarding how students are grouped.
Final Conclusion
- Statement (1) sufficiency: Yes, it provides exact data needed for calculations.
- Statement (2) sufficiency: No, it lacks specifics about student distribution.
Thus, the correct answer is (A): Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
If a/3 = 4/b , is a less than b?(1) b ≥ 4
(2) b ≤ 5- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
If a/3 = 4/b , is a less than b?
(1) b ≥ 4
(2) b ≤ 5
(2) b ≤ 5
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Rahul Kapoor answered |
Statement (1): b ≥ 4
This statement tells us that b is greater than or equal to 4. If b is greater than or equal to 4, then the fraction 4/b would be less than or equal to 1. Therefore, if a/3 = 4/b, a/3 would also be less than or equal to 1. Multiplying both sides of the equation by 3 gives us a ≤ 3. So, statement (1) alone is sufficient to determine that a is less than or equal to 3. However, we cannot determine the relationship between a and b.
Statement (2): b ≤ 5
This statement tells us that b is less than or equal to 5. However, it does not provide any information about the value of a. Therefore, statement (2) alone is not sufficient to determine the relationship between a and b.
When we consider both statements together, we have the following information:
b ≥ 4 (from statement 1)
b ≤ 5 (from statement 2)
b ≤ 5 (from statement 2)
Combining these inequalities, we know that b must be between 4 and 5, inclusive. However, we still do not have enough information to determine the relationship between a and b.
Since statement (1) alone is sufficient to determine that a ≤ 3, but statement (2) alone is not sufficient, the correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
How many of the 40 securities in a portfolio are domestic stocks?(1) 28 of the 40 securities are stocks.
(2) 35 of the 40 securities are domestic.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
How many of the 40 securities in a portfolio are domestic stocks?
(1) 28 of the 40 securities are stocks.
(2) 35 of the 40 securities are domestic.
(2) 35 of the 40 securities are domestic.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Rahul Kapoor answered |
Statement (1): 28 of the 40 securities are stocks.
From this statement alone, we know that out of the 40 securities in the portfolio, 28 are stocks. However, we don't have any information about the classification of these stocks as domestic or international. Statement (1) alone is not sufficient.
From this statement alone, we know that out of the 40 securities in the portfolio, 28 are stocks. However, we don't have any information about the classification of these stocks as domestic or international. Statement (1) alone is not sufficient.
Statement (2): 35 of the 40 securities are domestic.
From this statement alone, we know that out of the 40 securities in the portfolio, 35 are domestic. However, we don't have any information about the specific classification of these securities as stocks or other types of investments. Statement (2) alone is not sufficient.
From this statement alone, we know that out of the 40 securities in the portfolio, 35 are domestic. However, we don't have any information about the specific classification of these securities as stocks or other types of investments. Statement (2) alone is not sufficient.
Combining both statements, we have the following information:
- 28 of the 40 securities are stocks (Statement 1).
- 35 of the 40 securities are domestic (Statement 2).
Although we have information about the number of stocks and the number of domestic securities, we still don't know the overlap between these two categories. It is possible that all 28 stocks are domestic, or some of them could be international. Similarly, out of the 35 domestic securities, some could be stocks or other types of investments.
Without knowing the specific overlap between stocks and domestic securities, we cannot determine the number of domestic stocks in the portfolio.
Therefore, Statements (1) and (2) TOGETHER are not sufficient to answer the question. Additional data is needed, such as the overlap between stocks and domestic securities or more specific information about the composition of the portfolio.
Hence, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
If r is represented by the decimal 0.t5, what is the digit t?(1) r < 1/3
(2) r < 1/10- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
If r is represented by the decimal 0.t5, what is the digit t?
(1) r < 1/3
(2) r < 1/10
(2) r < 1/10
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Mrinalini Dasgupta answered |
Understanding the Problem
To find the digit t in the decimal representation of r = 0.t5, we need to analyze the constraints given by the statements.
Evaluating Statement (1)
- The statement indicates that r <>
- Converting 1/3 to decimal gives approximately 0.3333.
- For r = 0.t5 to be less than 0.3333, the digit t can be 0, 1, or 2 (since 0.05, 0.15, and 0.25 are all less than 0.3333).
- However, t could also be 3, leading to 0.35, which does not satisfy the condition.
- Thus, Statement (1) alone is insufficient as it does not uniquely determine t.
Evaluating Statement (2)
- This statement asserts that r <>
- Converting 1/10 to decimal gives 0.1.
- Therefore, for r = 0.t5 to be less than 0.1, t must be 0 (as 0.05 is the only valid option for t).
- This uniquely determines that t = 0.
Conclusion
- Statement (1) is insufficient on its own since it allows for multiple values of t.
- Statement (2) is sufficient because it uniquely identifies t as 0.
Thus, the correct answer is option 'B': Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
To find the digit t in the decimal representation of r = 0.t5, we need to analyze the constraints given by the statements.
Evaluating Statement (1)
- The statement indicates that r <>
- Converting 1/3 to decimal gives approximately 0.3333.
- For r = 0.t5 to be less than 0.3333, the digit t can be 0, 1, or 2 (since 0.05, 0.15, and 0.25 are all less than 0.3333).
- However, t could also be 3, leading to 0.35, which does not satisfy the condition.
- Thus, Statement (1) alone is insufficient as it does not uniquely determine t.
Evaluating Statement (2)
- This statement asserts that r <>
- Converting 1/10 to decimal gives 0.1.
- Therefore, for r = 0.t5 to be less than 0.1, t must be 0 (as 0.05 is the only valid option for t).
- This uniquely determines that t = 0.
Conclusion
- Statement (1) is insufficient on its own since it allows for multiple values of t.
- Statement (2) is sufficient because it uniquely identifies t as 0.
Thus, the correct answer is option 'B': Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Is x a positive number?(1) –5x – 3 > -2x
(2) x2 is positive.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
Is x a positive number?
(1) –5x – 3 > -2x
(2) x2 is positive.
(2) x2 is positive.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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|
Rahul Kapoor answered |
Statement 1: “-5x – 3 > -2x” can be simplified by adding 3 to both sides to yield “ -5x > -2x + 3” and then adding 2x to both sides to yield “-3x > 3.” Then, to isolate x, divide both sides by 3 and –x > 1. To change the sign of x, multiply both sides by a negative 1 and the statement becomes “x < -1.” This algebraic manipulation has answered the question directly. “No, x is a not positive. x is a negative number.” This statement is sufficient. The answer is either A or D.
Statement 2: x2 is positive allows for x to be either positive or negative. Since the answer is not consistent this statement is not sufficient.
The correct answer is A.
Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. How many apples did she buy?(1) She spent more than $6 on buying oranges
(2) She spent less than $10 on buying oranges- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. How many apples did she buy?
(1) She spent more than $6 on buying oranges
(2) She spent less than $10 on buying oranges
(2) She spent less than $10 on buying oranges
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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|
Sravya Joshi answered |
Statement 1: She spent more than $6 on buying oranges.
From this statement alone, we know that Joan spent more than $6 on oranges. However, we don't know the exact number of oranges she bought or the cost of each orange. Therefore, we cannot determine the number of apples she bought. This statement alone is not sufficient to answer the question.
Statement 2: She spent less than $10 on buying oranges.
From this statement alone, we know that Joan spent less than $10 on oranges. Again, we don't know the exact number of oranges she bought or the cost of each orange. Therefore, we cannot determine the number of apples she bought. This statement alone is not sufficient to answer the question.
Combining Statements 1 and 2:
By combining the two statements, we know that Joan spent more than $6 but less than $10 on oranges. This still does not provide enough information to determine the number of apples she bought. For example, if she spent $7 on oranges, she could have bought 7 oranges (total cost $7) and 1 apple (total cost $2), or she could have bought 6 oranges (total cost $6) and 2 apples (total cost $4). The number of apples she bought could be different in each scenario. Therefore, the combined statements are not sufficient to answer the question.
In conclusion, neither statement alone nor the combination of both statements provides enough information to determine the number of apples Joan bought. Thus, the correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
From this statement alone, we know that Joan spent more than $6 on oranges. However, we don't know the exact number of oranges she bought or the cost of each orange. Therefore, we cannot determine the number of apples she bought. This statement alone is not sufficient to answer the question.
Statement 2: She spent less than $10 on buying oranges.
From this statement alone, we know that Joan spent less than $10 on oranges. Again, we don't know the exact number of oranges she bought or the cost of each orange. Therefore, we cannot determine the number of apples she bought. This statement alone is not sufficient to answer the question.
Combining Statements 1 and 2:
By combining the two statements, we know that Joan spent more than $6 but less than $10 on oranges. This still does not provide enough information to determine the number of apples she bought. For example, if she spent $7 on oranges, she could have bought 7 oranges (total cost $7) and 1 apple (total cost $2), or she could have bought 6 oranges (total cost $6) and 2 apples (total cost $4). The number of apples she bought could be different in each scenario. Therefore, the combined statements are not sufficient to answer the question.
In conclusion, neither statement alone nor the combination of both statements provides enough information to determine the number of apples Joan bought. Thus, the correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
If x is a positive integer and w is a negative integer, what is the value of xw?(1) xw = 1/2
(2) w = -1- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
If x is a positive integer and w is a negative integer, what is the value of xw?
(1) xw = 1/2
(2) w = -1
(2) w = -1
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Aditya Chauhan answered |
Understanding the Problem
We need to determine the value of the product xw, given that x is a positive integer and w is a negative integer.
Analyzing Statement (1)
- The statement provides: xw = 1/2
- Since x is a positive integer and w is a negative integer, the product xw must be negative.
- However, 1/2 is a positive number.
- This creates a conflict because a positive integer multiplied by a negative integer cannot equal a positive value.
- Thus, statement (1) is sufficient to conclude that the situation described (xw = 1/2) is impossible.
Analyzing Statement (2)
- The statement provides: w = -1
- This means we can express xw as: x(-1) = -x
- While we know x is a positive integer, we cannot determine the exact value of xw without knowing the value of x.
- Therefore, statement (2) is not sufficient on its own.
Conclusion
- Statement (1) is sufficient to determine that the scenario cannot happen, thus providing a definitive answer regarding the impossibility of xw equaling a positive number.
- Statement (2) does not provide enough information to determine the value of xw.
Hence, the correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
We need to determine the value of the product xw, given that x is a positive integer and w is a negative integer.
Analyzing Statement (1)
- The statement provides: xw = 1/2
- Since x is a positive integer and w is a negative integer, the product xw must be negative.
- However, 1/2 is a positive number.
- This creates a conflict because a positive integer multiplied by a negative integer cannot equal a positive value.
- Thus, statement (1) is sufficient to conclude that the situation described (xw = 1/2) is impossible.
Analyzing Statement (2)
- The statement provides: w = -1
- This means we can express xw as: x(-1) = -x
- While we know x is a positive integer, we cannot determine the exact value of xw without knowing the value of x.
- Therefore, statement (2) is not sufficient on its own.
Conclusion
- Statement (1) is sufficient to determine that the scenario cannot happen, thus providing a definitive answer regarding the impossibility of xw equaling a positive number.
- Statement (2) does not provide enough information to determine the value of xw.
Hence, the correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
What is the value of x?(1) |x+2| ≤ 4
(2) x2 = 36- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
What is the value of x?
(1) |x+2| ≤ 4
(2) x2 = 36
(2) x2 = 36
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Chirag Roy answered |
The statement (1) is incomplete. Could you please provide the full statement?
Is positive integer z an odd integer?(1) z3 – 3 is an odd integer.
(2) z – 3 is an odd integer.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
Is positive integer z an odd integer?
(1) z3 – 3 is an odd integer.
(2) z – 3 is an odd integer.
(2) z – 3 is an odd integer.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Rahul Kapoor answered |
Statement (1): z3 - 3 is an odd integer.
If z3 - 3 is an odd integer, it means that z3 is an even integer because subtracting an odd integer from an even integer always results in an odd integer. For z3 to be an even integer, z must also be an even integer. This implies that z itself is an even integer. Therefore, statement (1) alone is sufficient to conclude that z is not an odd integer.
If z3 - 3 is an odd integer, it means that z3 is an even integer because subtracting an odd integer from an even integer always results in an odd integer. For z3 to be an even integer, z must also be an even integer. This implies that z itself is an even integer. Therefore, statement (1) alone is sufficient to conclude that z is not an odd integer.
Statement (2): z - 3 is an odd integer.
If z - 3 is an odd integer, it means that z is an even integer because subtracting an odd integer from an even integer always results in an odd integer. Therefore, statement (2) alone is sufficient to conclude that z is not an odd integer.
If z - 3 is an odd integer, it means that z is an even integer because subtracting an odd integer from an even integer always results in an odd integer. Therefore, statement (2) alone is sufficient to conclude that z is not an odd integer.
Both statements (1) and (2) individually provide sufficient information to determine that z is not an odd integer. Therefore, each statement alone is sufficient to answer the question asked.
Hence, the answer is D: EACH statement ALONE is sufficient to answer the question asked.
What is the number of 360-degree rotations that a bicycle wheel made while rolling 150 meters in a straight line without slipping?(1) It took 3 minutes for the bicycle wheel to travel the entire distance.
(2) The wheel made twenty 360-degree rotations per minute.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
What is the number of 360-degree rotations that a bicycle wheel made while rolling 150 meters in a straight line without slipping?
(1) It took 3 minutes for the bicycle wheel to travel the entire distance.
(2) The wheel made twenty 360-degree rotations per minute.
(2) The wheel made twenty 360-degree rotations per minute.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Rahul Kapoor answered |
Statement (1): It took 3 minutes for the bicycle wheel to travel the entire distance.
This statement provides information about the time it took for the wheel to cover the distance, but it does not give any details about the wheel's rotation or the speed at which it was rotating. Without information about the rotation, we cannot determine the number of 360-degree rotations the wheel made. Hence, statement (1) alone is not sufficient to answer the question.
This statement provides information about the time it took for the wheel to cover the distance, but it does not give any details about the wheel's rotation or the speed at which it was rotating. Without information about the rotation, we cannot determine the number of 360-degree rotations the wheel made. Hence, statement (1) alone is not sufficient to answer the question.
Statement (2): The wheel made twenty 360-degree rotations per minute.
This statement provides information about the number of 360-degree rotations the wheel made per minute, but it does not give any information about the distance traveled or the time it took to travel that distance. Without information about the distance or time, we cannot determine the number of rotations the wheel made while rolling 150 meters. Therefore, statement (2) alone is not sufficient to answer the question.
This statement provides information about the number of 360-degree rotations the wheel made per minute, but it does not give any information about the distance traveled or the time it took to travel that distance. Without information about the distance or time, we cannot determine the number of rotations the wheel made while rolling 150 meters. Therefore, statement (2) alone is not sufficient to answer the question.
When we consider both statements together, we know the time it took for the wheel to travel the entire distance (from statement 1) and the number of 360-degree rotations the wheel made per minute (from statement 2). With this information, we can determine the number of rotations the wheel made while rolling 150 meters. By converting the time given in statement 1 from minutes to seconds (3 minutes = 180 seconds) and multiplying it by the rotations per minute given in statement 2 (20 rotations/minute), we can calculate the total rotations:
Total rotations = (Rotations per minute) × (Time in minutes) = 20 rotations/minute × 3 minutes = 60 rotations
Therefore, both statements together are sufficient to answer the question. The correct answer is (C): BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
A mixture consists of flaxseed and cornmeal in the ratio 1 to 4, respectively. How many cups of flaxseed are used to make the mixture?(1) There are a total of 15 cups in the mixture.
(2) The ratio of the number of cups of flaxseed to the total number of cups in the mixture is 1 to 5.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
A mixture consists of flaxseed and cornmeal in the ratio 1 to 4, respectively. How many cups of flaxseed are used to make the mixture?
(1) There are a total of 15 cups in the mixture.
(2) The ratio of the number of cups of flaxseed to the total number of cups in the mixture is 1 to 5.
(2) The ratio of the number of cups of flaxseed to the total number of cups in the mixture is 1 to 5.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Rahul Kapoor answered |
Statement (1): There are a total of 15 cups in the mixture.
From this statement alone, we cannot determine the specific amounts of flaxseed and cornmeal in the mixture. It only provides the total quantity, but not the ratio or specific amounts of each ingredient. Statement (1) alone is not sufficient.
From this statement alone, we cannot determine the specific amounts of flaxseed and cornmeal in the mixture. It only provides the total quantity, but not the ratio or specific amounts of each ingredient. Statement (1) alone is not sufficient.
Statement (2): The ratio of the number of cups of flaxseed to the total number of cups in the mixture is 1 to 5.
From this statement alone, we know that the ratio of flaxseed to the total mixture is 1:5. However, we still don't have the specific total quantity of the mixture. Without knowing the total cups in the mixture, we cannot determine the exact amount of flaxseed. Statement (2) alone is not sufficient.
From this statement alone, we know that the ratio of flaxseed to the total mixture is 1:5. However, we still don't have the specific total quantity of the mixture. Without knowing the total cups in the mixture, we cannot determine the exact amount of flaxseed. Statement (2) alone is not sufficient.
Combining both statements, we have the following information:
- The total quantity is 15 cups (Statement 1).
- The ratio of flaxseed to the total mixture is 1:5 (Statement 2).
Using this information, we can determine the amounts of flaxseed and cornmeal in the mixture. Since the ratio of flaxseed to the total mixture is 1:5, we can calculate that the amount of flaxseed is (1/6) * 15 = 2.5 cups. Therefore, both statements together are sufficient to answer the question.
Hence, the correct answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
Each day, Sergio feeds his cat a 500-gram mixture of Brand X and Brand Y cat foods. If Sergio’s cat eats only this mix of cat food and she consumes 103 grams of fat per day, what is the amount of Brand X cat food that she receives each day?(1) Brand X cat food consists of 35 percent fat.
(2) Brand Y cat food consists of 11 percent fat.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
Each day, Sergio feeds his cat a 500-gram mixture of Brand X and Brand Y cat foods. If Sergio’s cat eats only this mix of cat food and she consumes 103 grams of fat per day, what is the amount of Brand X cat food that she receives each day?
(1) Brand X cat food consists of 35 percent fat.
(2) Brand Y cat food consists of 11 percent fat.
(2) Brand Y cat food consists of 11 percent fat.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
Wizius Careers answered |
Statement (1): Brand X cat food consists of 35 percent fat.
Statement (2): Brand Y cat food consists of 11 percent fat.
Statement (2): Brand Y cat food consists of 11 percent fat.
From Statement (1), we know the fat content of Brand X cat food. From Statement (2), we know the fat content of Brand Y cat food. In order to determine the amount of Brand X cat food in the mixture, we need to consider the fat content and weight of both brands.
Let's assume that Sergio feeds x grams of Brand X cat food and y grams of Brand Y cat food. We are given that the total mixture weighs 500 grams and contains 103 grams of fat.
From Statement (1), we can write the equation: 0.35x = (35/100)x grams of fat from Brand X cat food.
From Statement (2), we can write the equation: 0.11y = (11/100)y grams of fat from Brand Y cat food.
From Statement (2), we can write the equation: 0.11y = (11/100)y grams of fat from Brand Y cat food.
Since the cat consumes 103 grams of fat per day, we have the equation: (35/100)x + (11/100)y = 103.
Combining these equations, we have a system of two equations with two variables:
(35/100)x + (11/100)y = 103,
x + y = 500.
(35/100)x + (11/100)y = 103,
x + y = 500.
With these equations, we can solve for x, the amount of Brand X cat food in grams.
Therefore, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
If x and y are positive integers, what is the remainder when 5x is divided by y?(1) x = 3
(2) y = 4- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
If x and y are positive integers, what is the remainder when 5x is divided by y?
(1) x = 3
(2) y = 4
(2) y = 4
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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|
Saumya Sharma answered |
Statement 1:
x = 3
Statement 2:
y = 4
To find the remainder when 5x is divided by y, we need to know the values of both x and y. Let's evaluate each statement separately:
Statement 1:
x = 3
Using this statement alone, we can substitute the value of x into the expression 5x to get:
5x = 5 * 3 = 15
However, we still don't know the value of y, so we cannot determine the remainder when 5x is divided by y. Statement 1 alone is not sufficient.
Statement 2:
y = 4
Using this statement alone, we know the value of y but we don't have any information about x. Without knowing the value of x, we cannot determine the remainder when 5x is divided by y. Statement 2 alone is not sufficient.
Statements 1 and 2 together:
Using both statements together, we know that x = 3 and y = 4. Now we can substitute these values into the expression 5x to get:
5x = 5 * 3 = 15
Since y = 4, we can divide 15 by 4 to find the remainder:
15 ÷ 4 = 3 remainder 3
Therefore, when x = 3 and y = 4, the remainder when 5x is divided by y is 3.
Conclusion:
From the analysis above, we can conclude that statement 1 alone and statement 2 alone are not sufficient to answer the question. However, when both statements are considered together, they are sufficient to determine the remainder when 5x is divided by y. Therefore, the correct answer is option B.
x = 3
Statement 2:
y = 4
To find the remainder when 5x is divided by y, we need to know the values of both x and y. Let's evaluate each statement separately:
Statement 1:
x = 3
Using this statement alone, we can substitute the value of x into the expression 5x to get:
5x = 5 * 3 = 15
However, we still don't know the value of y, so we cannot determine the remainder when 5x is divided by y. Statement 1 alone is not sufficient.
Statement 2:
y = 4
Using this statement alone, we know the value of y but we don't have any information about x. Without knowing the value of x, we cannot determine the remainder when 5x is divided by y. Statement 2 alone is not sufficient.
Statements 1 and 2 together:
Using both statements together, we know that x = 3 and y = 4. Now we can substitute these values into the expression 5x to get:
5x = 5 * 3 = 15
Since y = 4, we can divide 15 by 4 to find the remainder:
15 ÷ 4 = 3 remainder 3
Therefore, when x = 3 and y = 4, the remainder when 5x is divided by y is 3.
Conclusion:
From the analysis above, we can conclude that statement 1 alone and statement 2 alone are not sufficient to answer the question. However, when both statements are considered together, they are sufficient to determine the remainder when 5x is divided by y. Therefore, the correct answer is option B.
Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?(1) w = 30
(2) y = 75- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?
(1) w = 30
(2) y = 75
(2) y = 75
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Manasa Gupta answered |
Understanding the Problem
To find the value of \( x \), we need to set up an equation based on the given information about the nut mixes.
- Brand W contains 24% cashews.
- Brand X contains 9% cashews.
- The mixture of \( w \) pounds of Brand W and \( x \) pounds of Brand X results in \( y \) pounds of a mixture that is 15% cashews.
The equation for the total amount of cashews in the mixture can be expressed as:
\[ 0.24w + 0.09x = 0.15y \]
Using Statement (1): w = 30
Substituting \( w = 30 \) into the equation:
\[ 0.24(30) + 0.09x = 0.15y \]
This simplifies to:
\[ 7.2 + 0.09x = 0.15y \]
With this single equation and the known value of \( w \), we can solve for \( x \) if we have \( y \).
Using Statement (2): y = 75
Substituting \( y = 75 \) into the equation:
\[ 0.24w + 0.09x = 0.15(75) \]
This simplifies to:
\[ 0.24w + 0.09x = 11.25 \]
With this single equation and the known value of \( y \), we can solve for \( x \) if we have \( w \).
Conclusion
- Statement (1) gives us a specific value for \( w \) but needs \( y \) to find \( x \).
- Statement (2) gives us a specific value for \( y \) but needs \( w \) to find \( x \).
Since each statement alone allows us to express \( x \) in terms of the other variable, both statements independently provide sufficient information to solve for \( x \).
Therefore, the correct answer is option D: Each statement alone is sufficient to answer the question.
To find the value of \( x \), we need to set up an equation based on the given information about the nut mixes.
- Brand W contains 24% cashews.
- Brand X contains 9% cashews.
- The mixture of \( w \) pounds of Brand W and \( x \) pounds of Brand X results in \( y \) pounds of a mixture that is 15% cashews.
The equation for the total amount of cashews in the mixture can be expressed as:
\[ 0.24w + 0.09x = 0.15y \]
Using Statement (1): w = 30
Substituting \( w = 30 \) into the equation:
\[ 0.24(30) + 0.09x = 0.15y \]
This simplifies to:
\[ 7.2 + 0.09x = 0.15y \]
With this single equation and the known value of \( w \), we can solve for \( x \) if we have \( y \).
Using Statement (2): y = 75
Substituting \( y = 75 \) into the equation:
\[ 0.24w + 0.09x = 0.15(75) \]
This simplifies to:
\[ 0.24w + 0.09x = 11.25 \]
With this single equation and the known value of \( y \), we can solve for \( x \) if we have \( w \).
Conclusion
- Statement (1) gives us a specific value for \( w \) but needs \( y \) to find \( x \).
- Statement (2) gives us a specific value for \( y \) but needs \( w \) to find \( x \).
Since each statement alone allows us to express \( x \) in terms of the other variable, both statements independently provide sufficient information to solve for \( x \).
Therefore, the correct answer is option D: Each statement alone is sufficient to answer the question.
A rental car agency purchases fleet vehicles in two sizes: a full-size car costs $10,000, and a compact costs $9,000. How many compact cars does the agency own?(1) The agency owns 7 total cars.
(2) The agency paid $66,000 for its cars.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
A rental car agency purchases fleet vehicles in two sizes: a full-size car costs $10,000, and a compact costs $9,000. How many compact cars does the agency own?
(1) The agency owns 7 total cars.
(2) The agency paid $66,000 for its cars.
(2) The agency paid $66,000 for its cars.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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EduRev GMAT answered |
Statement (1): The agency owns 7 total cars.
- This statement tells us that the total number of cars is 7, but it does not tell us how many are full-size and how many are compact.
- Without knowing the specific breakdown between the two types of cars, we cannot determine how many compact cars are owned. Therefore, Statement (1) alone is not sufficient.
Statement (2): The agency paid $66,000 for its cars.
- This statement tells us the total cost of all the cars, but we still don’t know how many are full-size and how many are compact.
- Let’s assume the agency owns "x" full-size cars and "y" compact cars. The cost of a full-size car is $10,000, and the cost of a compact car is $9,000.
- The total cost of all the cars can be expressed as:
10,000x + 9,000y = 66,000. - This is a system of equations, but without another equation, we can't solve for "y" (the number of compact cars) specifically. Therefore, Statement (2) alone is not sufficient.
Combining both statements:
- Statement (1) tells us the total number of cars is 7, so:
x + y = 7. - From Statement (2), we have:
10,000x + 9,000y = 66,000. - We now have a system of two equations:
- x + y = 7
- 10,000x + 9,000y = 66,000
-
We can solve this system of equations:
- From the first equation, x = 7 - y.
- Substitute x = 7 - y into the second equation:
10,000(7 - y) + 9,000y = 66,000
Simplifying:
70,000 - 10,000y + 9,000y = 66,000
70,000 - 1,000y = 66,000
-1,000y = -4,000
y = 4.
Thus, the agency owns 4 compact cars.
Both statements together are sufficient to determine the number of compact cars the agency owns.
Answer: c) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
If k and n are integers, is n divisible by 7 ?(1) n - 3= 2k
(2) 2k - 4 is divisible by 7.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
If k and n are integers, is n divisible by 7 ?
(1) n - 3= 2k
(2) 2k - 4 is divisible by 7.
(2) 2k - 4 is divisible by 7.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Advait Malik answered |
Statement (1): n - 3 = 2k
This equation tells us that n is 3 more than a multiple of 2, or in other words, n is odd. However, it does not give us any information about whether n is divisible by 7. For example, n could be 5, which is not divisible by 7, or it could be 11, which is also not divisible by 7. Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2): 2k - 4 is divisible by 7
This equation tells us that 2k is 4 more than a multiple of 7, or in other words, 2k is congruent to 4 modulo 7. We can rewrite this as 2k ≡ 4 (mod 7). To determine whether n is divisible by 7, we need to find the possible values of k that satisfy this congruence. Let's list out the possible values of 2k modulo 7:
2k ≡ 0 (mod 7) when k ≡ 0 (mod 7)
2k ≡ 2 (mod 7) when k ≡ 1 (mod 7)
2k ≡ 4 (mod 7) when k ≡ 2 (mod 7)
2k ≡ 6 (mod 7) when k ≡ 3 (mod 7)
2k ≡ 1 (mod 7) when k ≡ 4 (mod 7)
2k ≡ 3 (mod 7) when k ≡ 5 (mod 7)
2k ≡ 5 (mod 7) when k ≡ 6 (mod 7)
From this list, we can see that k must be congruent to 2 (mod 7) in order for 2k to be congruent to 4 (mod 7). However, this does not give us any information about whether n is divisible by 7. Therefore, statement (2) alone is not sufficient to answer the question.
Statements (1) and (2) together:
Combining the information from both statements, we know that n is odd (from statement (1)) and that 2k is congruent to 4 (mod 7) (from statement (2)). To determine whether n is divisible by 7, we need to find the possible values of n. Since n is odd, it can be expressed as n = 2m + 1 for some integer m. Substituting this into the equation from statement (1), we get:
2m + 1 - 3 = 2k
2m - 2 = 2k
m - 1 = k
Therefore, k must be one less than an integer. Combining this with the information from statement (2) that k is congruent to 2 (mod 7), we can conclude that k must be one less than a multiple of 7. In other words, k can be expressed as k = 7x - 1 for some integer x. Substituting this back into the equation for n, we get:
n = 2(7x - 1) + 1
n = 14
This equation tells us that n is 3 more than a multiple of 2, or in other words, n is odd. However, it does not give us any information about whether n is divisible by 7. For example, n could be 5, which is not divisible by 7, or it could be 11, which is also not divisible by 7. Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2): 2k - 4 is divisible by 7
This equation tells us that 2k is 4 more than a multiple of 7, or in other words, 2k is congruent to 4 modulo 7. We can rewrite this as 2k ≡ 4 (mod 7). To determine whether n is divisible by 7, we need to find the possible values of k that satisfy this congruence. Let's list out the possible values of 2k modulo 7:
2k ≡ 0 (mod 7) when k ≡ 0 (mod 7)
2k ≡ 2 (mod 7) when k ≡ 1 (mod 7)
2k ≡ 4 (mod 7) when k ≡ 2 (mod 7)
2k ≡ 6 (mod 7) when k ≡ 3 (mod 7)
2k ≡ 1 (mod 7) when k ≡ 4 (mod 7)
2k ≡ 3 (mod 7) when k ≡ 5 (mod 7)
2k ≡ 5 (mod 7) when k ≡ 6 (mod 7)
From this list, we can see that k must be congruent to 2 (mod 7) in order for 2k to be congruent to 4 (mod 7). However, this does not give us any information about whether n is divisible by 7. Therefore, statement (2) alone is not sufficient to answer the question.
Statements (1) and (2) together:
Combining the information from both statements, we know that n is odd (from statement (1)) and that 2k is congruent to 4 (mod 7) (from statement (2)). To determine whether n is divisible by 7, we need to find the possible values of n. Since n is odd, it can be expressed as n = 2m + 1 for some integer m. Substituting this into the equation from statement (1), we get:
2m + 1 - 3 = 2k
2m - 2 = 2k
m - 1 = k
Therefore, k must be one less than an integer. Combining this with the information from statement (2) that k is congruent to 2 (mod 7), we can conclude that k must be one less than a multiple of 7. In other words, k can be expressed as k = 7x - 1 for some integer x. Substituting this back into the equation for n, we get:
n = 2(7x - 1) + 1
n = 14
What is the sum of integers A and B?(1) |A| = -|B|
(2) |B| = -|A|- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
What is the sum of integers A and B?
(1) |A| = -|B|
(2) |B| = -|A|
(2) |B| = -|A|
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Rahul Kapoor answered |
Statement (1): |A| = -|B|
This statement states that the absolute value of A is equal to the negation of the absolute value of B. Since absolute values are always non-negative, the only way for |A| to be equal to -|B| is if both A and B are equal to 0. In that case, the sum of A and B is 0.
Statement (2): |B| = -|A|
This statement states that the absolute value of B is equal to the negation of the absolute value of A. Similar to statement (1), this implies that both A and B are equal to 0, resulting in a sum of 0.
From both statements, we can conclude that the sum of A and B is always 0.
Therefore, each statement alone is sufficient to answer the question asked. The answer is (D).
On a construction site, 16 of the men wear helmets, and 19 of the women do not wear helmets. How many people are there on the construction site?(1) There are 21 men on the construction site.
(2) There are 24 people that do not wear helmets on the construction site.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
On a construction site, 16 of the men wear helmets, and 19 of the women do not wear helmets. How many people are there on the construction site?
(1) There are 21 men on the construction site.
(2) There are 24 people that do not wear helmets on the construction site.
(2) There are 24 people that do not wear helmets on the construction site.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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BT Educators answered |
Statement (1): There are 21 men on the construction site.
This statement alone tells us the number of men, but it doesn't provide any information about the women or the number of people wearing or not wearing helmets. Therefore, we can't determine the total number of people on the site based on this statement alone.
This statement alone tells us the number of men, but it doesn't provide any information about the women or the number of people wearing or not wearing helmets. Therefore, we can't determine the total number of people on the site based on this statement alone.
Statement (2): There are 24 people that do not wear helmets on the construction site.
This statement provides information about the number of people not wearing helmets, but it doesn't give any details about the breakdown between men and women or the total number of people. Without additional information, we can't determine the total number of people on the site based on this statement alone.
This statement provides information about the number of people not wearing helmets, but it doesn't give any details about the breakdown between men and women or the total number of people. Without additional information, we can't determine the total number of people on the site based on this statement alone.
Since neither statement alone is sufficient to answer the question, we need to evaluate both statements together:
If we combine the information from both statements, we know that there are 21 men and 24 people not wearing helmets. However, we still don't have any information about the number of women or the number of people wearing helmets. Without these details, we can't determine the total number of people on the construction site.
Therefore, the correct answer is (E): Statements (1) and (2) together are not sufficient to answer the question, and additional data are needed.
Is x < y?
(1) z < y
(2) z < x- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
Is x < y?
(1) z < y
(2) z < x
(1) z < y
(2) z < x
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Wizius Careers answered |
Statement (1): z < y
This statement tells us that z is less than y. However, it does not provide any information about the relationship between x and y. We cannot determine if x is less than y based on this statement alone.
Statement (2): z < x
This statement tells us that z is less than x. However, it does not provide any information about the relationship between x and y. We cannot determine if x is less than y based on this statement alone.
When we consider both statements together, we have the following information:
z < y (from statement 1)
z < x (from statement 2)
z < x (from statement 2)
Combining these inequalities, we know that z is less than both y and x. However, we still do not have enough information to determine the relationship between x and y. It is possible that x is greater than y, or x is less than y. Therefore, even when both statements are considered together, we cannot determine if x is less than y.
Since neither statement alone, nor both statements together, provide sufficient information to answer the question, the correct answer is option E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
The average age of P, Q, R and S is 30 years. How old is R?(1) The sum of ages of P and R is 60 years.
(2) S is 10 years younger than R.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
The average age of P, Q, R and S is 30 years. How old is R?
(1) The sum of ages of P and R is 60 years.
(2) S is 10 years younger than R.
(2) S is 10 years younger than R.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Kiran Chauhan answered |
Understanding the Average Age
The average age of individuals P, Q, R, and S is 30 years. Therefore, the total age of the four individuals can be calculated as:
- Total age = Average age × Number of individuals = 30 × 4 = 120 years.
This means P + Q + R + S = 120.
Analyzing Statement (1)
- The sum of ages of P and R is 60 years.
- From this, we can express the age of Q and S as Q + S = 120 - (P + R) = 120 - 60 = 60.
However, we do not know the individual ages of P or R. Thus, Statement (1) alone does not provide enough information to determine R's age.
Analyzing Statement (2)
- S is 10 years younger than R.
- We can express S’s age as S = R - 10.
Using this, we can substitute into the total age equation: P + Q + R + (R - 10) = 120, which simplifies to P + Q + 2R - 10 = 120.
However, without knowing P and Q's ages, we still cannot deduce R's age. Hence, Statement (2) alone is also insufficient.
Combining Both Statements
When we combine both statements:
- From Statement (1): P + R = 60.
- From Statement (2): S = R - 10.
Using these together does not yield a specific value for R. We still do not have concrete values for P or Q that allow us to solve for R.
Conclusion
Since neither statement is sufficient individually, and their combination does not lead to a definitive solution for R's age, the correct answer is:
- e) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
The average age of individuals P, Q, R, and S is 30 years. Therefore, the total age of the four individuals can be calculated as:
- Total age = Average age × Number of individuals = 30 × 4 = 120 years.
This means P + Q + R + S = 120.
Analyzing Statement (1)
- The sum of ages of P and R is 60 years.
- From this, we can express the age of Q and S as Q + S = 120 - (P + R) = 120 - 60 = 60.
However, we do not know the individual ages of P or R. Thus, Statement (1) alone does not provide enough information to determine R's age.
Analyzing Statement (2)
- S is 10 years younger than R.
- We can express S’s age as S = R - 10.
Using this, we can substitute into the total age equation: P + Q + R + (R - 10) = 120, which simplifies to P + Q + 2R - 10 = 120.
However, without knowing P and Q's ages, we still cannot deduce R's age. Hence, Statement (2) alone is also insufficient.
Combining Both Statements
When we combine both statements:
- From Statement (1): P + R = 60.
- From Statement (2): S = R - 10.
Using these together does not yield a specific value for R. We still do not have concrete values for P or Q that allow us to solve for R.
Conclusion
Since neither statement is sufficient individually, and their combination does not lead to a definitive solution for R's age, the correct answer is:
- e) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
If Danielle ran a race at a constant speed, at what time did she finish?(1) Danielle started the race at 8:00 a.m.
(2) At 9:30 a.m. Danielle was halfway through the race, and at 10:00 a.m., she was 2/3 of the way through the race.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer thequestion asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
If Danielle ran a race at a constant speed, at what time did she finish?
(1) Danielle started the race at 8:00 a.m.
(2) At 9:30 a.m. Danielle was halfway through the race, and at 10:00 a.m., she was 2/3 of the way through the race.
(2) At 9:30 a.m. Danielle was halfway through the race, and at 10:00 a.m., she was 2/3 of the way through the race.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer thequestion asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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|
Rahul Kapoor answered |
From statement (1), we know that Danielle started the race at 8:00 a.m. However, we don't have any information about her speed or the duration of the race. Therefore, statement (1) alone is not sufficient to determine the time she finished.
From statement (2), we know that at 9:30 a.m., Danielle was halfway through the race, and at 10:00 a.m., she was 2/3 of the way through the race. This implies that the second half of the race took 30 minutes (from 9:30 a.m. to 10:00 a.m.), and the last third of the race also took 30 minutes (from 9:30 a.m. to 10:00 a.m.). However, we still don't have information about Danielle's speed or the length of the entire race. Therefore, statement (2) alone is not sufficient to determine the time she finished.
By combining both statements, we know that Danielle started the race at 8:00 a.m., and at 10:00 a.m., she was 2/3 of the way through the race. This means she took 2 hours (from 8:00 a.m. to 10:00 a.m.) to complete 2/3 of the race. However, we still don't have enough information to determine the exact time she finished or the speed at which she ran.
Therefore, both statements together are sufficient to determine the time Danielle finished. The answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
In Madison School, 120 students are members of the chess club or drama club or both. If 50 of these students are not members of the chess club, how many of these students are members of both the chess and the drama club?(1) 35 of the students are members of both the chess club and the forensic society
(2) 45 of the students are members of both the drama club and the forensic society- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
In Madison School, 120 students are members of the chess club or drama club or both. If 50 of these students are not members of the chess club, how many of these students are members of both the chess and the drama club?
(1) 35 of the students are members of both the chess club and the forensic society
(2) 45 of the students are members of both the drama club and the forensic society
(2) 45 of the students are members of both the drama club and the forensic society
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Rahul Kapoor answered |
Statement (1): 35 of the students are members of both the chess club and the forensic society.
This statement provides information about the overlap between the chess club and the forensic society, but it doesn't give any information about the drama club. Without information about the drama club, we can't determine the number of students who are members of both the chess club and the drama club based on this statement alone.
This statement provides information about the overlap between the chess club and the forensic society, but it doesn't give any information about the drama club. Without information about the drama club, we can't determine the number of students who are members of both the chess club and the drama club based on this statement alone.
Statement (2): 45 of the students are members of both the drama club and the forensic society.
This statement provides information about the overlap between the drama club and the forensic society, but it doesn't give any information about the chess club. Without information about the chess club, we can't determine the number of students who are members of both the chess club and the drama club based on this statement alone.
This statement provides information about the overlap between the drama club and the forensic society, but it doesn't give any information about the chess club. Without information about the chess club, we can't determine the number of students who are members of both the chess club and the drama club based on this statement alone.
Since neither statement alone is sufficient to answer the question, we need to evaluate both statements together:
Even when we combine the information from both statements, we still don't have any direct information about the overlap between the chess club and the drama club. We only have information about the overlaps between each club and the forensic society. Therefore, we can't determine the number of students who are members of both the chess club and the drama club based on these two statements alone.
Hence, the correct answer is (E): Statements (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.
If |m + 4| = 2, what is the value of m?(1) m < 0
(2) m2 + 8m + 12 = 0- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
If |m + 4| = 2, what is the value of m?
(1) m < 0
(2) m2 + 8m + 12 = 0
(2) m2 + 8m + 12 = 0
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Hridoy Gupta answered |
The value of m can be either positive or negative, so we need more information to determine its value.
Statement (1) alone is not sufficient to find the value of m.
Therefore, the answer is (E) Statement (1) alone is not sufficient to answer the question.
Statement (1) alone is not sufficient to find the value of m.
Therefore, the answer is (E) Statement (1) alone is not sufficient to answer the question.
A and B are running in opposite direction on a circular track with radius of 7 miles. What will be the sum of their respective speeds?1) A and B both starts from same point and cover same distance before first meeting.
2) A can cover entire circular track in 10 min.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer thequestion asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
A and B are running in opposite direction on a circular track with radius of 7 miles. What will be the sum of their respective speeds?
1) A and B both starts from same point and cover same distance before first meeting.
2) A can cover entire circular track in 10 min.
2) A can cover entire circular track in 10 min.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer thequestion asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Sounak Iyer answered |
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Since A and B both start from the same point and cover the same distance before their first meeting, we can conclude that their speeds are equal. Let's assume their speed is x miles per hour.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
If A can cover the entire circular track in 10 minutes, we can determine A's speed by converting the time to hours. 10 minutes is equivalent to 10/60 = 1/6 hours. Therefore, A's speed is 7/(1/6) = 42 miles per hour.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
From statement (1), we know that A and B have the same speed, which means their speeds are equal to x miles per hour.
From statement (2), we know that A's speed is 42 miles per hour.
Since A and B are running in opposite directions, their speeds add up to give the sum of their respective speeds. Therefore, the sum of their speeds is x + 42 miles per hour.
By combining both statements, we can conclude that the sum of their respective speeds is x + 42 miles per hour. Therefore, both statements together are sufficient to answer the question.
Therefore, the correct answer is option 'C'.
Since A and B both start from the same point and cover the same distance before their first meeting, we can conclude that their speeds are equal. Let's assume their speed is x miles per hour.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
If A can cover the entire circular track in 10 minutes, we can determine A's speed by converting the time to hours. 10 minutes is equivalent to 10/60 = 1/6 hours. Therefore, A's speed is 7/(1/6) = 42 miles per hour.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
From statement (1), we know that A and B have the same speed, which means their speeds are equal to x miles per hour.
From statement (2), we know that A's speed is 42 miles per hour.
Since A and B are running in opposite directions, their speeds add up to give the sum of their respective speeds. Therefore, the sum of their speeds is x + 42 miles per hour.
By combining both statements, we can conclude that the sum of their respective speeds is x + 42 miles per hour. Therefore, both statements together are sufficient to answer the question.
Therefore, the correct answer is option 'C'.
Scott grew 100 plants from black and white seeds. Only one plant grows from one seed. She may get red or blue flowers from the black seed. She may get red or white flowers from the white seeds. How many black seeds does she have?
I. The number of plants with white flowers = 10.
II. The number of plants with red flowers = 70.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
Scott grew 100 plants from black and white seeds. Only one plant grows from one seed. She may get red or blue flowers from the black seed. She may get red or white flowers from the white seeds. How many black seeds does she have?
I. The number of plants with white flowers = 10.
II. The number of plants with red flowers = 70.
I. The number of plants with white flowers = 10.
II. The number of plants with red flowers = 70.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Rahul Kapoor answered |
Statement (I): The number of plants with white flowers is 10.
This statement tells us the number of plants with white flowers, but it doesn't provide any information about the number of black seeds or the relationship between the colors of the seeds and the colors of the flowers. Statement (I) alone is not sufficient to answer the question.
Statement (II): The number of plants with red flowers is 70.
This statement tells us the number of plants with red flowers, but similar to Statement (I), it doesn't provide any information about the number of black seeds or the relationship between the colors of the seeds and the colors of the flowers. Statement (II) alone is not sufficient to answer the question.
When we consider both statements together, we have information about the number of plants with white flowers and the number of plants with red flowers. However, we still don't have any information about the relationship between the colors of the seeds and the colors of the flowers. Without knowing this relationship, we cannot determine the number of black seeds.
Therefore, Statements (I) and (II) together are not sufficient to answer the question asked. The answer is E: Statements (1) and (2) together are NOT sufficient to answer the question asked, and additional data are needed.
A certain company currently has how many employees?(1) If 5 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company.
(2) If no additional employees are hired by the company and 5 of the present employees resign, there will be fewer than 13 employees in the company.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
A certain company currently has how many employees?
(1) If 5 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company.
(2) If no additional employees are hired by the company and 5 of the present employees resign, there will be fewer than 13 employees in the company.
(2) If no additional employees are hired by the company and 5 of the present employees resign, there will be fewer than 13 employees in the company.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Wizius Careers answered |
(1) If 5 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company.
E + 5 > = 20 = E > = 15
With this we will not be able to exactly determine number of employees.
Hence, (1) ⇒ is NOT SUFFICIENT
(2) If no additional employees are hired by the company and 5 of the present employees resign, there will be fewer than 13 employees in the company.[b]
E − 5 < 13 = E < 18
Once again this gives us a higher limit for E but still we cannot determine exact value of E
Hence, (2) ⇒ is NOT SUFFICIENT
Lets combine (1) & (2)
We get:
E >= 15
E < 18
E can be 15, 16, 17
As we are getting multiple values this is not sufficient.
(1) & (2) combined ⇒ is NOT SUFFICIENT
Hence, Answer is E
E + 5 > = 20 = E > = 15
With this we will not be able to exactly determine number of employees.
Hence, (1) ⇒ is NOT SUFFICIENT
(2) If no additional employees are hired by the company and 5 of the present employees resign, there will be fewer than 13 employees in the company.[b]
E − 5 < 13 = E < 18
Once again this gives us a higher limit for E but still we cannot determine exact value of E
Hence, (2) ⇒ is NOT SUFFICIENT
Lets combine (1) & (2)
We get:
E >= 15
E < 18
E can be 15, 16, 17
As we are getting multiple values this is not sufficient.
(1) & (2) combined ⇒ is NOT SUFFICIENT
Hence, Answer is E
Alisha was writing a travel blog about the preferences of travelers. She asked 50 travelers whether they enjoyed traveling by plane or by train. If all of the travelers enjoyed traveling by either plane or train or both, how many enjoyed traveling by both plane and train?(1) 25 travelers enjoyed traveling by plane.
(2) All of the travelers who enjoyed traveling by plane also enjoyed traveling by train.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
Alisha was writing a travel blog about the preferences of travelers. She asked 50 travelers whether they enjoyed traveling by plane or by train. If all of the travelers enjoyed traveling by either plane or train or both, how many enjoyed traveling by both plane and train?
(1) 25 travelers enjoyed traveling by plane.
(2) All of the travelers who enjoyed traveling by plane also enjoyed traveling by train.
(2) All of the travelers who enjoyed traveling by plane also enjoyed traveling by train.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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BT Educators answered |
Statement (1): 25 travelers enjoyed traveling by plane.
From this statement alone, we know that 25 travelers enjoyed traveling by plane. However, we don't have any information about their preferences for traveling by train or the overlap between the two groups. Statement (1) alone is not sufficient.
From this statement alone, we know that 25 travelers enjoyed traveling by plane. However, we don't have any information about their preferences for traveling by train or the overlap between the two groups. Statement (1) alone is not sufficient.
Statement (2): All of the travelers who enjoyed traveling by plane also enjoyed traveling by train.
From this statement alone, we know that all the travelers who enjoyed traveling by plane also enjoyed traveling by train. This means that the travelers who enjoyed traveling by both plane and train are included in the group of travelers who enjoyed traveling by plane. However, we don't have any information about the total number of travelers or the number of travelers who enjoyed traveling by train only. Statement (2) alone is not sufficient.
From this statement alone, we know that all the travelers who enjoyed traveling by plane also enjoyed traveling by train. This means that the travelers who enjoyed traveling by both plane and train are included in the group of travelers who enjoyed traveling by plane. However, we don't have any information about the total number of travelers or the number of travelers who enjoyed traveling by train only. Statement (2) alone is not sufficient.
Combining both statements, we have the following information:
- 25 travelers enjoyed traveling by plane (Statement 1).
- All of the travelers who enjoyed traveling by plane also enjoyed traveling by train (Statement 2).
From statement (2), we know that the travelers who enjoyed traveling by both plane and train are included in the group of travelers who enjoyed traveling by plane. Since statement (1) tells us that 25 travelers enjoyed traveling by plane, and all of them also enjoyed traveling by train (according to statement 2), we can conclude that the number of travelers who enjoyed traveling by both plane and train is 25.
Therefore, both statements together are sufficient to determine that 25 travelers enjoyed traveling by both plane and train. Hence, the correct answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
If a, b, k, and m are positive integers, is ak factor of bm?(1) a is a factor of b.
(2) k = m- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
If a, b, k, and m are positive integers, is ak factor of bm?
(1) a is a factor of b.
(2) k = m
(2) k = m
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Rahul Kapoor answered |
Statement (1): a is a factor of b.
If a is a factor of b, then ak will be a factor of bk for any positive integer k. Therefore, statement (1) alone is sufficient to answer the question.
Statement (2): k = m.
If k = m, then ak will be a factor of bm for any positive integer a and b. Therefore, statement (2) alone is sufficient to answer the question.
When we consider both statements together, we have the information that a is a factor of b and k = m. Combining these conditions, we can conclude that ak is a factor of bm. Therefore, both statements together are also sufficient to answer the question.
Since both statements alone are sufficient, and together they are also sufficient, the answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
In a college alumni meet, 30% of the students were those who were studying in college and the rest were alumni of the college. What percent of the students, including alumni and non alumni, were males who participated in the meet?(1) 10% of the alumni students who came were females
(2) 20% of college studying students who participated were males.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
In a college alumni meet, 30% of the students were those who were studying in college and the rest were alumni of the college. What percent of the students, including alumni and non alumni, were males who participated in the meet?
(1) 10% of the alumni students who came were females
(2) 20% of college studying students who participated were males.
(2) 20% of college studying students who participated were males.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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BT Educators answered |
Statement (1): 10% of the alumni students who came were females.
This statement provides information about the gender distribution among the alumni students who attended the meet. However, it doesn't provide any information about the gender distribution among the college studying students. Without this information, we can't determine the overall percentage of males who participated in the meet.
This statement provides information about the gender distribution among the alumni students who attended the meet. However, it doesn't provide any information about the gender distribution among the college studying students. Without this information, we can't determine the overall percentage of males who participated in the meet.
Statement (2): 20% of college studying students who participated were males.
This statement provides information about the gender distribution among the college studying students who participated in the meet. However, it doesn't provide any information about the gender distribution among the alumni students. Without this information, we can't determine the overall percentage of males who participated in the meet.
This statement provides information about the gender distribution among the college studying students who participated in the meet. However, it doesn't provide any information about the gender distribution among the alumni students. Without this information, we can't determine the overall percentage of males who participated in the meet.
Since neither statement alone is sufficient to answer the question, we need to evaluate both statements together:
By combining the information from both statements, we know that 10% of the alumni students who attended were females, and 20% of the college studying students who participated were males. However, we still don't have the specific proportions of alumni and college studying students in the total student population. Without this information, we can't determine the overall percentage of males who participated in the meet.
Therefore, the correct answer is (C): Both statements (1) and (2) together are sufficient to answer the question asked, but neither statement alone is sufficient.
What is the units digit of 4^n?(1) n = 2x + 1, where x is a positive integer.
(2) n = 2k – 1, where k is a positive integer.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
What is the units digit of 4^n?
(1) n = 2x + 1, where x is a positive integer.
(2) n = 2k – 1, where k is a positive integer.
(2) n = 2k – 1, where k is a positive integer.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Moumita Sen answered |
The units digit of 4^n will depend on the value of n.
Statement (1) tells us that n = 2x + 1, where x is a positive integer. This means that n is an odd number. Since the units digit of 4 raised to any odd power is 4, we can determine that the units digit of 4^n is 4.
Statement (2) tells us that n = 2k, where k is an integer. This means that n is an even number. Since the units digit of 4 raised to any even power is 6, we can determine that the units digit of 4^n is 6.
Therefore, the units digit of 4^n is either 4 or 6, depending on whether n is odd or even.
Both statements are individually sufficient to determine the units digit of 4^n.
Statement (1) tells us that n = 2x + 1, where x is a positive integer. This means that n is an odd number. Since the units digit of 4 raised to any odd power is 4, we can determine that the units digit of 4^n is 4.
Statement (2) tells us that n = 2k, where k is an integer. This means that n is an even number. Since the units digit of 4 raised to any even power is 6, we can determine that the units digit of 4^n is 6.
Therefore, the units digit of 4^n is either 4 or 6, depending on whether n is odd or even.
Both statements are individually sufficient to determine the units digit of 4^n.
If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.
(2) n and 23 are each divisible by the same number of positive integers.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of two different prime numbers.
(2) n and 23 are each divisible by the same number of positive integers.
(2) n and 23 are each divisible by the same number of positive integers.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Kalyan Nair answered |
Statement (1): n is the product of two different prime numbers.
- If n is the product of two different prime numbers, then n can be expressed as p*q, where p and q are distinct prime numbers.
- The number of positive integers by which n is divisible can be determined by finding the number of factors of n.
- The number of factors of n can be calculated by finding the product of the exponents of each prime factor and adding 1 to each exponent, and then multiplying the results.
- For example, if n = p^a * q^b, where p and q are prime numbers and a and b are positive integers, then the number of factors of n is (a+1)*(b+1).
- Therefore, statement (1) alone is sufficient to determine the number of positive integers by which n is divisible.
Statement (2): n and 23 are each divisible by the same number of positive integers.
- This statement does not provide direct information about the factors of n.
- It only states that the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible.
- However, this information is not sufficient to determine the exact number of positive integers by which n is divisible.
- Therefore, statement (2) alone is not sufficient to determine the number of positive integers by which n is divisible.
Combined statements:
- Combining both statements, we know that n is the product of two different prime numbers (statement 1) and the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible (statement 2).
- Since 23 is a prime number, it is only divisible by 1 and itself, so it has 2 positive divisors.
- Therefore, the number of positive integers by which n is divisible is also 2, as stated in statement 2.
- Hence, both statements together are sufficient to determine that n is divisible by 2 positive integers.
- Therefore, the correct answer is option D.
- If n is the product of two different prime numbers, then n can be expressed as p*q, where p and q are distinct prime numbers.
- The number of positive integers by which n is divisible can be determined by finding the number of factors of n.
- The number of factors of n can be calculated by finding the product of the exponents of each prime factor and adding 1 to each exponent, and then multiplying the results.
- For example, if n = p^a * q^b, where p and q are prime numbers and a and b are positive integers, then the number of factors of n is (a+1)*(b+1).
- Therefore, statement (1) alone is sufficient to determine the number of positive integers by which n is divisible.
Statement (2): n and 23 are each divisible by the same number of positive integers.
- This statement does not provide direct information about the factors of n.
- It only states that the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible.
- However, this information is not sufficient to determine the exact number of positive integers by which n is divisible.
- Therefore, statement (2) alone is not sufficient to determine the number of positive integers by which n is divisible.
Combined statements:
- Combining both statements, we know that n is the product of two different prime numbers (statement 1) and the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible (statement 2).
- Since 23 is a prime number, it is only divisible by 1 and itself, so it has 2 positive divisors.
- Therefore, the number of positive integers by which n is divisible is also 2, as stated in statement 2.
- Hence, both statements together are sufficient to determine that n is divisible by 2 positive integers.
- Therefore, the correct answer is option D.
If B is a positive integer such that the difference between its only two distinct factors is odd, what is the value of B+1?- a)2
- b)3
- c)5
- d)6
- e)8
Correct answer is option 'B'. Can you explain this answer?
If B is a positive integer such that the difference between its only two distinct factors is odd, what is the value of B+1?
a)
2
b)
3
c)
5
d)
6
e)
8
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Rahul Kapoor answered |
Let's consider the factors of B. Since B has only two distinct factors, they must be 1 and B itself. The difference between these factors is B - 1.
Given that the difference between the two distinct factors is odd, we can conclude that B - 1 is an odd number. Therefore, B must be an even number.
To find the value of B+1, we add 1 to the even number B. Adding 1 to an even number always results in an odd number. Therefore, B+1 will be an odd number.
Among the answer choices, the only odd number is 3. Hence, the correct answer is (B) 3
A certain granola recipe calls for a simple mixture of raisins costing $3.50 per pound with oats. At a cost of $2.00 per pound for the granola mixture, how many pounds of oats must be added to 10 pounds of raisins?(1) The granola mixture is packaged in one-pound bags.
(2) Oats cost $1.00 per pound.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
A certain granola recipe calls for a simple mixture of raisins costing $3.50 per pound with oats. At a cost of $2.00 per pound for the granola mixture, how many pounds of oats must be added to 10 pounds of raisins?
(1) The granola mixture is packaged in one-pound bags.
(2) Oats cost $1.00 per pound.
(2) Oats cost $1.00 per pound.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Rahul Kapoor answered |
Statement (1): The granola mixture is packaged in one-pound bags.
From this statement alone, we know that the granola mixture is packaged in one-pound bags. However, we don't have any information about the proportion or ratio of oats to raisins in the mixture or the total weight of the mixture. Statement (1) alone is not sufficient.
From this statement alone, we know that the granola mixture is packaged in one-pound bags. However, we don't have any information about the proportion or ratio of oats to raisins in the mixture or the total weight of the mixture. Statement (1) alone is not sufficient.
Statement (2): Oats cost $1.00 per pound.
From this statement alone, we know the cost per pound of oats. Since we are told that the granola mixture costs $2.00 per pound, and the raisins cost $3.50 per pound, we can deduce that the oats constitute the difference in cost between the granola mixture and the raisins. Therefore, for every pound of oats added, the cost of the mixture decreases by $1.50 per pound. With this information, we can calculate the number of pounds of oats needed to balance the cost.
From this statement alone, we know the cost per pound of oats. Since we are told that the granola mixture costs $2.00 per pound, and the raisins cost $3.50 per pound, we can deduce that the oats constitute the difference in cost between the granola mixture and the raisins. Therefore, for every pound of oats added, the cost of the mixture decreases by $1.50 per pound. With this information, we can calculate the number of pounds of oats needed to balance the cost.
Since 10 pounds of raisins are used and the cost difference is $1.50 per pound, the total cost difference for the 10 pounds of raisins is $1.50 * 10 = $15.00. Since oats cost $1.00 per pound, the number of pounds of oats needed to balance the cost is $15.00 / $1.00 = 15 pounds.
Hence, statement (2) alone is sufficient to answer the question, but statement (1) alone is not sufficient. Therefore, the correct answer is (B).
Is x an odd integer?(1) x is the square root of an integer.
(2) x is the square of an integer.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
Is x an odd integer?
(1) x is the square root of an integer.
(2) x is the square of an integer.
(2) x is the square of an integer.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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|
Rahul Kapoor answered |
Statement (1): x is the square root of an integer.
From this statement alone, we can deduce that x is a positive or negative integer, or zero. However, we don't have any information about whether x is odd or even. For example, x could be the square root of 4, which is an even integer, or it could be the square root of 9, which is an odd integer. Therefore, statement (1) alone is not sufficient to determine if x is an odd integer.
From this statement alone, we can deduce that x is a positive or negative integer, or zero. However, we don't have any information about whether x is odd or even. For example, x could be the square root of 4, which is an even integer, or it could be the square root of 9, which is an odd integer. Therefore, statement (1) alone is not sufficient to determine if x is an odd integer.
Statement (2): x is the square of an integer.
From this statement alone, we can determine that x must be a non-negative integer (including zero). However, we still don't have any information about whether x is odd or even. For example, x could be the square of 2, which is an even integer, or it could be the square of 3, which is an odd integer. Therefore, statement (2) alone is not sufficient to determine if x is an odd integer.
From this statement alone, we can determine that x must be a non-negative integer (including zero). However, we still don't have any information about whether x is odd or even. For example, x could be the square of 2, which is an even integer, or it could be the square of 3, which is an odd integer. Therefore, statement (2) alone is not sufficient to determine if x is an odd integer.
Since neither statement alone provides enough information to determine if x is an odd integer, and the two statements together don't provide any additional information, we need additional data to answer the question. Hence, the correct answer is E: Statements (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.
How many of the girls in a group of 200 children have an average score of 80 in their final exams?(1) 45% of the children have an average score of 80 in their final exams.
(2) 50% of the children in the group are girls.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
How many of the girls in a group of 200 children have an average score of 80 in their final exams?
(1) 45% of the children have an average score of 80 in their final exams.
(2) 50% of the children in the group are girls.
(2) 50% of the children in the group are girls.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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BT Educators answered |
Statement (1): 45% of the children have an average score of 80 in their final exams.
From this statement alone, we know that 45% of the children have an average score of 80. However, we don't have any information about the gender distribution within this group or the total number of girls in the group. Statement (1) alone is not sufficient.
From this statement alone, we know that 45% of the children have an average score of 80. However, we don't have any information about the gender distribution within this group or the total number of girls in the group. Statement (1) alone is not sufficient.
Statement (2): 50% of the children in the group are girls.
From this statement alone, we know that 50% of the children in the group are girls. However, we don't have any information about their average scores or the total number of children in the group. Statement (2) alone is not sufficient.
From this statement alone, we know that 50% of the children in the group are girls. However, we don't have any information about their average scores or the total number of children in the group. Statement (2) alone is not sufficient.
Combining both statements, we have the following information:
- 45% of the children have an average score of 80 in their final exams (Statement 1).
- 50% of the children in the group are girls (Statement 2).
Although we have information about the percentage of children with an average score of 80 (Statement 1) and the percentage of girls in the group (Statement 2), we still don't know the exact numbers or how these two groups overlap.
For example, if there are 200 children in total, Statement 2 tells us that 100 of them are girls. However, we don't know how many of these girls have an average score of 80. Additionally, we don't know the number of boys in the group or the distribution of average scores among them.
Therefore, Statements (1) and (2) TOGETHER are not sufficient to determine the number of girls with an average score of 80 in the group. Additional data is needed to answer the question accurately.
Hence, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Five persons sat next to each other around a circular table to play cards. Did Grace sit next to Bill?(1) Dora sat next to Ethyl and Carl.
(2) Grace sat next to Carl.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
Five persons sat next to each other around a circular table to play cards. Did Grace sit next to Bill?
(1) Dora sat next to Ethyl and Carl.
(2) Grace sat next to Carl.
(2) Grace sat next to Carl.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Rahul Kapoor answered |
Statement (1): Dora sat next to Ethyl and Carl.
This statement provides information about the seating arrangement, but it does not mention anything about Grace or Bill. Therefore, it does not provide any direct information about whether Grace sat next to Bill.
Statement (2): Grace sat next to Carl.
This statement provides information specifically about Grace's seating arrangement, stating that she sat next to Carl. However, it does not provide any information about Bill or their relative positions.
When we consider each statement alone:
- Statement (1) alone tells us about the seating arrangement involving Dora, Ethyl, and Carl, but it does not provide any direct information about Grace or Bill. It does not help us determine if Grace sat next to Bill.
- Statement (2) alone tells us that Grace sat next to Carl, but it does not provide any information about Bill. It does not help us determine if Grace sat next to Bill either.
Therefore, statement (1) alone is sufficient to answer the question because it provides information about the seating arrangement involving Dora, Ethyl, and Carl. Since Dora sat next to Ethyl and Carl, there is no room for Grace to sit next to Bill. Thus, Grace did not sit next to Bill.
The answer is A.
If the number x is obtained by reversing the order of the digits in the positive 3-digit integer y, is x > y?(1) The tens digit of y is 3.
(2) The rightmost digit of x is 1 and the rightmost digit of y is 9.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
If the number x is obtained by reversing the order of the digits in the positive 3-digit integer y, is x > y?
(1) The tens digit of y is 3.
(2) The rightmost digit of x is 1 and the rightmost digit of y is 9.
(2) The rightmost digit of x is 1 and the rightmost digit of y is 9.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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|
Wizius Careers answered |
Statement (1): The tens digit of y is 3.
This statement provides some information about y, but it doesn't give any specific information about the hundreds or units digit of y, which are important for comparing x and y. Alone, this statement is not sufficient.
This statement provides some information about y, but it doesn't give any specific information about the hundreds or units digit of y, which are important for comparing x and y. Alone, this statement is not sufficient.
Statement (2): The rightmost digit of x is 1, and the rightmost digit of y is 9.
This statement gives specific information about the rightmost digits of both x and y. Since x is obtained by reversing the digits of y, the rightmost digits of x and y will be the same. Therefore, x must also end with 9. As a result, we can conclude that x is greater than y. Alone, this statement is sufficient to answer the question.
This statement gives specific information about the rightmost digits of both x and y. Since x is obtained by reversing the digits of y, the rightmost digits of x and y will be the same. Therefore, x must also end with 9. As a result, we can conclude that x is greater than y. Alone, this statement is sufficient to answer the question.
Since statement (2) alone is sufficient to answer the question, but statement (1) alone is not, the answer is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
In a certain community orchestra, 40 percent of the members are string players. If 28 percent of the members are female string players, how many of the members are female string players?(1) Exactly 120 of the members are string players.
(2) Exactly 35 percent of the players who are not string players are male.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
In a certain community orchestra, 40 percent of the members are string players. If 28 percent of the members are female string players, how many of the members are female string players?
(1) Exactly 120 of the members are string players.
(2) Exactly 35 percent of the players who are not string players are male.
(2) Exactly 35 percent of the players who are not string players are male.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
BT Educators answered |
Statement (1): Exactly 120 of the members are string players.
From this statement alone, we know that there are exactly 120 string players in the community orchestra. However, we don't have any information about the total number of members or the breakdown of male and female string players. Statement (1) alone is not sufficient.
From this statement alone, we know that there are exactly 120 string players in the community orchestra. However, we don't have any information about the total number of members or the breakdown of male and female string players. Statement (1) alone is not sufficient.
Statement (2): Exactly 35 percent of the players who are not string players are male.
From this statement alone, we know the gender distribution of non-string players, but we don't have any information about the total number of members or the percentage of female string players. Statement (2) alone is not sufficient.
From this statement alone, we know the gender distribution of non-string players, but we don't have any information about the total number of members or the percentage of female string players. Statement (2) alone is not sufficient.
Combining both statements, we have the following information:
- Exactly 120 of the members are string players (Statement 1).
- Exactly 35 percent of the players who are not string players are male (Statement 2).
From Statement 1, we know that there are 120 string players, but we don't have information about the total number of members to calculate the percentage of female string players. However, we can determine the total number of non-string players by subtracting 120 from the total number of members.
From Statement 2, we know the percentage of male non-string players, but we still don't have information about the total number of members or the percentage of female string players.
Therefore, Statement 1 alone is sufficient to answer the question because we can calculate the number of female string players using the given percentage from Statement 2. The percentage of female string players can be determined by subtracting the percentage of male non-string players (35%) from the total percentage of female players (100% - 35%). Once we have the percentage, we can multiply it by the total number of string players (120) to find the number of female string players.
Hence, the correct answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
What is the volume of milk present in a mixture of milk and water?(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
What is the volume of milk present in a mixture of milk and water?
(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.
(2) The initial mixture had 2 parts of water to 1 part milk.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
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Rahul Kapoor answered |
Statement (1): When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
From this statement alone, we know that when 2 liters of milk is added, the resulting mixture has equal quantities of milk and water. However, we don't have any information about the initial quantities or proportions of milk and water in the mixture. Statement (1) alone is not sufficient.
From this statement alone, we know that when 2 liters of milk is added, the resulting mixture has equal quantities of milk and water. However, we don't have any information about the initial quantities or proportions of milk and water in the mixture. Statement (1) alone is not sufficient.
Statement (2): The initial mixture had 2 parts of water to 1 part milk.
From this statement alone, we know the initial ratio of water to milk in the mixture. However, we don't have any information about the actual volumes or quantities of the mixture. Statement (2) alone is not sufficient.
From this statement alone, we know the initial ratio of water to milk in the mixture. However, we don't have any information about the actual volumes or quantities of the mixture. Statement (2) alone is not sufficient.
Combining both statements, we have the following information:
When 2 liters of milk is added, the resulting mixture has equal quantities of milk and water (Statement 1).
The initial mixture had a ratio of 2 parts water to 1 part milk (Statement 2).
Using this information, we can determine the volume of milk in the mixture. Since the resultant mixture has equal quantities of milk and water when 2 liters of milk is added, we can infer that the initial mixture had 2 liters of water and 1 liter of milk. Therefore, the volume of milk in the mixture is 1 liter.
The initial mixture had a ratio of 2 parts water to 1 part milk (Statement 2).
Using this information, we can determine the volume of milk in the mixture. Since the resultant mixture has equal quantities of milk and water when 2 liters of milk is added, we can infer that the initial mixture had 2 liters of water and 1 liter of milk. Therefore, the volume of milk in the mixture is 1 liter.
Hence, the correct answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
If x and y are positive integers, what is the value of x + y ?
(1) 2x 3y = 72
(2) 2x 2y = 32
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
If x and y are positive integers, what is the value of x + y ?
(1) 2x 3y = 72
(2) 2x 2y = 32
(1) 2x 3y = 72
(2) 2x 2y = 32
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Rahul Kapoor answered |
Statement (1): 2x + 3y = 72
From this equation, we have one equation with two variables. Although we cannot directly solve for the values of x and y, we can find multiple solutions that satisfy the equation. Therefore, we can determine the value of x + y.
For example, if we let x = 9 and y = 18, the equation is satisfied: 2(9) + 3(18) = 72. In this case, x + y = 9 + 18 = 27.
However, if we choose different values for x and y that satisfy the equation, we will obtain a different sum of x + y.
Statement (1) alone is sufficient to determine the value of x + y.
Statement (2): 2x + 2y = 32
Similar to statement (1), this equation gives us one equation with two variables. Again, we cannot directly solve for the values of x and y, but we can find multiple solutions that satisfy the equation and determine the value of x + y.
For example, if we let x = 8 and y = 8, the equation is satisfied: 2(8) + 2(8) = 32. In this case, x + y = 8 + 8 = 16.
However, if we choose different values for x and y that satisfy the equation, we will obtain a different sum of x + y.
Statement (2) alone is sufficient to determine the value of x + y.
Since each statement alone is sufficient to determine the value of x + y, the answer is (D) EACH statement ALONE is sufficient to answer the question asked.
For all integers n, the function f is defined by f(n) = an, where a is a constant. What is the value of f(1)?(1) f(2) = 100
(2) f(3) = -1,000- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
For all integers n, the function f is defined by f(n) = an, where a is a constant. What is the value of f(1)?
(1) f(2) = 100
(2) f(3) = -1,000
(2) f(3) = -1,000
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Saumya Sharma answered |
Understanding the Function f
The function f is defined as f(n) = an, where 'a' is a constant. We need to find the value of f(1).
Statement (1)
- This statement provides the information that f(2) = 100.
- Substituting into the function gives us:
- f(2) = a * 2 = 100
- Therefore, a = 100 / 2 = 50.
- We can now determine f(1):
- f(1) = a * 1 = 50.
Thus, Statement (1) is sufficient to find f(1).
Statement (2)
- This statement tells us that f(3) = -1,000.
- Using the function, we have:
- f(3) = a * 3 = -1,000
- Hence, a = -1,000 / 3.
- While we can find the value of 'a', we cannot compute f(1) directly:
- f(1) = a * 1 = -1,000 / 3, which is a value, but we need to analyze its sufficiency.
Since it provides a specific value for a but does not lead to a unique value for f(1) without knowing the exact value of a, Statement (2) alone is not sufficient.
Conclusion
- Statement (1) is sufficient to determine f(1).
- Statement (2) alone does not provide enough information for a unique answer.
Hence, the correct answer is option 'B': Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
The function f is defined as f(n) = an, where 'a' is a constant. We need to find the value of f(1).
Statement (1)
- This statement provides the information that f(2) = 100.
- Substituting into the function gives us:
- f(2) = a * 2 = 100
- Therefore, a = 100 / 2 = 50.
- We can now determine f(1):
- f(1) = a * 1 = 50.
Thus, Statement (1) is sufficient to find f(1).
Statement (2)
- This statement tells us that f(3) = -1,000.
- Using the function, we have:
- f(3) = a * 3 = -1,000
- Hence, a = -1,000 / 3.
- While we can find the value of 'a', we cannot compute f(1) directly:
- f(1) = a * 1 = -1,000 / 3, which is a value, but we need to analyze its sufficiency.
Since it provides a specific value for a but does not lead to a unique value for f(1) without knowing the exact value of a, Statement (2) alone is not sufficient.
Conclusion
- Statement (1) is sufficient to determine f(1).
- Statement (2) alone does not provide enough information for a unique answer.
Hence, the correct answer is option 'B': Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?(1) If r = s, then r θ s = 0.
(2) If r ≠ s, then r θ s ≠ s θ r.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?
(1) If r = s, then r θ s = 0.
(2) If r ≠ s, then r θ s ≠ s θ r.
(2) If r ≠ s, then r θ s ≠ s θ r.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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Rahul Kapoor answered |
Statement (1): If r = s, then r θ s = 0.
From this statement, we know that if r is equal to s, then the result of the operation θ between r and s is 0. However, this statement does not provide specific information about the operation θ. We cannot determine which operation (+, −, ×, or ÷) corresponds to θ based solely on this statement.
Statement (2): If r ≠ s, then r θ s ≠ s θ r.
From this statement, we know that if r is not equal to s, then the result of the operation θ between r and s is not equal to the result of the operation θ between s and r. This statement provides a rule about the commutativity of the operation θ, indicating that the operation θ is not commutative. However, we still do not know the specific operation θ.
When we consider both statements together, we know that if r = s, then r θ s = 0, and if r ≠ s, then r θ s ≠ s θ r. These statements do not provide enough information to determine the exact operation θ. We only know that the operation θ must satisfy these conditions.
Therefore, Statement (1) alone is sufficient to establish a rule about the result of the operation θ, but we cannot determine the specific operation θ. The correct answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Is the integer K an odd integer?(1) K = 3M where M is an integer.
(2) K = 6J where J is an integer.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
Is the integer K an odd integer?
(1) K = 3M where M is an integer.
(2) K = 6J where J is an integer.
(2) K = 6J where J is an integer.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
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Advait Roy answered |
Statement (1): K = 3M where M is an integer.
This statement tells us that K is a multiple of 3, but it does not provide any information about whether K is odd or even. For example, if M = 1, then K = 3, which is odd. However, if M = 2, then K = 6, which is even. Therefore, statement (1) alone is not sufficient to determine whether K is an odd integer.
Statement (2): K = 6J where J is an integer.
Similarly, this statement tells us that K is a multiple of 6, but it does not provide any information about whether K is odd or even. For example, if J = 1, then K = 6, which is even. However, if J = 2, then K = 12, which is also even. Therefore, statement (2) alone is not sufficient to determine whether K is an odd integer.
Statements (1) and (2) together:
Combining the information from both statements, we have K = 3M and K = 6J. We can rewrite the second equation as K = 2(3J). Since 3J is an integer (since J is an integer), K must be divisible by 2. Therefore, K is always even.
Conclusion:
From statement (1) alone, we cannot determine whether K is an odd integer. From statement (2) alone, we also cannot determine whether K is an odd integer. However, when we consider both statements together, we can conclude that K is always even. Therefore, statement (2) alone is sufficient to answer the question asked.
Answer:
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
This statement tells us that K is a multiple of 3, but it does not provide any information about whether K is odd or even. For example, if M = 1, then K = 3, which is odd. However, if M = 2, then K = 6, which is even. Therefore, statement (1) alone is not sufficient to determine whether K is an odd integer.
Statement (2): K = 6J where J is an integer.
Similarly, this statement tells us that K is a multiple of 6, but it does not provide any information about whether K is odd or even. For example, if J = 1, then K = 6, which is even. However, if J = 2, then K = 12, which is also even. Therefore, statement (2) alone is not sufficient to determine whether K is an odd integer.
Statements (1) and (2) together:
Combining the information from both statements, we have K = 3M and K = 6J. We can rewrite the second equation as K = 2(3J). Since 3J is an integer (since J is an integer), K must be divisible by 2. Therefore, K is always even.
Conclusion:
From statement (1) alone, we cannot determine whether K is an odd integer. From statement (2) alone, we also cannot determine whether K is an odd integer. However, when we consider both statements together, we can conclude that K is always even. Therefore, statement (2) alone is sufficient to answer the question asked.
Answer:
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
What is the value of n ?(1) n2 = 1
(2) n3 = 1- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
What is the value of n ?
(1) n2 = 1
(2) n3 = 1
(2) n3 = 1
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
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EduRev GMAT answered |
To determine the value of n, we need to analyze each statement individually and then together if necessary.
Statement (1): n2 = 1
This equation can be solved as follows: n2 = 1 Taking the square root of both sides, we get: n = plus or minus 1 So, n can be either 1 or -1. This means that statement (1) alone is not sufficient to determine a unique value for n.
Statement (2): n3 = 1
This equation can be solved as follows: n3 = 1 The only real number solution to this equation is: n = 1 So, statement (2) alone is sufficient to determine that n = 1.
Conclusion
Since statement (2) alone is sufficient to determine the value of n, but statement (1) alone is not, the correct answer is:
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
What is the value of the sum of a sequence of x consecutive even integers?(1) x = 5
(2) The least integer in the sequence is 6- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'C'. Can you explain this answer?
What is the value of the sum of a sequence of x consecutive even integers?
(1) x = 5
(2) The least integer in the sequence is 6
(2) The least integer in the sequence is 6
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
|
Wizius Careers answered |
Statement 1: x = 5
We don't know where the sequence starts. For example:
Case a: the 5 numbers are {2, 4, 6, 8, 10}, in which case the sum = 30
Case b: the 5 numbers are {4, 6, 8, 10, 12}, in which case the sum = 40
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
We don't know where the sequence starts. For example:
Case a: the 5 numbers are {2, 4, 6, 8, 10}, in which case the sum = 30
Case b: the 5 numbers are {4, 6, 8, 10, 12}, in which case the sum = 40
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The least integer in the sequence is 6
We don't know how many integers are in the sequence. For example:
Case a: the numbers are {6, 8}, in which case the sum = 14
Case b: the numbers are {6, 8, 10}, in which case the sum = 24
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
We don't know how many integers are in the sequence. For example:
Case a: the numbers are {6, 8}, in which case the sum = 14
Case b: the numbers are {6, 8, 10}, in which case the sum = 24
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
We now know that the numbers are {6, 8, 10, 12, 14}, in which case the sum = 50
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
We now know that the numbers are {6, 8, 10, 12, 14}, in which case the sum = 50
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
What is the units digit of 3n?(1) n = 2x + 1, where x is a positive integer.
(2) n = 2k – 1, where k is a positive integer.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'E'. Can you explain this answer?
What is the units digit of 3n?
(1) n = 2x + 1, where x is a positive integer.
(2) n = 2k – 1, where k is a positive integer.
(2) n = 2k – 1, where k is a positive integer.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
|
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Rahul Kapoor answered |
Statement (1): n = 2x + 1, where x is a positive integer.
This statement provides information about the form of n, indicating that n is an odd integer. However, knowing that n is odd doesn't provide enough specific information to determine the units digit of 3n. For example, if n = 3, then 3n = 3 * 3 = 9, and the units digit is 9. But if n = 5, then 3n = 3 * 5 = 15, and the units digit is 5. The units digit of 3n can vary depending on the specific value of n. Statement (1) alone is not sufficient.
This statement provides information about the form of n, indicating that n is an odd integer. However, knowing that n is odd doesn't provide enough specific information to determine the units digit of 3n. For example, if n = 3, then 3n = 3 * 3 = 9, and the units digit is 9. But if n = 5, then 3n = 3 * 5 = 15, and the units digit is 5. The units digit of 3n can vary depending on the specific value of n. Statement (1) alone is not sufficient.
Statement (2): n = 2k - 1, where k is a positive integer.
This statement also provides information about the form of n, indicating that n is an odd integer. Similar to statement (1), knowing that n is odd doesn't provide enough specific information to determine the units digit of 3n. For example, if n = 1, then 3n = 3 * 1 = 3, and the units digit is 3. But if n = 3, then 3n = 3 * 3 = 9, and the units digit is 9. Again, the units digit of 3n can vary depending on the specific value of n. Statement (2) alone is not sufficient.
This statement also provides information about the form of n, indicating that n is an odd integer. Similar to statement (1), knowing that n is odd doesn't provide enough specific information to determine the units digit of 3n. For example, if n = 1, then 3n = 3 * 1 = 3, and the units digit is 3. But if n = 3, then 3n = 3 * 3 = 9, and the units digit is 9. Again, the units digit of 3n can vary depending on the specific value of n. Statement (2) alone is not sufficient.
When we consider both statements together, we still don't have enough information to determine the units digit of 3n. Both statements provide similar information about the form of n, but they don't give any specific values for n that would allow us to determine the units digit of 3n uniquely. Therefore, even when considering both statements together, we still need additional data to answer the question.
Hence, the answer is E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
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