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How many keystrokes are needed to type numbers from 1 to 1000?- a)3001
- b)2893
- c)2704
- d)2890
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
How many keystrokes are needed to type numbers from 1 to 1000?
a)
3001
b)
2893
c)
2704
d)
2890
e)
None of these
|
EduRev GMAT answered |
While typing numbers from 1 to 1000, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.
Each of these numbers requires one keystroke.
That is 9 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 900 three-digit numbers: from 100 to 999.
Each of these numbers requires 3 keystrokes.
Therefore, 2700 keystrokes to type the 3-digit numbers.
Each of these numbers requires 3 keystrokes.
Therefore, 2700 keystrokes to type the 3-digit numbers.
1000 is a four-digit number which requires 4 keystrokes.
Totally, therefore, one requires 9 + 180 + 2700 + 4 = 2893 keystrokes.
Choice B is the correct answer.
Choice B is the correct answer.
Watch out for the common mistake that many of us make of counting only 89 2-digit numbers and 899 3-digit numbers. The temptation is to say, 99 - 10 = 89. So, 89 2-digit numbers exist. 99 - 10 means that we are not counting 10 as a 2-digit number. The correct approach is: of the 99 numbers from 1 to 99, we are not counting the first 9 single digit numbers. So, we have 99 - 9 = 90 2-digit numbers. The same logic applies when we count 3-digit numbers.
Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $ 400 at the end of another 5 years. What was the rate of interest in which he invested his sum?- a)12%
- b)12.5%
- c)6.67%
- d)6.25%
- e)8.33%
Correct answer is option 'E'. Can you explain this answer?
Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $ 400 at the end of another 5 years. What was the rate of interest in which he invested his sum?
a)
12%
b)
12.5%
c)
6.67%
d)
6.25%
e)
8.33%
|
|
EduRev GMAT answered |
Step 1: Compute principal invested
Concept: Simple interest earned remains same year after year.
Concept: Simple interest earned remains same year after year.
Initial amount invested = P
Value of investment (Amount) at the end of year 3 = $300
Value of investment (Amount) at the end of year 8 (another 5 years) = $400
Therefore, the interest earned for the 5 year period between the 3rd year and 8th year = $400 - $300 = $100.
Value of investment (Amount) at the end of year 3 = $300
Value of investment (Amount) at the end of year 8 (another 5 years) = $400
Therefore, the interest earned for the 5 year period between the 3rd year and 8th year = $400 - $300 = $100.
So, interest earned per year = 100/5 = $20.
Therefore, interest earned for 3 years = 3 × 20 = $60.
Hence, initial amount invested P = Amount after 3 years - interest for 3 years
P = $300 − $60 = $240
Step 2: Find the rate of interest
Simple interest = $20, Principal P = $240, n = 1 year.
Rate of interest is 8.33%.
Therefore, interest earned for 3 years = 3 × 20 = $60.
Hence, initial amount invested P = Amount after 3 years - interest for 3 years
P = $300 − $60 = $240
Step 2: Find the rate of interest
Simple interest = $20, Principal P = $240, n = 1 year.
Rate of interest is 8.33%.
If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?- a)121
- b)3267
- c)363
- d)33
- e)None of the above
Correct answer is option 'C'. Can you explain this answer?
If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?
a)
121
b)
3267
c)
363
d)
33
e)
None of the above
|
|
EduRev GMAT answered |
Step 1: Prime factorize the given expression
a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311
Step 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33
112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should be a part of 'a'
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should be a part of 'a'
33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.
The question is "what is the smallest possible value of 'a'?"
The smallest value that 'a' can take is 363
The smallest value that 'a' can take is 363
Choice C is the correct answer.
What is the standard deviation (SD) of the four numbers p, q, r, and s?Statement 1: The sum of p, q, r, and s is 24.
Statement 2: The sum of the squares of p, q, r, and s is 224.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
- c)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient
- e)Statements (1) and (2) TOGETHER are NOT sufficient
Correct answer is option 'C'. Can you explain this answer?
What is the standard deviation (SD) of the four numbers p, q, r, and s?
Statement 1: The sum of p, q, r, and s is 24.
Statement 2: The sum of the squares of p, q, r, and s is 224.
Statement 2: The sum of the squares of p, q, r, and s is 224.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
c)
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient
e)
Statements (1) and (2) TOGETHER are NOT sufficient
|
Maya Choudhury answered |
Statement 1:
The sum of p, q, r, and s is 24.
This statement alone does not provide enough information to calculate the standard deviation because we need individual values of p, q, r, and s to determine the spread from the mean.
Statement 2:
The sum of the squares of p, q, r, and s is 224.
This statement also does not give us the individual values of p, q, r, and s, which are required to calculate the standard deviation.
Both Statements Together:
When we combine both statements, we can solve for the individual values of p, q, r, and s. From Statement 1, we know that the sum of p, q, r, and s is 24. From Statement 2, we know that the sum of their squares is 224. Using these two equations, we can solve for the values of p, q, r, and s. Once we have these values, we can calculate the standard deviation.
Therefore, both statements together are sufficient to determine the standard deviation of the four numbers p, q, r, and s.
The sum of p, q, r, and s is 24.
This statement alone does not provide enough information to calculate the standard deviation because we need individual values of p, q, r, and s to determine the spread from the mean.
Statement 2:
The sum of the squares of p, q, r, and s is 224.
This statement also does not give us the individual values of p, q, r, and s, which are required to calculate the standard deviation.
Both Statements Together:
When we combine both statements, we can solve for the individual values of p, q, r, and s. From Statement 1, we know that the sum of p, q, r, and s is 24. From Statement 2, we know that the sum of their squares is 224. Using these two equations, we can solve for the values of p, q, r, and s. Once we have these values, we can calculate the standard deviation.
Therefore, both statements together are sufficient to determine the standard deviation of the four numbers p, q, r, and s.
How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?- a)25
- b)8
- c)6
- d)5
- e)2
Correct answer is option 'C'. Can you explain this answer?
How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?
a)
25
b)
8
c)
6
d)
5
e)
2
|
|
EduRev GMAT answered |
25! means factorial 25 whose value = 25 × 24 × 23 × 22 × .... × 1
When a number that is a multiple of 5 is multiplied with an even number, it results in a trailing zero.
(Product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied)
(Product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied)
In 25!, the following numbers have 5 as their factor: 5, 10, 15, 20, and 25.
25 is the square of 5 and hence it has two 5s in it.
In toto, it is equivalent of having six 5s.
25 is the square of 5 and hence it has two 5s in it.
In toto, it is equivalent of having six 5s.
There are at least 6 even numbers in 25!
Hence, the number 25! will have 6 trailing zeroes in it.
Hence, the number 25! will have 6 trailing zeroes in it.
Choice C is the correct answer.
Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and that of set A?- a)2500
- b)5050
- c)11325
- d)6275
- e)2550
Correct answer is option 'A'. Can you explain this answer?
Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and that of set A?
a)
2500
b)
5050
c)
11325
d)
6275
e)
2550
|
|
Bhavya Khanna answered |
To find the difference between the sum of elements in Set A and Set B, we need to calculate the sum of each set separately and then subtract the sum of Set A from the sum of Set B.
Set A: Even numbers between 2 and 50 inclusive
Set B: Even numbers between 102 and 150 inclusive
Calculating the sum of Set A:
We know that the set contains all even numbers between 2 and 50 inclusive. To find the sum, we can use the formula for the sum of an arithmetic series:
Sum = (first term + last term) * (number of terms) / 2
The first term in Set A is 2, the last term is 50, and the number of terms is (50-2)/2 + 1 = 25. Plugging these values into the formula:
Sum of Set A = (2 + 50) * (25) / 2 = 52 * 25 / 2 = 1300
Calculating the sum of Set B:
Similarly, we can find the sum of Set B using the same formula. The first term in Set B is 102, the last term is 150, and the number of terms is (150-102)/2 + 1 = 25.
Sum of Set B = (102 + 150) * (25) / 2 = 252 * 25 / 2 = 6300
Subtracting the sum of Set A from the sum of Set B:
Difference = Sum of Set B - Sum of Set A = 6300 - 1300 = 5000
Therefore, the difference between the sum of elements in Set B and Set A is 5000. However, none of the given answer choices match this result. Therefore, there may be an error in the answer choices provided.
Set A: Even numbers between 2 and 50 inclusive
Set B: Even numbers between 102 and 150 inclusive
Calculating the sum of Set A:
We know that the set contains all even numbers between 2 and 50 inclusive. To find the sum, we can use the formula for the sum of an arithmetic series:
Sum = (first term + last term) * (number of terms) / 2
The first term in Set A is 2, the last term is 50, and the number of terms is (50-2)/2 + 1 = 25. Plugging these values into the formula:
Sum of Set A = (2 + 50) * (25) / 2 = 52 * 25 / 2 = 1300
Calculating the sum of Set B:
Similarly, we can find the sum of Set B using the same formula. The first term in Set B is 102, the last term is 150, and the number of terms is (150-102)/2 + 1 = 25.
Sum of Set B = (102 + 150) * (25) / 2 = 252 * 25 / 2 = 6300
Subtracting the sum of Set A from the sum of Set B:
Difference = Sum of Set B - Sum of Set A = 6300 - 1300 = 5000
Therefore, the difference between the sum of elements in Set B and Set A is 5000. However, none of the given answer choices match this result. Therefore, there may be an error in the answer choices provided.
If "x" is an integer, which of the following inequalities has (have) a finite range of values of "x" satisfying it (them)?- a)x2 + 5x + 6 > 0
- b)|x + 2| > 4
- c)9x - 7 < 3x + 14
- d)x2 - 4x + 3 < 0
- e)(B) and (D)
Correct answer is option 'D'. Can you explain this answer?
If "x" is an integer, which of the following inequalities has (have) a finite range of values of "x" satisfying it (them)?
a)
x2 + 5x + 6 > 0
b)
|x + 2| > 4
c)
9x - 7 < 3x + 14
d)
x2 - 4x + 3 < 0
e)
(B) and (D)
|
|
EduRev GMAT answered |
Step 1: Find the values of "x" that will satisfy the four inequalities
Choice A: x2 + 5x + 6 > 0
Factorize the given expression: x2 + 5x + 6 > 0 = (x + 2)(x + 3) > 0.
This inequality will hold good when both (x + 2) and (x + 3) are simultaneously positive OR are simultaneously negative.
Factorize the given expression: x2 + 5x + 6 > 0 = (x + 2)(x + 3) > 0.
This inequality will hold good when both (x + 2) and (x + 3) are simultaneously positive OR are simultaneously negative.
Possibility 1: Both (x + 2) and (x + 3) are positive.
i.e., x + 2 > 0 AND x + 3 > 0
i.e., x > -2 AND x > -3
Essentially translates to x > -2
i.e., x + 2 > 0 AND x + 3 > 0
i.e., x > -2 AND x > -3
Essentially translates to x > -2
Possibility 2: Both (x + 2) and (x + 3) are negative.
i.e., x + 2 < 0 AND x + 3 < 0
i.e., x < -2 AND x < -3
Essentially translates to x < -3
i.e., x + 2 < 0 AND x + 3 < 0
i.e., x < -2 AND x < -3
Essentially translates to x < -3
Evaluating both the possibilities, we get the range of values of "x" that satisfy this inequality to be x > -2 or x < -3. i.e., "x" does not lie between -3 and -2.
i.e., x takes values lesser than -3 or greater than -2.
The range of values that x takes is infinite.
i.e., x takes values lesser than -3 or greater than -2.
The range of values that x takes is infinite.
Choice B: |x + 2| > 4
|x + 2| > 4 is a modulus function and therefore, has two possibilities
|x + 2| > 4 is a modulus function and therefore, has two possibilities
Possiblity 1: x + 2 > 4
i.e., x > 2
i.e., x > 2
Possiblity 2: (x + 2) < -4.
i.e., x < -6
Evaluating the two options together, we get the values of "x" that satisfy the inequality as x > 2 OR x < -6.
i.e., "x" does not lie between -6 and 2.
An infinite range of values.
i.e., x < -6
Evaluating the two options together, we get the values of "x" that satisfy the inequality as x > 2 OR x < -6.
i.e., "x" does not lie between -6 and 2.
An infinite range of values.
Choice C: 9x - 7 < 3x + 14
Simplifying, we get 6x < 21 or x < 3.5.
An infinite range of values.
Simplifying, we get 6x < 21 or x < 3.5.
An infinite range of values.
Choice D: x2 - 4x + 3 < 0
Factorizing x2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0.
This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative.
Factorizing x2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0.
This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative.
Possibility 1: (x -3) is positive and (x - 1) is negative.
i.e., x - 3 > 0 AND x -1 < 0
i.e., x > 3 AND x < 1
Such a number DOES NOT exist. It is an infeasible solution.
i.e., x - 3 > 0 AND x -1 < 0
i.e., x > 3 AND x < 1
Such a number DOES NOT exist. It is an infeasible solution.
Possibility 2: (x - 3) is negative and (x - 1) is positive.
i.e., x - 3 < 0 AND x - 1 > 0
i.e., x < 3 AND x > 1
Essentially translates to 1 < x < 3 Finite range of values for "x".
i.e., x - 3 < 0 AND x - 1 > 0
i.e., x < 3 AND x > 1
Essentially translates to 1 < x < 3 Finite range of values for "x".
Choice D is the correct answer.
In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects?- a)5%
- b)15%
- c)0%
- d)25%
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects?
a)
5%
b)
15%
c)
0%
d)
25%
e)
None of these
|
|
Avantika Dey answered |
Understanding the Problem
To find the percentage of students who did not enroll in either Math or Economics, we can use the principle of inclusion-exclusion.
Given Data
- Percentage of students enrolled in Math = 40%
- Percentage of students enrolled in Economics = 70%
- Percentage of students enrolled in both subjects = 15%
Applying Inclusion-Exclusion Principle
We can calculate the percentage of students enrolled in at least one of the two subjects using the formula:
\[
\text{Percentage enrolled in either Math or Economics} = P(M) + P(E) - P(M \cap E)
\]
Where:
- \( P(M) \) = Percentage enrolled in Math = 40%
- \( P(E) \) = Percentage enrolled in Economics = 70%
- \( P(M \cap E) \) = Percentage enrolled in both = 15%
Calculation
Substituting the values:
\[
P(M \cup E) = 40\% + 70\% - 15\%
\]
\[
P(M \cup E) = 95\%
\]
Finding Students Not Enrolled in Either Subject
To find the percentage of students who did not enroll in either Math or Economics, we subtract the percentage enrolled in at least one subject from 100%:
\[
\text{Percentage not enrolled in either} = 100\% - P(M \cup E)
\]
\[
\text{Percentage not enrolled in either} = 100\% - 95\% = 5\%
\]
Conclusion
Therefore, the percentage of students who did not enroll for either Math or Economics is **5%**, which corresponds to option 'A'.
To find the percentage of students who did not enroll in either Math or Economics, we can use the principle of inclusion-exclusion.
Given Data
- Percentage of students enrolled in Math = 40%
- Percentage of students enrolled in Economics = 70%
- Percentage of students enrolled in both subjects = 15%
Applying Inclusion-Exclusion Principle
We can calculate the percentage of students enrolled in at least one of the two subjects using the formula:
\[
\text{Percentage enrolled in either Math or Economics} = P(M) + P(E) - P(M \cap E)
\]
Where:
- \( P(M) \) = Percentage enrolled in Math = 40%
- \( P(E) \) = Percentage enrolled in Economics = 70%
- \( P(M \cap E) \) = Percentage enrolled in both = 15%
Calculation
Substituting the values:
\[
P(M \cup E) = 40\% + 70\% - 15\%
\]
\[
P(M \cup E) = 95\%
\]
Finding Students Not Enrolled in Either Subject
To find the percentage of students who did not enroll in either Math or Economics, we subtract the percentage enrolled in at least one subject from 100%:
\[
\text{Percentage not enrolled in either} = 100\% - P(M \cup E)
\]
\[
\text{Percentage not enrolled in either} = 100\% - 95\% = 5\%
\]
Conclusion
Therefore, the percentage of students who did not enroll for either Math or Economics is **5%**, which corresponds to option 'A'.
Direction: Read the following Passage and Answer the following Question.
As urban landscapes continue to expand, the rise of vertical farming is becoming a crucial element in the quest for sustainable city living. Vertical farms, which grow crops in stacked layers within a controlled environment, offer a revolutionary approach to agriculture in urban settings. This innovative method of farming is not just about saving space; it's about reimagining how we produce food in the face of growing environmental challenges.One of the key advantages of vertical farming is its minimal use of water and pesticides. Unlike traditional agriculture, which relies heavily on these resources, vertical farms use hydroponic systems that circulate water efficiently and eliminate the need for soil and large-scale pesticide use. This approach significantly reduces the environmental impact of farming.Another significant benefit is the reduction in food miles. Vertical farms can be established within urban areas, drastically cutting down the distance food travels from farm to consumer. This not only ensures fresher produce but also reduces transportation emissions, contributing to lower carbon footprints.However, vertical farming faces its own set of challenges. The initial setup and operational costs can be high, making it difficult for these farms to compete with traditional agriculture in terms of cost. Additionally, the energy requirements for maintaining controlled environments, such as lighting and temperature control, are substantial. Critics argue that unless renewable energy sources power these farms, they may not be as sustainable as they seem.Despite these challenges, the potential of vertical farming in reshaping urban agriculture remains immense. As technology advances, the efficiency of these farms is expected to improve, making them a vital component in the development of sustainable cities.
Q. Which of the following concerns about vertical farming is mentioned in the passage?- a)It leads to a loss of agricultural biodiversity.
- b)It can only produce a limited range of crops.
- c)It requires a significant amount of energy for controlled environments.
- d)It contributes to urban sprawl.
- e)It depends heavily on chemical fertilizers.
Correct answer is option 'C'. Can you explain this answer?
Direction: Read the following Passage and Answer the following Question.
As urban landscapes continue to expand, the rise of vertical farming is becoming a crucial element in the quest for sustainable city living. Vertical farms, which grow crops in stacked layers within a controlled environment, offer a revolutionary approach to agriculture in urban settings. This innovative method of farming is not just about saving space; it's about reimagining how we produce food in the face of growing environmental challenges.
As urban landscapes continue to expand, the rise of vertical farming is becoming a crucial element in the quest for sustainable city living. Vertical farms, which grow crops in stacked layers within a controlled environment, offer a revolutionary approach to agriculture in urban settings. This innovative method of farming is not just about saving space; it's about reimagining how we produce food in the face of growing environmental challenges.
One of the key advantages of vertical farming is its minimal use of water and pesticides. Unlike traditional agriculture, which relies heavily on these resources, vertical farms use hydroponic systems that circulate water efficiently and eliminate the need for soil and large-scale pesticide use. This approach significantly reduces the environmental impact of farming.
Another significant benefit is the reduction in food miles. Vertical farms can be established within urban areas, drastically cutting down the distance food travels from farm to consumer. This not only ensures fresher produce but also reduces transportation emissions, contributing to lower carbon footprints.
However, vertical farming faces its own set of challenges. The initial setup and operational costs can be high, making it difficult for these farms to compete with traditional agriculture in terms of cost. Additionally, the energy requirements for maintaining controlled environments, such as lighting and temperature control, are substantial. Critics argue that unless renewable energy sources power these farms, they may not be as sustainable as they seem.
Despite these challenges, the potential of vertical farming in reshaping urban agriculture remains immense. As technology advances, the efficiency of these farms is expected to improve, making them a vital component in the development of sustainable cities.
Q. Which of the following concerns about vertical farming is mentioned in the passage?
Q. Which of the following concerns about vertical farming is mentioned in the passage?
a)
It leads to a loss of agricultural biodiversity.
b)
It can only produce a limited range of crops.
c)
It requires a significant amount of energy for controlled environments.
d)
It contributes to urban sprawl.
e)
It depends heavily on chemical fertilizers.
|
|
EduRev GMAT answered |
This is a DETAIL question. The passage mentions that vertical farming requires substantial energy for maintaining controlled environments, such as lighting and temperature control (Choice C). The other concerns listed in the options, such as loss of biodiversity (Choice A), limited crop range (Choice B), contribution to urban sprawl (Choice D), or heavy dependence on chemical fertilizers (Choice E), are not mentioned in the passage.
The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?- a)m + 4
- b)n + 6
- c)n + 3
- d)m + 5
- e)n + 4
Correct answer is option 'E'. Can you explain this answer?
The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?
a)
m + 4
b)
n + 6
c)
n + 3
d)
m + 5
e)
n + 4
|
|
Tanishq Yadav answered |
Understanding the Problem
To find the average of 5 consecutive integers starting with m, we first define these integers:
- m, m+1, m+2, m+3, m+4
The average (n) of these integers can be calculated as:
- Average (n) = (m + (m+1) + (m+2) + (m+3) + (m+4)) / 5
This simplifies to:
- n = (5m + 10) / 5 = m + 2
Finding the Average of 9 Consecutive Integers
Now, we need to find the average of 9 consecutive integers starting with (m + 2):
- The integers are: (m + 2), (m + 3), (m + 4), (m + 5), (m + 6), (m + 7), (m + 8), (m + 9), (m + 10)
The average of these integers is:
- Average = ((m + 2) + (m + 3) + (m + 4) + (m + 5) + (m + 6) + (m + 7) + (m + 8) + (m + 9) + (m + 10)) / 9
This simplifies to:
- Average = (9m + 54) / 9 = m + 6
Relating it to n
Since we previously found that n = m + 2, we can express the average of the 9 integers in terms of n:
- Average = m + 6 = (n - 2) + 6 = n + 4
Conclusion
Thus, the average of the 9 consecutive integers starting with (m + 2) is:
- n + 4
This confirms that the correct answer is option 'E'.
To find the average of 5 consecutive integers starting with m, we first define these integers:
- m, m+1, m+2, m+3, m+4
The average (n) of these integers can be calculated as:
- Average (n) = (m + (m+1) + (m+2) + (m+3) + (m+4)) / 5
This simplifies to:
- n = (5m + 10) / 5 = m + 2
Finding the Average of 9 Consecutive Integers
Now, we need to find the average of 9 consecutive integers starting with (m + 2):
- The integers are: (m + 2), (m + 3), (m + 4), (m + 5), (m + 6), (m + 7), (m + 8), (m + 9), (m + 10)
The average of these integers is:
- Average = ((m + 2) + (m + 3) + (m + 4) + (m + 5) + (m + 6) + (m + 7) + (m + 8) + (m + 9) + (m + 10)) / 9
This simplifies to:
- Average = (9m + 54) / 9 = m + 6
Relating it to n
Since we previously found that n = m + 2, we can express the average of the 9 integers in terms of n:
- Average = m + 6 = (n - 2) + 6 = n + 4
Conclusion
Thus, the average of the 9 consecutive integers starting with (m + 2) is:
- n + 4
This confirms that the correct answer is option 'E'.
If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?- a)25% loss
- b)25% profit
- c)20% loss
- d)20% profit
- e)5% profit
Correct answer is option 'C'. Can you explain this answer?
If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?
a)
25% loss
b)
25% profit
c)
20% loss
d)
20% profit
e)
5% profit
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Athira Choudhury answered |
Understanding Cost Price and Selling Price
To determine the profit or loss percentage, we first need to define the cost price (CP) and selling price (SP) based on the information provided.
Given Values
- Cost price of 20 articles = CP of 20 articles
- Selling price of 25 articles = SP of 25 articles
Calculating Cost Price and Selling Price
Let's assume the cost price of one article is 'x'.
- The total cost price of 20 articles = 20x
Now, let’s denote the selling price of one article as 'y'.
- The total selling price of 25 articles = 25y
According to the problem, these two values are equal:
Equation
20x = 25y
Finding Selling Price in terms of Cost Price
To find the relationship between 'x' and 'y', rearranging gives us:
y = (20/25)x = (4/5)x
This means the selling price of one article is 4/5 of its cost price.
Calculating Profit or Loss
To find the profit or loss:
- Since SP < cp,="" there="" is="" a="">
Loss Calculation
Loss per article = CP - SP
= x - (4/5)x
= (1/5)x
To find the percentage loss:
Percentage Loss
Percentage Loss = (Loss / CP) * 100
= [(1/5)x / x] * 100
= 20%
Conclusion
The merchant incurs a 20% loss on the transaction. Thus, the correct answer is option 'C'.
To determine the profit or loss percentage, we first need to define the cost price (CP) and selling price (SP) based on the information provided.
Given Values
- Cost price of 20 articles = CP of 20 articles
- Selling price of 25 articles = SP of 25 articles
Calculating Cost Price and Selling Price
Let's assume the cost price of one article is 'x'.
- The total cost price of 20 articles = 20x
Now, let’s denote the selling price of one article as 'y'.
- The total selling price of 25 articles = 25y
According to the problem, these two values are equal:
Equation
20x = 25y
Finding Selling Price in terms of Cost Price
To find the relationship between 'x' and 'y', rearranging gives us:
y = (20/25)x = (4/5)x
This means the selling price of one article is 4/5 of its cost price.
Calculating Profit or Loss
To find the profit or loss:
- Since SP < cp,="" there="" is="" a="">
Loss Calculation
Loss per article = CP - SP
= x - (4/5)x
= (1/5)x
To find the percentage loss:
Percentage Loss
Percentage Loss = (Loss / CP) * 100
= [(1/5)x / x] * 100
= 20%
Conclusion
The merchant incurs a 20% loss on the transaction. Thus, the correct answer is option 'C'.
If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?- a)-22.5
- b)16
- c)-10.5
- d)-17.5
- e)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?
a)
-22.5
b)
16
c)
-10.5
d)
-17.5
e)
Cannot be determined
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EduRev GMAT answered |
Approach to solve: If 1.5 is a root of the quadratic equation, substituting x = 1.5 in the equation will satisfy the equation.
The given quadratic equation is x2 + mx + 24 = 0
Substitute x = 1.5 in the above equation because 1.5 is a root of the equation.
(1.5)2 + 1.5m + 24 = 0
2.25 + 1.5m + 24 = 0
1.5m = -26.25 Or m = −26.251.5−26.251.5 = -17.5
Substitute x = 1.5 in the above equation because 1.5 is a root of the equation.
(1.5)2 + 1.5m + 24 = 0
2.25 + 1.5m + 24 = 0
1.5m = -26.25 Or m = −26.251.5−26.251.5 = -17.5
Alternative Method
Step 1: Sum and Product of Roots of Quadratic Equations Theory
For quadratic equations of the form ax2 + bx + c = 0, whose roots are α and β,
Sum of the roots, α + β =
, and product of the roots, αβ = c/a.
From the question stem, we know that one of the roots is 1.5. Let α be 1.5.
Sum of the roots, α + β =
, and product of the roots, αβ = c/a.From the question stem, we know that one of the roots is 1.5. Let α be 1.5.
Step 2: Compute the second root of the equation
Product of the roots of the quadratic equation x2 + mx + 24 = 0 is c/a = (24/1) = 24.
i.e., α * β = 24 where α is 1.5.
1.5 * β = 24
β = (24/1.5)
β = 16
i.e., α * β = 24 where α is 1.5.
1.5 * β = 24
β = (24/1.5)
β = 16
Step 3: Compute the value of ‘m’
In the given equation, m is the co-efficient of the x term.
We know that the sum of the roots of quadratic equations of the form ax2 + bx + c = 0 is −b/a = −m/1 = -m
Sum of the roots = 16 + 1.5 = 17.5
Sum of the roots = -m
If –m = 17.5, the value of m = -17.5
We know that the sum of the roots of quadratic equations of the form ax2 + bx + c = 0 is −b/a = −m/1 = -m
Sum of the roots = 16 + 1.5 = 17.5
Sum of the roots = -m
If –m = 17.5, the value of m = -17.5
Choice D is the correct answer.
Is the positive integer 'x' divisible by 12?Statement 1: x is divisible by 6Statement 2: x is divisible by 8- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
- c)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient
- e)Statements (1) and (2) TOGETHER are NOT sufficient
Correct answer is option 'C'. Can you explain this answer?
Is the positive integer 'x' divisible by 12?
Statement 1: x is divisible by 6
Statement 2: x is divisible by 8
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
c)
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient
e)
Statements (1) and (2) TOGETHER are NOT sufficient
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EduRev GMAT answered |
Step 1: Understand the Question Stem
What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
What is the test of divisibility for 12?
The test of divisibility for 12 is that the number should be divisible by both 3 and 4. Essentially, x should be divisible by 3 and 22.
The test of divisibility for 12 is that the number should be divisible by both 3 and 4. Essentially, x should be divisible by 3 and 22.
Step 2: Evaluate Statement (1) ALONE: x is divisible by 6
Approach: Look for a counter example
Example: x = 6. It is divisible by 6. However, it is NOT divisible by 12.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.
If x is divisible by 6, we can infer that it is divisible by 3 and 2. But we cannot deduce whether it is also divisible by 22 - which is essential to deduce that x is divisible by 12.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Step 3: Evaluate Statement (2) ALONE: x is divisible by 8
If x is divisible by 8, then x will definitely be divisible by 4.
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example
Example: x = 8. It is divisible by 8. However, it is NOT divisible by 12.
Counter Example:x = 24. It is divisible by 8. It is divisible by 12 as well.
Knowing that x is divisible by 8 is not enough to answer the question.
Counter Example:x = 24. It is divisible by 8. It is divisible by 12 as well.
Knowing that x is divisible by 8 is not enough to answer the question.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Eliminate choice B. Choices narrow down to C or E.
Step 4: Evaluate Statements (1) & (2) Together: x is divisible by 6 & x is divisible by 8
From statement 1, if x is divisible by 6, it is definitely divisible by 3.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.
Statement TOGETHER are sufficient. Choice C is the answer.
Direction: Read the following Passage and Answer the following Question.
As an instrument of intellectual culture, the study of Physics is profitable to all; as bearing upon special functions, its value, though not so great, is still more tangible. Why, for example, should Members of Parliament be ignorant of the subjects concerning which they are called upon to legislate? In this land of practical physics, why should they be unable to form an independent opinion upon a physical question? Why should the member of a parliamentary committee be left at the mercy of interested disputants when a scientific question is discussed, until he deems the nap a blessing which rescues him from the bewilderments of the committee-room? The education which does not supply the want here referred to, fails in its duty to England.With regard to our working people, in the ordinary sense of the term ‘working’, the study of Physics would, I imagine, be profitable, not only as a means of intellectual culture, but also as a moral influence to woo them from pursuits which now degrade them. A man's reformation oftener depends upon the indirect, than upon the direct action of the will. The will must be exerted in the choice of employment which shall break the force of temptation by erecting a barrier against it. The drunkard, for example, is in a perilous condition if he contents himself merely with saying, or swearing, that he will avoid strong drink. His thoughts, if not attracted by another force, will revert to the public-house, and to rescue him permanently from this, you must give him an equivalent. By investing the objects of hourly intercourse with an interest which prompts reflection, new enjoyments would be opened to the working man, and every one of these would be a point of force to protect him against temptation.Q. Which of the following does the author suggest in the passage about the Members of Parliament?- a)They do not have any knowledge of Physics
- b)They cannot be asked to legislate on matters that they are ignorant of
- c)They prefer taking a nap to legislating on issues that they don't know much about
- d)It is not a prerequisite that they legislate only on those matters that they have adequate knowledge of
- e)They sometimes allow their personal interests to override the broader good of the people at large
Correct answer is option 'D'. Can you explain this answer?
Direction: Read the following Passage and Answer the following Question.
As an instrument of intellectual culture, the study of Physics is profitable to all; as bearing upon special functions, its value, though not so great, is still more tangible. Why, for example, should Members of Parliament be ignorant of the subjects concerning which they are called upon to legislate? In this land of practical physics, why should they be unable to form an independent opinion upon a physical question? Why should the member of a parliamentary committee be left at the mercy of interested disputants when a scientific question is discussed, until he deems the nap a blessing which rescues him from the bewilderments of the committee-room? The education which does not supply the want here referred to, fails in its duty to England.
As an instrument of intellectual culture, the study of Physics is profitable to all; as bearing upon special functions, its value, though not so great, is still more tangible. Why, for example, should Members of Parliament be ignorant of the subjects concerning which they are called upon to legislate? In this land of practical physics, why should they be unable to form an independent opinion upon a physical question? Why should the member of a parliamentary committee be left at the mercy of interested disputants when a scientific question is discussed, until he deems the nap a blessing which rescues him from the bewilderments of the committee-room? The education which does not supply the want here referred to, fails in its duty to England.
With regard to our working people, in the ordinary sense of the term ‘working’, the study of Physics would, I imagine, be profitable, not only as a means of intellectual culture, but also as a moral influence to woo them from pursuits which now degrade them. A man's reformation oftener depends upon the indirect, than upon the direct action of the will. The will must be exerted in the choice of employment which shall break the force of temptation by erecting a barrier against it. The drunkard, for example, is in a perilous condition if he contents himself merely with saying, or swearing, that he will avoid strong drink. His thoughts, if not attracted by another force, will revert to the public-house, and to rescue him permanently from this, you must give him an equivalent. By investing the objects of hourly intercourse with an interest which prompts reflection, new enjoyments would be opened to the working man, and every one of these would be a point of force to protect him against temptation.
Q. Which of the following does the author suggest in the passage about the Members of Parliament?
a)
They do not have any knowledge of Physics
b)
They cannot be asked to legislate on matters that they are ignorant of
c)
They prefer taking a nap to legislating on issues that they don't know much about
d)
It is not a prerequisite that they legislate only on those matters that they have adequate knowledge of
e)
They sometimes allow their personal interests to override the broader good of the people at large
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EduRev GMAT answered |
The opening para clearly states that Members of Parliament are at times called upon to legislate on matters that they are ignorant of. Thus it is not a prerequisite that they have to be knowledgeable about the matter on which they are legislating i.e. (D) should be the correct answer
A: Extreme. It's true that some of them are ignorant of physics but this cannot be generalised to the entire group
B: Opposite as explained above
C: No such preference is mentioned in the passage
E: While this may be true in the real world, there is nothing in the passage to suggest the same
A: Extreme. It's true that some of them are ignorant of physics but this cannot be generalised to the entire group
B: Opposite as explained above
C: No such preference is mentioned in the passage
E: While this may be true in the real world, there is nothing in the passage to suggest the same
All English Springer Spaniels have long hair. All Rottweilers have short hair. Each of Tina's dogs is a cross between an English Springer Spaniel and a Rottweiler. Therefore, Tina's dogs have medium-length hair.Q. Which one of the following uses flawed reasoning that most closely resembles the flawed reasoning used in the argument above?- a)All typists who practice at least one hour per day can type one hundred words per minute. But some typists who do not practice can also type one hundred words per minute. Mike, a typist, practices thirty minutes per day. Therefore, Mike types fifty words per minute.
- b)All economists know linear algebra. All physicists know relativistic mechanics. Wilma is both an economist and a physicist. Therefore, Wilma knows both linear algebra and relativistic mechanics.
- c)All halogen gases are toxic to humans. All non-radioactive noble gases are non-toxic to humans. "Nobagen" gas is a mixture of a halogen gas and a noble gas. Therefore, "nobagen" gas is moderately toxic to humans.
- d)All players on the Wildcats have brown hair. All players on the Razorbacks have red hair. Members of the Moye family are on both the Wildcats and the Razorbacks. Therefore, some members of the Moye family have brown hair and others have red hair.
- e)All cars made by Chord are very well made. All cars made by Fysler are very poorly made. Half of the cars on Jim's lot are very well made and the other half are very poorly made. Therefore, half of the cars on Jim's lot are Chords and half are Fyslers.
Correct answer is option 'C'. Can you explain this answer?
All English Springer Spaniels have long hair. All Rottweilers have short hair. Each of Tina's dogs is a cross between an English Springer Spaniel and a Rottweiler. Therefore, Tina's dogs have medium-length hair.
Q. Which one of the following uses flawed reasoning that most closely resembles the flawed reasoning used in the argument above?
a)
All typists who practice at least one hour per day can type one hundred words per minute. But some typists who do not practice can also type one hundred words per minute. Mike, a typist, practices thirty minutes per day. Therefore, Mike types fifty words per minute.
b)
All economists know linear algebra. All physicists know relativistic mechanics. Wilma is both an economist and a physicist. Therefore, Wilma knows both linear algebra and relativistic mechanics.
c)
All halogen gases are toxic to humans. All non-radioactive noble gases are non-toxic to humans. "Nobagen" gas is a mixture of a halogen gas and a noble gas. Therefore, "nobagen" gas is moderately toxic to humans.
d)
All players on the Wildcats have brown hair. All players on the Razorbacks have red hair. Members of the Moye family are on both the Wildcats and the Razorbacks. Therefore, some members of the Moye family have brown hair and others have red hair.
e)
All cars made by Chord are very well made. All cars made by Fysler are very poorly made. Half of the cars on Jim's lot are very well made and the other half are very poorly made. Therefore, half of the cars on Jim's lot are Chords and half are Fyslers.
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EduRev GMAT answered |
The flawed reasoning used in the passage is that a combination of two "parent" items with different attributes necessarily yields a "child" product having attributes that are averages of its parents' attributes. The correct answer uses parallel reasoning inasmuch as the argument uses the fact that halogen and noble gases differ with respect to toxicity to conclude that a combination of such gases would yield a gas having toxicity that is the average of the toxicity of its "parent" gases.
Business School Dean: We are all in agreement that we must cut unnecessary costs in order to afford our popular international study programs, a hallmark of our unique offering that prospective students know us for. But cutting the marketing budget would be a terrible idea; after all, our unique international programs cannot attract prospective students if we do not properly market them.Q. The portions highlighted in underlined play which of the following roles?- a)The first is a conclusion that the dean supports; the second is evidence for that conclusion.
- b)The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion.
- c)The first is a consideration that supports the dean’s conclusion; the second is that conclusion.
- d)The first is a conclusion that the dean opposes; the second is a conclusion that the dean supports.
- e)The first is a consideration that the dean agrees with; the second is the dean’s conclusion.
Correct answer is option 'B'. Can you explain this answer?
Business School Dean: We are all in agreement that we must cut unnecessary costs in order to afford our popular international study programs, a hallmark of our unique offering that prospective students know us for. But cutting the marketing budget would be a terrible idea; after all, our unique international programs cannot attract prospective students if we do not properly market them.
Q. The portions highlighted in underlined play which of the following roles?
a)
The first is a conclusion that the dean supports; the second is evidence for that conclusion.
b)
The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion.
c)
The first is a consideration that supports the dean’s conclusion; the second is that conclusion.
d)
The first is a conclusion that the dean opposes; the second is a conclusion that the dean supports.
e)
The first is a consideration that the dean agrees with; the second is the dean’s conclusion.
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EduRev GMAT answered |
As you assess the argument and scan the answer choices, it should become clear that you will need to determine the dean's conclusion. A few things are important in finding that: 1) note the word "but" to begin the second sentence. Transition language like that often signifies that the author is transitioning between contextual information and her main point, so you should pay even closer attention past "but" to find the conclusion there. 2) Remember the "why test" - in order to be a conclusion, a statement must be backed up with a reason "why" it's true somewhere else in the argument.
Note that the non-underlined initial clause of that sentence "cutting the marketing budget would be a terrible idea" does have a reason why: because if you did that, students wouldn't know about these great programs. The underlined portion does not have a reason why: "our unique programs cannot attract students if we do not properly market them" is given as a fact without the rest of the argument explaining why.
From that, you should see that the second underlined portion exists to support the author's conclusion. This will narrow you down to choices "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion." and "The first is a conclusion that the dean supports; the second is evidence for that conclusion.".
From there, play the answers against each other. "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion." says that the second portion is used to support the dean's conclusion, while "The first is a conclusion that the dean supports; the second is evidence for that conclusion." says that it's evidence for "that conclusion," meaning the first underlined portion. "our unique programs cannot attract students if we do not properly market them" does support the conclusion that cutting marketing would be a bad idea (choice "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion.") but it doesn't support the idea that "we should cut unnecessary costs" (choice "The first is a conclusion that the dean supports; the second is evidence for that conclusion."). So the correct answer is "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion.".
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.- a)25 days
- b)30 days
- c)60 days
- d)65 days
- e)36 days
Correct answer is option 'C'. Can you explain this answer?
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose.
a)
25 days
b)
30 days
c)
60 days
d)
65 days
e)
36 days
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Ameya Yadav answered |
Given information:
- Jose and Jane can complete a task together in 20 days
- Jose completes half the work alone in x days
- Jane completes the second half of the work alone in y days
- When Jose and Jane work separately, the task is completed in 45 days
Calculating individual work rates:
Let's assume the total work is represented by 1 unit.
- Together, Jose and Jane's work rate = 1/20
- Jose's work rate = 1/x (completing half the work)
- Jane's work rate = 1/y (completing the second half)
Formulating equations:
- When working together: 1/20 = 1/x + 1/y
- When working separately: Jose's work (1/2) + Jane's work (1/2) = 45 days
Solving the equations:
Given that Jane is more efficient than Jose, we can assume that Jane's work rate is faster. Since Jane completes the second half of the work, she should take less time than Jose to complete the same amount of work.
- From the equation 1/20 = 1/x + 1/y, we know that 1/x + 1/y is less than 1/20 (as Jane is more efficient)
- Therefore, when Jose completes half the work alone, it takes him longer than 20 days
- Hence, Jose will take 60 days to complete the task alone (option c)
Therefore, Jose will take 60 days to complete the task if he worked alone.
- Jose and Jane can complete a task together in 20 days
- Jose completes half the work alone in x days
- Jane completes the second half of the work alone in y days
- When Jose and Jane work separately, the task is completed in 45 days
Calculating individual work rates:
Let's assume the total work is represented by 1 unit.
- Together, Jose and Jane's work rate = 1/20
- Jose's work rate = 1/x (completing half the work)
- Jane's work rate = 1/y (completing the second half)
Formulating equations:
- When working together: 1/20 = 1/x + 1/y
- When working separately: Jose's work (1/2) + Jane's work (1/2) = 45 days
Solving the equations:
Given that Jane is more efficient than Jose, we can assume that Jane's work rate is faster. Since Jane completes the second half of the work, she should take less time than Jose to complete the same amount of work.
- From the equation 1/20 = 1/x + 1/y, we know that 1/x + 1/y is less than 1/20 (as Jane is more efficient)
- Therefore, when Jose completes half the work alone, it takes him longer than 20 days
- Hence, Jose will take 60 days to complete the task alone (option c)
Therefore, Jose will take 60 days to complete the task if he worked alone.
If a and b are positive integers, is (a + b) prime?
Statement 1: 13a = 43b
Statement 2: 8a = 15b- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
- c)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient
- e)Statements (1) and (2) TOGETHER are NOT sufficient
Correct answer is option 'A'. Can you explain this answer?
If a and b are positive integers, is (a + b) prime?
Statement 1: 13a = 43b
Statement 2: 8a = 15b
Statement 1: 13a = 43b
Statement 2: 8a = 15b
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
c)
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient
e)
Statements (1) and (2) TOGETHER are NOT sufficient
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Talent Skill Learning answered |
Step 1: Evaluate Statement 1 ALONE
Statement 1: 13a = 43b
a/b = 43/13
a : b :: 43 : 13
So, a = 43x and b = 13x
a + b = 43x + 13x = 56x
56 is not prime. Therefore, 56x cannot be prime.
We are able to answer the question with a DEFNITE NO.
Hence, statement 1 alone is sufficient.
Eliminate answer option B, C, and E.
Statement 1: 13a = 43b
a/b = 43/13
a : b :: 43 : 13
So, a = 43x and b = 13x
a + b = 43x + 13x = 56x
56 is not prime. Therefore, 56x cannot be prime.
We are able to answer the question with a DEFNITE NO.
Hence, statement 1 alone is sufficient.
Eliminate answer option B, C, and E.
Step 2: Evaluate Statement 2 ALONE
Statement 2: 8a = 15b
a/b = 15/8
a : b :: 15 : 8
So, a = 15x and b = 8x
a + b = 15x + 8x = 23x
23 is prime.
If x is 1, a + b will be prime. For other values of x, a + b will not be prime.
We are not able to answer the question with a DEFNITE Yes or No.
Hence, statement 2 alone is not sufficient.
Eliminate answer option D.
Statement 1 alone is sufficient. Statement 2 is NOT sufficient.
Choice A is the correct answer.
Statement 2: 8a = 15b
a/b = 15/8
a : b :: 15 : 8
So, a = 15x and b = 8x
a + b = 15x + 8x = 23x
23 is prime.
If x is 1, a + b will be prime. For other values of x, a + b will not be prime.
We are not able to answer the question with a DEFNITE Yes or No.
Hence, statement 2 alone is not sufficient.
Eliminate answer option D.
Statement 1 alone is sufficient. Statement 2 is NOT sufficient.
Choice A is the correct answer.
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?- a)50
- b)52
- c)49
- d)48
- e)44
Correct answer is option 'D'. Can you explain this answer?
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
a)
50
b)
52
c)
49
d)
48
e)
44
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EduRev GMAT answered |
The average of 5 positive integers is 40. i.e., the sum of these integers = 5 × 40 = 200
Let the least of these 5 numbers be x.
Because the range of the set is 10, the largest of these 5 numbers will be x + 10.
Because the range of the set is 10, the largest of these 5 numbers will be x + 10.
If we have to maximize the largest of these numbers, we have to minimize all the other numbers.
That is 4 of these numbers are all at the least value possible = x.
That is 4 of these numbers are all at the least value possible = x.
So, x + x + x + x + x + 10 = 200
Or x = 38.
So, the maximum value possible for the largest of these 5 integers is 48.
Or x = 38.
So, the maximum value possible for the largest of these 5 integers is 48.
Choice D is the correct answer.
PassageMost educated people of the eighteenth century, such as the Founding Fathers, subscribed to Natural Rights Theory, the idea that every human being has a considerable number of innate rights, simply by virtue of being a human person. When the US Constitution was sent to the states for ratification, many at that time felt that the federal government outlined by the Constitution would be too strong, and that rights of individual citizens against the government had to be clarified. This led to the Bill of Rights, the first ten amendments, which were ratified at the same time as the Constitution. The first eight of these amendments list specific rights of citizens. Some leaders feared that listing some rights could be interpreted to mean that citizens didn’t have other, unlisted rights. Toward this end, James Madison and others produced the Ninth Amendment, which states: the fact that certain rights are listed in the Constitution shall not be construed to imply that other rights of the people are deniedConstitutional traditionalists interpret the Ninth Amendment as a rule for reading the rest of the constitution. They would argue that “Ninth Amendment rights” are a misconceived notion: the amendment does not, by itself, create federally enforceable rights. In particular, this strict reasoning would be opposed to the creation of any new rights based on the amendment. Rather, according to this view, the amendment merely protects those rights that citizens already have, whether they are explicitly listed in the Constitution or simply implicit in people’s lives and in American tradition.More liberal interpreters of the US Constitution have a much more expansive view of the Ninth Amendment. In their view, the Ninth Amendment guarantees to American citizens a vast universe of potential rights, some of which we have enjoyed for two centuries, and others that the Founding Fathers could not possibly have conceived. These scholars point out that some rights, such as voting rights of women or minorities, were not necessarily viewed as rights by the majority of citizens in late eighteenth century America, but are taken as fundamental and unquestionable in modern America. While those rights cited are protected specifically by other amendments and laws, the argument asserts that other unlisted right also could evolve from unthinkable to perfectly acceptable, and the Ninth Amendment would protect these as-yet-undefined rights.Q. The author cites the scholars referring to “voting rights of women or minorities” in order to- a)cite unquestionably justified Ninth Amendment rights
- b)demonstrate how changing priorities can alter perspectives on fundamental human rights
- c)argue for the modern extension of Natural Rights Theory
- d)refute the traditionalist interpretation of the Ninth Amendment
- e)champion the rights of all citizens in the democratic process
Correct answer is option 'B'. Can you explain this answer?
Passage
Most educated people of the eighteenth century, such as the Founding Fathers, subscribed to Natural Rights Theory, the idea that every human being has a considerable number of innate rights, simply by virtue of being a human person. When the US Constitution was sent to the states for ratification, many at that time felt that the federal government outlined by the Constitution would be too strong, and that rights of individual citizens against the government had to be clarified. This led to the Bill of Rights, the first ten amendments, which were ratified at the same time as the Constitution. The first eight of these amendments list specific rights of citizens. Some leaders feared that listing some rights could be interpreted to mean that citizens didn’t have other, unlisted rights. Toward this end, James Madison and others produced the Ninth Amendment, which states: the fact that certain rights are listed in the Constitution shall not be construed to imply that other rights of the people are denied
Constitutional traditionalists interpret the Ninth Amendment as a rule for reading the rest of the constitution. They would argue that “Ninth Amendment rights” are a misconceived notion: the amendment does not, by itself, create federally enforceable rights. In particular, this strict reasoning would be opposed to the creation of any new rights based on the amendment. Rather, according to this view, the amendment merely protects those rights that citizens already have, whether they are explicitly listed in the Constitution or simply implicit in people’s lives and in American tradition.
More liberal interpreters of the US Constitution have a much more expansive view of the Ninth Amendment. In their view, the Ninth Amendment guarantees to American citizens a vast universe of potential rights, some of which we have enjoyed for two centuries, and others that the Founding Fathers could not possibly have conceived. These scholars point out that some rights, such as voting rights of women or minorities, were not necessarily viewed as rights by the majority of citizens in late eighteenth century America, but are taken as fundamental and unquestionable in modern America. While those rights cited are protected specifically by other amendments and laws, the argument asserts that other unlisted right also could evolve from unthinkable to perfectly acceptable, and the Ninth Amendment would protect these as-yet-undefined rights.
Q. The author cites the scholars referring to “voting rights of women or minorities” in order to
a)
cite unquestionably justified Ninth Amendment rights
b)
demonstrate how changing priorities can alter perspectives on fundamental human rights
c)
argue for the modern extension of Natural Rights Theory
d)
refute the traditionalist interpretation of the Ninth Amendment
e)
champion the rights of all citizens in the democratic process
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Manasa Kulkarni answered |
Explanation:
Changing Perspectives on Fundamental Human Rights:
- The scholars refer to the voting rights of women and minorities to demonstrate how societal priorities and perspectives on fundamental human rights can change over time.
- In the late eighteenth century, these rights were not necessarily viewed as essential by the majority of citizens, but they are now considered fundamental and unquestionable in modern America.
Expansive View of the Ninth Amendment:
- The scholars who have a more liberal interpretation of the US Constitution believe that the Ninth Amendment guarantees American citizens a vast universe of potential rights.
- They argue that some rights, like the voting rights of women and minorities, were not initially recognized but have evolved over time to be considered fundamental rights.
- This perspective supports the idea that the Ninth Amendment protects not just explicitly listed rights but also those that may emerge and evolve in society.
Protection of Unlisted Rights:
- The Ninth Amendment is seen as a safeguard for rights that are not explicitly mentioned in the Constitution but are inherent in people's lives and American tradition.
- It is believed to protect the potential for new rights to be recognized and upheld, based on changing societal norms and values.
- This interpretation allows for the adaptation of the Constitution to reflect evolving understandings of human rights and freedoms.
Changing Perspectives on Fundamental Human Rights:
- The scholars refer to the voting rights of women and minorities to demonstrate how societal priorities and perspectives on fundamental human rights can change over time.
- In the late eighteenth century, these rights were not necessarily viewed as essential by the majority of citizens, but they are now considered fundamental and unquestionable in modern America.
Expansive View of the Ninth Amendment:
- The scholars who have a more liberal interpretation of the US Constitution believe that the Ninth Amendment guarantees American citizens a vast universe of potential rights.
- They argue that some rights, like the voting rights of women and minorities, were not initially recognized but have evolved over time to be considered fundamental rights.
- This perspective supports the idea that the Ninth Amendment protects not just explicitly listed rights but also those that may emerge and evolve in society.
Protection of Unlisted Rights:
- The Ninth Amendment is seen as a safeguard for rights that are not explicitly mentioned in the Constitution but are inherent in people's lives and American tradition.
- It is believed to protect the potential for new rights to be recognized and upheld, based on changing societal norms and values.
- This interpretation allows for the adaptation of the Constitution to reflect evolving understandings of human rights and freedoms.
Jake invests $5000 at 10% simple annual interest and another amount of money at x percent simple interest. What amount of money did Jake invests at x percent interest?(1) The total amount of interest earned on all investments at the end of one year is $800.(2) x = 6%.- a)Statements (1) and (2) TOGETHER are not sufficient.
- b)Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
- c)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)Each Statement ALONE is sufficient.
- e)Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Correct answer is option 'C'. Can you explain this answer?
Jake invests $5000 at 10% simple annual interest and another amount of money at x percent simple interest. What amount of money did Jake invests at x percent interest?
(1) The total amount of interest earned on all investments at the end of one year is $800.
(2) x = 6%.
a)
Statements (1) and (2) TOGETHER are not sufficient.
b)
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
c)
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
Each Statement ALONE is sufficient.
e)
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
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EduRev GMAT answered |
(1) The total amount of interest earned on all investments at the end of one year is $800.
Let A be the amount of money invested at x percent. The total interest earned on both investments is:
We cannot calculate A because x is also unknown. Statement (1) Alone is not sufficient then.
(2) x = 6%
Statement (2) Alone is not sufficient.
Combining both statements, we have:
Both Statements together are sufficient but neither statement alone is sufficient.
Both Statements together are sufficient but neither statement alone is sufficient.
PassageMeasuring more than five feet tall and ten feet long, the Javan rhinoceros is often called the rarest large mammal on earth. None exist in zoos. Like the Indian rhino, the Javan has only one horn; African and Sumatran rhinos have two. While the Javan rhino habitat once extended across southern Asia, now there are fewer than one hundred of the animals in Indonesia and under a dozen in Vietnam. Very little is known about Javan rhinos because they lead secretive and solitary lives in remote jungles. Until recently, scientists debated whether females even have horns, and most scientific work has had to rely on DNA garnered from dung. The near extinction of the Javan rhino is the direct result of human actions. For centuries, farmers, who favored the same habitat, viewed them as crop eating pests and shot them on sight. During the colonial period, hunters slaughtered thousands. Now, human efforts to save them may well prove futile. The Vietnamese herd is probably doomed, as too few remain to maintain the necessary genetic variation. Rhinos from Java cannot supplement the Vietnamese numbers because in the millions of years since Indonesia separated from the mainland, the two groups have evolved into separate sub-species. In Indonesia, the rhinos are protected on the Ujung Kulon peninsula, which is unsettled by humans, and still have sufficient genetic diversity to have a chance at survival. Ironically, however, the lack of human disturbance allows mature forests to replace the shrubby vegetation the animals prefer. Thus, human benevolence may prove little better for these rhinos than past human maltreatment.Q. Which of the following can be inferred from the passage?- a)Javan rhinos are one of the most endangered animals on the planet.
- b)More is known about the genetics of the Javan rhino than is known about its mating patterns.
- c)Hunters killed more Javan rhinos in Vietnam than in Indonesia.
- d)Most animal extinctions are the result of human actions.
- e)Genetic diversity is the most important factor for the survival of a species.
Correct answer is option 'B'. Can you explain this answer?
Passage
Measuring more than five feet tall and ten feet long, the Javan rhinoceros is often called the rarest large mammal on earth. None exist in zoos. Like the Indian rhino, the Javan has only one horn; African and Sumatran rhinos have two. While the Javan rhino habitat once extended across southern Asia, now there are fewer than one hundred of the animals in Indonesia and under a dozen in Vietnam. Very little is known about Javan rhinos because they lead secretive and solitary lives in remote jungles. Until recently, scientists debated whether females even have horns, and most scientific work has had to rely on DNA garnered from dung.
The near extinction of the Javan rhino is the direct result of human actions. For centuries, farmers, who favored the same habitat, viewed them as crop eating pests and shot them on sight. During the colonial period, hunters slaughtered thousands. Now, human efforts to save them may well prove futile. The Vietnamese herd is probably doomed, as too few remain to maintain the necessary genetic variation. Rhinos from Java cannot supplement the Vietnamese numbers because in the millions of years since Indonesia separated from the mainland, the two groups have evolved into separate sub-species. In Indonesia, the rhinos are protected on the Ujung Kulon peninsula, which is unsettled by humans, and still have sufficient genetic diversity to have a chance at survival. Ironically, however, the lack of human disturbance allows mature forests to replace the shrubby vegetation the animals prefer. Thus, human benevolence may prove little better for these rhinos than past human maltreatment.
Q. Which of the following can be inferred from the passage?
a)
Javan rhinos are one of the most endangered animals on the planet.
b)
More is known about the genetics of the Javan rhino than is known about its mating patterns.
c)
Hunters killed more Javan rhinos in Vietnam than in Indonesia.
d)
Most animal extinctions are the result of human actions.
e)
Genetic diversity is the most important factor for the survival of a species.
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Avantika Sengupta answered |
Explanation:
More is known about the genetics of the Javan rhino than is known about its mating patterns.
- The passage mentions that very little is known about Javan rhinos due to their secretive and solitary nature in remote jungles.
- Scientists have debated whether females even have horns, and most scientific work has had to rely on DNA garnered from dung.
- This indicates that there is more information available about the genetics of the Javan rhino (through DNA analysis) compared to their mating patterns or other behaviors.
Therefore, the correct answer is option B: More is known about the genetics of the Javan rhino than is known about its mating patterns.
More is known about the genetics of the Javan rhino than is known about its mating patterns.
- The passage mentions that very little is known about Javan rhinos due to their secretive and solitary nature in remote jungles.
- Scientists have debated whether females even have horns, and most scientific work has had to rely on DNA garnered from dung.
- This indicates that there is more information available about the genetics of the Javan rhino (through DNA analysis) compared to their mating patterns or other behaviors.
Therefore, the correct answer is option B: More is known about the genetics of the Javan rhino than is known about its mating patterns.
French cuisine is famous for its frequent and liberal use of cream and cheese, both high in saturated fat. For years, medical studies have shown the strong correlation between diets high in saturated fat and coronary heart disease, and yet, France has a much lower incidence of such disease than found in comparable countries like the United States. This is the so-called French Paradox.Q. Which of the following, if true, helps to explain the French Paradox?- a)Certain kinds of cheese can have as much as five times the amount of saturated fat that cream has.
- b)People in the United States, per capita, eat almost the same amount of saturated fat on average as do people in France.
- c)The United States imports more cheese from France than from any other country.
- d)Red wine, typically served with French food, helps to clean the buildup of fats in the arteries, reducing the risk of heart disease.
- e)It is typically for a French person to have either cream or cheese at each of the three meals in a day.
Correct answer is option 'D'. Can you explain this answer?
French cuisine is famous for its frequent and liberal use of cream and cheese, both high in saturated fat. For years, medical studies have shown the strong correlation between diets high in saturated fat and coronary heart disease, and yet, France has a much lower incidence of such disease than found in comparable countries like the United States. This is the so-called French Paradox.
Q. Which of the following, if true, helps to explain the French Paradox?
a)
Certain kinds of cheese can have as much as five times the amount of saturated fat that cream has.
b)
People in the United States, per capita, eat almost the same amount of saturated fat on average as do people in France.
c)
The United States imports more cheese from France than from any other country.
d)
Red wine, typically served with French food, helps to clean the buildup of fats in the arteries, reducing the risk of heart disease.
e)
It is typically for a French person to have either cream or cheese at each of the three meals in a day.
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EduRev GMAT answered |
Both (B) and (E) make the paradox harder to explain. Answers (A) and (C) are off-the-wall irrelevant. Choice (A) says that cheese has more fat then cream, but the French are eating both of those, so it doesn’t matter: either way, the French are eating high fat food. (C) changes the topic to imports, which is completely unrelated to the direct relationship of diet and epidemiology.
Only (D) resolves the paradox. Since the French drink red wine, which in moderation cleans the arteries, this explains how they could eat high fat foods and have a much lower risk of heart disease
Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?- a)$2000
- b)$6000
- c)$4000
- d)$1333
- e)$3000
Correct answer is option 'E'. Can you explain this answer?
Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?
a)
$2000
b)
$6000
c)
$4000
d)
$1333
e)
$3000
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EduRev GMAT answered |
Step 1: Deduce profit for Effort and Investments
Total profit earned will be divided into two parts: 1/3 will be for efforts and 2/3 for investments made.
Mary and Mike get equal share for their efforts.
If x is the share that each of Mike and Mary get for efforts, 2x is the share of profit for total efforts.
1/3 of total profit goes toward effort.
Hence, the total profit earned will be 6x.
Total profit earned will be divided into two parts: 1/3 will be for efforts and 2/3 for investments made.
Mary and Mike get equal share for their efforts.
If x is the share that each of Mike and Mary get for efforts, 2x is the share of profit for total efforts.
1/3 of total profit goes toward effort.
Hence, the total profit earned will be 6x.
Step 2: Share of profit for investments made
4x is the profit to be distributed for investments made.
4x will be divided in the ratio of amount invested by Mary and Mike.
As Mary and Mike invested $700 and $300 respectively, share of profit on investments will be divided in the ratio 7 : 3
Hence, if Mary receives 7y, Mike will receive 3y.
Total profit on investments is 10y which is equal to 4x
10y = 4x ... (1)
4x will be divided in the ratio of amount invested by Mary and Mike.
As Mary and Mike invested $700 and $300 respectively, share of profit on investments will be divided in the ratio 7 : 3
Hence, if Mary receives 7y, Mike will receive 3y.
Total profit on investments is 10y which is equal to 4x
10y = 4x ... (1)
Step 3: Compute total profit earned
Difference between amount shared between Mike and Mary is $800.
7y − 3y = 800
y = $200
Total profits on investment 10y = 2000
From equation 1, 10y = 4x
So, x = 2000/4 = $500
Total profit earned 6x = $3000
7y − 3y = 800
y = $200
Total profits on investment 10y = 2000
From equation 1, 10y = 4x
So, x = 2000/4 = $500
Total profit earned 6x = $3000
How is PRODUCT written in that code language?I. In a certain code language, AIEEE is written as BJFFF.II. In a certain code language, GYPSY is written as FXORX- a)If data in the statement I alone is sufficient to answer the question.
- b)If data in the statement II alone is sufficient to answer the question.
- c)If data either in the statement I alone or statement II alone are sufficient to answer the question.
- d)If data given in both I & II together are not sufficient to answer the question.
- e)If data in both statements I & II together are necessary to answer the question.
Correct answer is option 'E'. Can you explain this answer?
How is PRODUCT written in that code language?
I. In a certain code language, AIEEE is written as BJFFF.
II. In a certain code language, GYPSY is written as FXORX
a)
If data in the statement I alone is sufficient to answer the question.
b)
If data in the statement II alone is sufficient to answer the question.
c)
If data either in the statement I alone or statement II alone are sufficient to answer the question.
d)
If data given in both I & II together are not sufficient to answer the question.
e)
If data in both statements I & II together are necessary to answer the question.
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Talent Skill Learning answered |
From I: All vowels are coded as next alphabets
From II: All consonants are coded as previous alphabets
So from both the statements.
From II: All consonants are coded as previous alphabets
So from both the statements.
Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump Z, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?- a)6
- b)12
- c)15
- d)18
- e)24
Correct answer is option 'B'. Can you explain this answer?
Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump Z, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
a)
6
b)
12
c)
15
d)
18
e)
24
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Avantika Dey answered |
Let's break down the information provided in the question:
- Pump X pumped out 1/4 of the water in the tank in 2 hours
- Pumps Y and Z, along with Pump X, pumped out the remaining water in 3 hours
- Pump Y alone would have taken 18 hours to pump out the remaining water
We need to find out how long it would take Pump Z to pump out all the water from the tank. Let's calculate the rates of each pump:
- Pump X's rate = 1/4 of the tank in 2 hours = 1/8 of the tank per hour
- Pumps X, Y, and Z combined rate = 3/4 of the tank in 3 hours = 1/4 of the tank per hour
- Pump Y's rate = 1/4 of the tank in 18 hours = 1/72 of the tank per hour
Now, we can find Pump Z's rate by subtracting Pump Y's rate from the combined rate:
Pump Z's rate = Combined rate - Pump Y's rate
Pump Z's rate = 1/4 - 1/72 = 17/72 of the tank per hour
To find out how long Pump Z would take to pump out all the water, we need to divide the total tank capacity by Pump Z's rate:
Time taken by Pump Z = 1 / (17/72) = 72/17 ≈ 4.24 hours
Therefore, Pump Z would take approximately 4.24 hours to pump out all of the water from the tank, which is closest to option B (12 hours).
- Pump X pumped out 1/4 of the water in the tank in 2 hours
- Pumps Y and Z, along with Pump X, pumped out the remaining water in 3 hours
- Pump Y alone would have taken 18 hours to pump out the remaining water
We need to find out how long it would take Pump Z to pump out all the water from the tank. Let's calculate the rates of each pump:
- Pump X's rate = 1/4 of the tank in 2 hours = 1/8 of the tank per hour
- Pumps X, Y, and Z combined rate = 3/4 of the tank in 3 hours = 1/4 of the tank per hour
- Pump Y's rate = 1/4 of the tank in 18 hours = 1/72 of the tank per hour
Now, we can find Pump Z's rate by subtracting Pump Y's rate from the combined rate:
Pump Z's rate = Combined rate - Pump Y's rate
Pump Z's rate = 1/4 - 1/72 = 17/72 of the tank per hour
To find out how long Pump Z would take to pump out all the water, we need to divide the total tank capacity by Pump Z's rate:
Time taken by Pump Z = 1 / (17/72) = 72/17 ≈ 4.24 hours
Therefore, Pump Z would take approximately 4.24 hours to pump out all of the water from the tank, which is closest to option B (12 hours).
PassageRoughly 40 per cent of the African American population of the Southern United States left the South between 1915 and 1960, primarily for the industrial cities of the North. While there was some African American migration to the North during the nineteenth century, most accounts point to 1915 as the start of what historians call the Great Migration. There were at least three catalysts of the Great Migration. First, World War I increased labour demand in the industrial North. Second, the war in Europe cut off immigration, which led many Northern employers to send labour agents to recruit African American labour in the South. Finally, a boll weevil infestation ruined cotton crops and reduced labour demand in much of the South in the 1910s and 1920s.In short, the Great Migration began in 1915 and not earlier, because it was only then that the North-South income gap became large enough to start such a large-scale migration. Less clear, however, is why migration continued and even accelerated, in subsequent decades, at the same time that North-South income differences were narrowing.We propose that once started, migration develops momentum over time as current migration reduces the difficulty and cost of future migration. Economists have typically assumed that people migrate if their expected earnings in the destination exceed those of the origin enough to outweigh the difficulties and one-time costs of migration. Previous research suggests that the difficulties and costs arise from several sources. First, the uncertainty that potential migrants face concerning housing and labour-market conditions in the destination presents a significant hindrance. Second, there is a simple cost in terms of time and money of physically moving from the origin to the destination. Third, new migrants must familiarize themselves with local labour- and housing-market institutions once they arrive; they must find housing and work, and they must often adapt to a new culture or language.Empirical studies show that during the Great Migration, information was passed through letters that were often read by dozens of people and through conversation when migrants made trips back to their home communities. Thus early migrants provided information about labor- and housing-market conditions to friends and relatives who had not yet made the trip. First-time African American migrants often travelled with earlier migrants returning to the North after a visit to the South, which reduced physical costs. Additionally, previous migrants reduced new migrants' cost of adapting to a new locale and culture by providing them with temporary housing, food, and even credit. Previous migrants also provided a cultural cushion for later migrants, so that they did not have to struggle as hard with their new surroundings.Q. Which one of the following most accurately expresses the main point of the passage?- a)Approximately 40 per cent of the African American population left the Southern U.S. between 1915 and 1960—an event historians refer to as the Great Migration.
- b)The Great Migration was triggered by an increased labour demand in the North due to the onset of World War I and reduced labour demand in the South due to aboll weevil infestation.
- c)Because earlier migrants helped defray the financial costs of migration for later migrants, African American migration to the North accelerated at a time when income differences were narrowing.
- d)In migration movements, earlier migrants reduce the physical costs of moving and provide a cultural and linguistic cushion for later migrants.
- e)Although the Great Migration was initially triggered by the income differential between the North and South, other factors must be cited in order to explain its duration over several decades.
Correct answer is option 'E'. Can you explain this answer?
Passage
Roughly 40 per cent of the African American population of the Southern United States left the South between 1915 and 1960, primarily for the industrial cities of the North. While there was some African American migration to the North during the nineteenth century, most accounts point to 1915 as the start of what historians call the Great Migration. There were at least three catalysts of the Great Migration. First, World War I increased labour demand in the industrial North. Second, the war in Europe cut off immigration, which led many Northern employers to send labour agents to recruit African American labour in the South. Finally, a boll weevil infestation ruined cotton crops and reduced labour demand in much of the South in the 1910s and 1920s.
In short, the Great Migration began in 1915 and not earlier, because it was only then that the North-South income gap became large enough to start such a large-scale migration. Less clear, however, is why migration continued and even accelerated, in subsequent decades, at the same time that North-South income differences were narrowing.
We propose that once started, migration develops momentum over time as current migration reduces the difficulty and cost of future migration. Economists have typically assumed that people migrate if their expected earnings in the destination exceed those of the origin enough to outweigh the difficulties and one-time costs of migration. Previous research suggests that the difficulties and costs arise from several sources. First, the uncertainty that potential migrants face concerning housing and labour-market conditions in the destination presents a significant hindrance. Second, there is a simple cost in terms of time and money of physically moving from the origin to the destination. Third, new migrants must familiarize themselves with local labour- and housing-market institutions once they arrive; they must find housing and work, and they must often adapt to a new culture or language.
Empirical studies show that during the Great Migration, information was passed through letters that were often read by dozens of people and through conversation when migrants made trips back to their home communities. Thus early migrants provided information about labor- and housing-market conditions to friends and relatives who had not yet made the trip. First-time African American migrants often travelled with earlier migrants returning to the North after a visit to the South, which reduced physical costs. Additionally, previous migrants reduced new migrants' cost of adapting to a new locale and culture by providing them with temporary housing, food, and even credit. Previous migrants also provided a cultural cushion for later migrants, so that they did not have to struggle as hard with their new surroundings.
Q. Which one of the following most accurately expresses the main point of the passage?
a)
Approximately 40 per cent of the African American population left the Southern U.S. between 1915 and 1960—an event historians refer to as the Great Migration.
b)
The Great Migration was triggered by an increased labour demand in the North due to the onset of World War I and reduced labour demand in the South due to aboll weevil infestation.
c)
Because earlier migrants helped defray the financial costs of migration for later migrants, African American migration to the North accelerated at a time when income differences were narrowing.
d)
In migration movements, earlier migrants reduce the physical costs of moving and provide a cultural and linguistic cushion for later migrants.
e)
Although the Great Migration was initially triggered by the income differential between the North and South, other factors must be cited in order to explain its duration over several decades.
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Arnab Kumar answered |
The Main Point of the Passage
The passage discusses the Great Migration of African Americans from the Southern United States to the North, emphasizing the factors that initiated and sustained this movement.
Key Aspects of the Great Migration
- The Great Migration began around 1915, primarily due to:
- Increased labor demand in the North due to World War I.
- Reduced labor demand in the South caused by a boll weevil infestation.
Continuation of Migration
- While initial migration was driven by income disparities, the passage explains how migration persisted even as these disparities narrowed.
- It highlights that earlier migrants played a crucial role in easing the transition for new migrants.
Importance of Earlier Migrants
- Early migrants provided:
- Information: Shared insights into labor and housing conditions.
- Support: Offered temporary housing, food, and financial assistance.
- Cultural Adaptation: Helped newcomers navigate their new environment.
Conclusion
- Option 'E' captures the essence of the passage by indicating that although the Great Migration was sparked by income differences between North and South, the sustained migration over decades required additional explanations, particularly the support provided by earlier migrants. This interconnectedness illustrates how migration momentum builds over time, making 'E' the most comprehensive and accurate choice.
The passage discusses the Great Migration of African Americans from the Southern United States to the North, emphasizing the factors that initiated and sustained this movement.
Key Aspects of the Great Migration
- The Great Migration began around 1915, primarily due to:
- Increased labor demand in the North due to World War I.
- Reduced labor demand in the South caused by a boll weevil infestation.
Continuation of Migration
- While initial migration was driven by income disparities, the passage explains how migration persisted even as these disparities narrowed.
- It highlights that earlier migrants played a crucial role in easing the transition for new migrants.
Importance of Earlier Migrants
- Early migrants provided:
- Information: Shared insights into labor and housing conditions.
- Support: Offered temporary housing, food, and financial assistance.
- Cultural Adaptation: Helped newcomers navigate their new environment.
Conclusion
- Option 'E' captures the essence of the passage by indicating that although the Great Migration was sparked by income differences between North and South, the sustained migration over decades required additional explanations, particularly the support provided by earlier migrants. This interconnectedness illustrates how migration momentum builds over time, making 'E' the most comprehensive and accurate choice.
A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?- a)28
- b)42
- c)84
- d)128
- e)More than two answers are correct
Correct answer is option 'D'. Can you explain this answer?
A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?
a)
28
b)
42
c)
84
d)
128
e)
More than two answers are correct
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EduRev GMAT answered |
For AB to be a terminating decimal b must have the form 2a ∗ 5b.
Every option except 128 contains a 77, and since A and B do not share any factor (are co-prime) 7 will not cancel out of the denominator.
So B can only be 128 = 27.
Every option except 128 contains a 77, and since A and B do not share any factor (are co-prime) 7 will not cancel out of the denominator.
So B can only be 128 = 27.
A child learning to play the piano will not succeed unless the child has an instrument at home on which to practice. However, good-quality pianos, whether new or secondhand, are costly. Buying one is justified only if the child has the necessary talent and perseverance, which is precisely what one cannot know in advance. Consequently, parents should buy an inexpensive secondhand instrument at first and upgrade if and when the child's ability and inclination are proven.
Q. Which of the following, if true, casts the most serious doubt on the course of action recommended for parents?
- a)Learners, particularly those with genuine musical talent, are apt to lose interest in the instrument if they have to play on a piano that fails to produce a pleasing sound.
- b)Reputable piano teachers do not accept children as pupils unless they know that the children can practice on a piano at home.
- c)Ideally, the piano on which a child practices at home should be located in a room away from family activities going on at the same time.
- d)Very young beginners often make remarkable progress at playing the piano at first, but then appear to stand still for a considerable period of time.
- e)In some parents, spending increasing amounts of money on having their children learn to play the piano produces increasing anxiety to hear immediate results.
Correct answer is option 'D'. Can you explain this answer?
A child learning to play the piano will not succeed unless the child has an instrument at home on which to practice. However, good-quality pianos, whether new or secondhand, are costly. Buying one is justified only if the child has the necessary talent and perseverance, which is precisely what one cannot know in advance. Consequently, parents should buy an inexpensive secondhand instrument at first and upgrade if and when the child's ability and inclination are proven.
Q. Which of the following, if true, casts the most serious doubt on the course of action recommended for parents?
a)
Learners, particularly those with genuine musical talent, are apt to lose interest in the instrument if they have to play on a piano that fails to produce a pleasing sound.
b)
Reputable piano teachers do not accept children as pupils unless they know that the children can practice on a piano at home.
c)
Ideally, the piano on which a child practices at home should be located in a room away from family activities going on at the same time.
d)
Very young beginners often make remarkable progress at playing the piano at first, but then appear to stand still for a considerable period of time.
e)
In some parents, spending increasing amounts of money on having their children learn to play the piano produces increasing anxiety to hear immediate results.
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EduRev GMAT answered |
The argument talks about 'child' (say 3 - 12 yrs). Option (D) talks about 'very young' which implies a little child (say 3 - 5 yrs). Since very young will be a subset of child, most of my interest in the option is already lost. It is like saying "some children will..." and that is usually irrelevant.
Secondly it uses "beginners" which means the stage at which they have the second hand cheap instrument. They may show promise but will stop suddenly. Well, all the more reason to wait and watch with a temporary instrument. If you begin with an expensive one, it will go waste.
If we know that kids show progress initially and then stand still, we would buy a cheaper instrument and see whether they are showing continuous progress to buy an expensive one later.
Secondly it uses "beginners" which means the stage at which they have the second hand cheap instrument. They may show promise but will stop suddenly. Well, all the more reason to wait and watch with a temporary instrument. If you begin with an expensive one, it will go waste.
If we know that kids show progress initially and then stand still, we would buy a cheaper instrument and see whether they are showing continuous progress to buy an expensive one later.
How many integral divisors does the number 120 have?- a)14
- b)16
- c)12
- d)20
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
How many integral divisors does the number 120 have?
a)
14
b)
16
c)
12
d)
20
e)
None of these
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EduRev GMAT answered |
Step 1: Express the number in terms of its prime factors
120 = 23 * 3 * 5.
The three prime factors are 2, 3 and 5.
The powers of these prime factors are 3, 1 and 1 respectively.
The three prime factors are 2, 3 and 5.
The powers of these prime factors are 3, 1 and 1 respectively.
Step 2: Find the number of factors as follows
To find the number of factors / integral divisors that 120 has, increment the powers of each of the prime factors by 1 and then multiply them.
Number of factors = (3 + 1) * (1 + 1) * (1 + 1) = 4 * 2 * 2 =16
Choice B is the correct answer.
Key Takeaway
How to find the number of factors of a number? Method: Prime Factorization
Let the number be 'n'.
Step 1: Prime factorize 'n'. Let n = ap * bq, where 'a' and 'b' are the only prime factors of 'n'.
Step 2: Number of factors equals product of powers of primes incremented by 1.
i.e., number of factors = (p + 1)(q + 1)
How to find the number of factors of a number? Method: Prime Factorization
Let the number be 'n'.
Step 1: Prime factorize 'n'. Let n = ap * bq, where 'a' and 'b' are the only prime factors of 'n'.
Step 2: Number of factors equals product of powers of primes incremented by 1.
i.e., number of factors = (p + 1)(q + 1)
Direction: Read the following Passage and Answer the following Question.Is there any knowledge in the world which is so certain that no reasonable man could doubt it? This question, which at first sight might not seem difficult, is really one of the most difficult that can be asked. When we have realized the obstacles in the way of a straightforward and confident answer, we shall be well launched on the study of philosophy—for philosophy is merely the attempt to answer such ultimate questions, not carelessly and dogmatically, as we do in ordinary life and even in the sciences, but critically, after exploring all that makes such questions puzzling, and after realizing all the vagueness and confusion that underlie our ordinary ideas.In daily life, we assume as certain many things which, on a closer scrutiny, are found to be so full of apparent contradictions that only a great amount of thought enables us to know what it is that we really may believe. In the search for certainty, it is natural to begin with our present experiences, and in some sense, no doubt, knowledge is to be derived from them. But any statement as to what it is that our immediate experiences make us know is very likely to be wrong. It seems to me that I am now sitting in a chair, at a table of a certain shape, on which I see sheets of paper with writing or print. By turning my head I see out of the window buildings and clouds and the sun. I believe that the sun is about ninety-three million miles from the earth; that it is a hot globe many times bigger than the earth; that, owing to the earth's rotation, it rises every morning, and will continue to do so for an indefinite time in the future. I believe that, if any other normal person comes into my room, he will see the same chairs and tables and books and papers as I see, and that the table which I see is the same as the table which I feel pressing against my arm. All this seems to be so evident as to be hardly worth stating, except in answer to a man who doubts whether I know anything. Yet all this may be reasonably doubted, and all of it requires much careful discussion before we can be sure that we have stated it in a form that is wholly true.Q. Suppose you state that 'you are sitting in a garden observing a yellow butterfly'. According to the passage:- a)Your statement could be doubted
- b)The butterfly may actually be a blue one
- c)The butterfly may not be there at all
- d)You have been dogmatic in making that statement
- e)You are correct in making that statement
Correct answer is option 'A'. Can you explain this answer?
Direction: Read the following Passage and Answer the following Question.
Is there any knowledge in the world which is so certain that no reasonable man could doubt it? This question, which at first sight might not seem difficult, is really one of the most difficult that can be asked. When we have realized the obstacles in the way of a straightforward and confident answer, we shall be well launched on the study of philosophy—for philosophy is merely the attempt to answer such ultimate questions, not carelessly and dogmatically, as we do in ordinary life and even in the sciences, but critically, after exploring all that makes such questions puzzling, and after realizing all the vagueness and confusion that underlie our ordinary ideas.
In daily life, we assume as certain many things which, on a closer scrutiny, are found to be so full of apparent contradictions that only a great amount of thought enables us to know what it is that we really may believe. In the search for certainty, it is natural to begin with our present experiences, and in some sense, no doubt, knowledge is to be derived from them. But any statement as to what it is that our immediate experiences make us know is very likely to be wrong. It seems to me that I am now sitting in a chair, at a table of a certain shape, on which I see sheets of paper with writing or print. By turning my head I see out of the window buildings and clouds and the sun. I believe that the sun is about ninety-three million miles from the earth; that it is a hot globe many times bigger than the earth; that, owing to the earth's rotation, it rises every morning, and will continue to do so for an indefinite time in the future. I believe that, if any other normal person comes into my room, he will see the same chairs and tables and books and papers as I see, and that the table which I see is the same as the table which I feel pressing against my arm. All this seems to be so evident as to be hardly worth stating, except in answer to a man who doubts whether I know anything. Yet all this may be reasonably doubted, and all of it requires much careful discussion before we can be sure that we have stated it in a form that is wholly true.
Q. Suppose you state that 'you are sitting in a garden observing a yellow butterfly'. According to the passage:
a)
Your statement could be doubted
b)
The butterfly may actually be a blue one
c)
The butterfly may not be there at all
d)
You have been dogmatic in making that statement
e)
You are correct in making that statement
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EduRev GMAT answered |
From the last paragraph, it clearly follows that even the most simplistic of our observations can be doubted. Hence the answer has to be (A)
Jennifer: Video rental outlets in Centerville together handled 10,000 fewer video rentals in 1994 than in 1993. The decline in rentals was probably due almost entirely to the February 1994 opening of Videorama, the first and only video rental outlet in the area that, in addition to renting videos, also sold them cheaply. Brad: There must be another explanation: as you yourself said, the decline was on the order of 10,000 rentals. Yet Videorama sold only 4,000 videos in 1994.Q. Which of the following, if true, would most seriously weaken the force of the objection that Brad presents to Jennifer's explanation?- a)In 1994 Videorama rented out more videos than it sold.
- b)In 1994 two new outlets that rent but that do not sell videos opened in Centerville.
- c)Most of the video rental outlets in Centerville rent videos at a discount on certain nights of the week.
- d)People often buy videos of movies that they have previously seen in a theater.
- e)People who own videos frequently loan them to their friends.
Correct answer is option 'A'. Can you explain this answer?
Jennifer: Video rental outlets in Centerville together handled 10,000 fewer video rentals in 1994 than in 1993. The decline in rentals was probably due almost entirely to the February 1994 opening of Videorama, the first and only video rental outlet in the area that, in addition to renting videos, also sold them cheaply. Brad: There must be another explanation: as you yourself said, the decline was on the order of 10,000 rentals. Yet Videorama sold only 4,000 videos in 1994.
Q. Which of the following, if true, would most seriously weaken the force of the objection that Brad presents to Jennifer's explanation?
a)
In 1994 Videorama rented out more videos than it sold.
b)
In 1994 two new outlets that rent but that do not sell videos opened in Centerville.
c)
Most of the video rental outlets in Centerville rent videos at a discount on certain nights of the week.
d)
People often buy videos of movies that they have previously seen in a theater.
e)
People who own videos frequently loan them to their friends.
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EduRev GMAT answered |
Jennifer attributes the decline in video rentals to the opening of Videorama, but Brad objects. What weakens Brad's objection?
A. In 1994 Videorama rented out more videos than it sold.
- Explanation: This suggests that Videorama was a significant player in the video rental market, potentially weakening Brad's objection.
Correct Answer: A
B. In 1994 two new outlets that rent but that do not sell videos opened in Centerville.
- Explanation: This introduces new information but doesn't necessarily weaken Brad's objection.
C. Most of the video rental outlets in Centerville rent videos at a discount on certain nights of the week.
- Explanation: This introduces a different factor affecting video rentals but doesn't directly address Brad's objection.
D. People often buy videos of movies that they have previously seen in a theater.
- Explanation: This is unrelated to the decline in video rentals.
E. People who own videos frequently loan them to their friends.
- Explanation: This is also unrelated to the decline in video rentals.
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?- a)$ 5500
- b)$ 11000
- c)$ 22000
- d)$ 2750
- e)$ 44000
Correct answer is option 'D'. Can you explain this answer?
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
a)
$ 5500
b)
$ 11000
c)
$ 22000
d)
$ 2750
e)
$ 44000
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EduRev GMAT answered |
Step 1: Compute interest for each year for both simple and compound interest
Simple Interest:
Concept: Simple interest earned is same value year on year.
Shawn received $550 as interest for 2 years.
Simple interest earned for first year = 550/2 = $275
The simple interest for second year is also $275.
Concept: Simple interest earned is same value year on year.
Shawn received $550 as interest for 2 years.
Simple interest earned for first year = 550/2 = $275
The simple interest for second year is also $275.
In Compound interest: Shawn received $605 as interest for 2 years.
Concept: Interest earned is same for both simple and compound interest in the first year.
Compund interest earned for first year = $275.
Compund interest earned for second year = 605 − 275 = $330
Extra interest received from compound interest = $55.
Interest for each year
Concept: Interest earned is same for both simple and compound interest in the first year.
Compund interest earned for first year = $275.
Compund interest earned for second year = 605 − 275 = $330
Extra interest received from compound interest = $55.
Interest for each year
Step 2: Find the rate of interest
Concept: In Compound interest, interest earned on first year's interest will get added in second year and contributes to the additional interest when invested in compound interest.
Compound interest for first year = $275.
Therefore, $55 is the interest earned during the second year on $275.
Therefore, the rate of interest =
Therefore, $55 is the interest earned during the second year on $275.
Therefore, the rate of interest =
Step 3: Compute the principal invested
At 20% rate of interest, the simple interest earned for 1 year = $275
or P = $1375
or P = $1375
Shawn had invested equal sums in both the bonds.
His total savings before investing = 2 × 1375 = $2750
Total savings = $2750
His total savings before investing = 2 × 1375 = $2750
Total savings = $2750
Choice D is the correct answer.
If x > 0, how many integer values of (x, y) will satisfy the equation 5x + 4|y| = 55?- a)3
- b)6
- c)5
- d)4
- e)Infinitely many
Correct answer is option 'C'. Can you explain this answer?
If x > 0, how many integer values of (x, y) will satisfy the equation 5x + 4|y| = 55?
a)
3
b)
6
c)
5
d)
4
e)
Infinitely many
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EduRev GMAT answered |
5x + 4|y| = 55
The equation can be rewritten as 4|y| = 55 - 5x.
Inference 1: Because |y| is non-negative, 4|y| will be non-negative.
Therefore, (55 - 5x) cannot take negative values.
The equation can be rewritten as 4|y| = 55 - 5x.
Inference 1: Because |y| is non-negative, 4|y| will be non-negative.
Therefore, (55 - 5x) cannot take negative values.
Inference 2: Because x and y are integers, 4|y| will be a multiple of 4.
Therefore, (55 - 5x) will also be a multiple of 4.
Therefore, (55 - 5x) will also be a multiple of 4.
Inference 3: 55 is a multiple of 5. 5x is a multiple of 5 for integer x.
So, 55 - 5x will always be a multiple of 5 for any integer value of x.
So, 55 - 5x will always be a multiple of 5 for any integer value of x.
Combining Inference 2 and Inference 3: 55 - 5x will be a multiple of 4 and 5.
i.e., 55 - 5x will be a multiple of 20.
i.e., 55 - 5x will be a multiple of 20.
Integer values of x > 0 that will satisfy the condition that (55 - 5x) is a multiple of 20:
1. x = 3, 55 - 5x = 55 - 15 = 40.
2. x = 7, 55 - 5x = 55 - 35 = 20
3. x = 11, 55 - 5x = 55 - 55 = 0.
When x = 15, (55 - 5x) = (55 - 75) = -20.
Because (55 - 5x) has to non-negative, x = 15 or values greater than 15 are not possible.
So, x can take only 3 values viz., 3, 7, and 11.
2. x = 7, 55 - 5x = 55 - 35 = 20
3. x = 11, 55 - 5x = 55 - 55 = 0.
When x = 15, (55 - 5x) = (55 - 75) = -20.
Because (55 - 5x) has to non-negative, x = 15 or values greater than 15 are not possible.
So, x can take only 3 values viz., 3, 7, and 11.
Possible values of y when x = 3, x = 7, and x = 11
We have 3 possible values for 55 - 5x. So, we will have these 3 values possible for 4|y|.
Possibility 1: 4|y| = 40 or |y| = 10. So, y = 10 or -10.
Possibility 2: 4|y| = 20 or |y| = 5. So, y = 5 or -5.
Possibility 3: 4|y| = 0 or |y| = 0. So, y = 0.
Number of values possible for y = 5.
Possibility 1: 4|y| = 40 or |y| = 10. So, y = 10 or -10.
Possibility 2: 4|y| = 20 or |y| = 5. So, y = 5 or -5.
Possibility 3: 4|y| = 0 or |y| = 0. So, y = 0.
Number of values possible for y = 5.
The correct choice is (C) and the correct answer is 5.
Direction: Read the following Passage and Answer the following Question.
As urban landscapes continue to expand, the rise of vertical farming is becoming a crucial element in the quest for sustainable city living. Vertical farms, which grow crops in stacked layers within a controlled environment, offer a revolutionary approach to agriculture in urban settings. This innovative method of farming is not just about saving space; it's about reimagining how we produce food in the face of growing environmental challenges.One of the key advantages of vertical farming is its minimal use of water and pesticides. Unlike traditional agriculture, which relies heavily on these resources, vertical farms use hydroponic systems that circulate water efficiently and eliminate the need for soil and large-scale pesticide use. This approach significantly reduces the environmental impact of farming.Another significant benefit is the reduction in food miles. Vertical farms can be established within urban areas, drastically cutting down the distance food travels from farm to consumer. This not only ensures fresher produce but also reduces transportation emissions, contributing to lower carbon footprints.However, vertical farming faces its own set of challenges. The initial setup and operational costs can be high, making it difficult for these farms to compete with traditional agriculture in terms of cost. Additionally, the energy requirements for maintaining controlled environments, such as lighting and temperature control, are substantial. Critics argue that unless renewable energy sources power these farms, they may not be as sustainable as they seem.Despite these challenges, the potential of vertical farming in reshaping urban agriculture remains immense. As technology advances, the efficiency of these farms is expected to improve, making them a vital component in the development of sustainable cities.
Q. Based on the passage, which of the following can be inferred about vertical farms compared to traditional farms?- a)Vertical farms use more water and pesticides.
- b)Vertical farms are less expensive to operate.
- c)Vertical farms have a smaller environmental footprint.
- d)Vertical farms produce less fresh produce.
- e)Vertical farms require more soil for crop growth.
Correct answer is option 'C'. Can you explain this answer?
Direction: Read the following Passage and Answer the following Question.
As urban landscapes continue to expand, the rise of vertical farming is becoming a crucial element in the quest for sustainable city living. Vertical farms, which grow crops in stacked layers within a controlled environment, offer a revolutionary approach to agriculture in urban settings. This innovative method of farming is not just about saving space; it's about reimagining how we produce food in the face of growing environmental challenges.
As urban landscapes continue to expand, the rise of vertical farming is becoming a crucial element in the quest for sustainable city living. Vertical farms, which grow crops in stacked layers within a controlled environment, offer a revolutionary approach to agriculture in urban settings. This innovative method of farming is not just about saving space; it's about reimagining how we produce food in the face of growing environmental challenges.
One of the key advantages of vertical farming is its minimal use of water and pesticides. Unlike traditional agriculture, which relies heavily on these resources, vertical farms use hydroponic systems that circulate water efficiently and eliminate the need for soil and large-scale pesticide use. This approach significantly reduces the environmental impact of farming.
Another significant benefit is the reduction in food miles. Vertical farms can be established within urban areas, drastically cutting down the distance food travels from farm to consumer. This not only ensures fresher produce but also reduces transportation emissions, contributing to lower carbon footprints.
However, vertical farming faces its own set of challenges. The initial setup and operational costs can be high, making it difficult for these farms to compete with traditional agriculture in terms of cost. Additionally, the energy requirements for maintaining controlled environments, such as lighting and temperature control, are substantial. Critics argue that unless renewable energy sources power these farms, they may not be as sustainable as they seem.
Despite these challenges, the potential of vertical farming in reshaping urban agriculture remains immense. As technology advances, the efficiency of these farms is expected to improve, making them a vital component in the development of sustainable cities.
Q. Based on the passage, which of the following can be inferred about vertical farms compared to traditional farms?
Q. Based on the passage, which of the following can be inferred about vertical farms compared to traditional farms?
a)
Vertical farms use more water and pesticides.
b)
Vertical farms are less expensive to operate.
c)
Vertical farms have a smaller environmental footprint.
d)
Vertical farms produce less fresh produce.
e)
Vertical farms require more soil for crop growth.
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EduRev GMAT answered |
This is an INFERENCE question. The passage states that vertical farms use hydroponic systems that are more water-efficient and reduce the need for pesticides, and they also cut down food miles. From this, it can be inferred that vertical farms have a smaller environmental footprint compared to traditional farms (Choice C). The other options are either contradicted by the passage or not supported by the information given.
Five years ago, the town of Bayside, in the Katonic River Valley, had catastrophic flooding one spring, and consequently, most insurers now refuse to write flood insurance for houses in Bayside. The town of Dryadia, in the Phemptic River Valley, is much like Bayside in its proximity to a similar river at an almost identical point in the river valley. We can conclude that the only reason the same insurers do not write flood insurance for houses in Dryadia either is its similarity to Bayside in terms of where it is situated in the river valley.Q. Which of the following, if true, would most seriously undermine the argument?- a)A small number of independent insurers will write flood insurance for at least some houses in each of the two towns.
- b)It is hard for an homeowner to buy flood insurance if a large proportion of other houses in the same town have been flooded in recent years.
- c)In many other towns in the Katonic River Valley, it is hard for home-owners to buy flood insurance.
- d)The town of Dryadia has some flooding most springs.
- e)Flooding from spring surges in rivers is only one of the ways in which a home can become flooded.
Correct answer is option 'D'. Can you explain this answer?
Five years ago, the town of Bayside, in the Katonic River Valley, had catastrophic flooding one spring, and consequently, most insurers now refuse to write flood insurance for houses in Bayside. The town of Dryadia, in the Phemptic River Valley, is much like Bayside in its proximity to a similar river at an almost identical point in the river valley. We can conclude that the only reason the same insurers do not write flood insurance for houses in Dryadia either is its similarity to Bayside in terms of where it is situated in the river valley.
Q. Which of the following, if true, would most seriously undermine the argument?
a)
A small number of independent insurers will write flood insurance for at least some houses in each of the two towns.
b)
It is hard for an homeowner to buy flood insurance if a large proportion of other houses in the same town have been flooded in recent years.
c)
In many other towns in the Katonic River Valley, it is hard for home-owners to buy flood insurance.
d)
The town of Dryadia has some flooding most springs.
e)
Flooding from spring surges in rivers is only one of the ways in which a home can become flooded.
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Advait Roy answered |
Undermining the Argument:
Option D:
- This option states that the town of Dryadia experiences some flooding most springs.
- This information indicates that Dryadia faces a higher risk of flooding compared to Bayside.
- If Dryadia experiences flooding more frequently than Bayside, it suggests that insurers refusing to write flood insurance for houses in Dryadia may have a valid reason beyond just the similarity in location to Bayside.
- This undermines the argument that the sole reason for insurers refusing flood insurance in Dryadia is its proximity to the river valley, as the increased frequency of flooding in Dryadia could be a significant factor.
- Therefore, this information weakens the conclusion drawn in the argument and suggests that there may be other factors at play in insurers' decisions regarding flood insurance in Dryadia.
Option D:
- This option states that the town of Dryadia experiences some flooding most springs.
- This information indicates that Dryadia faces a higher risk of flooding compared to Bayside.
- If Dryadia experiences flooding more frequently than Bayside, it suggests that insurers refusing to write flood insurance for houses in Dryadia may have a valid reason beyond just the similarity in location to Bayside.
- This undermines the argument that the sole reason for insurers refusing flood insurance in Dryadia is its proximity to the river valley, as the increased frequency of flooding in Dryadia could be a significant factor.
- Therefore, this information weakens the conclusion drawn in the argument and suggests that there may be other factors at play in insurers' decisions regarding flood insurance in Dryadia.
y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?- a)-32
- b)-256
- c)-255
- d)-257
- e)0
Correct answer is option 'D'. Can you explain this answer?
y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
a)
-32
b)
-256
c)
-255
d)
-257
e)
0
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EduRev GMAT answered |
Step 1: Understand the equation and the points (h, 0) and (k, 0)
The given equation is a quadratic equation. A quadratic equation when plotted on a graph sheet (x - y plane) will result in a parabola.
The roots of the quadratic equation are computed by equating the quadratic expression to 0. i.e., the roots are the values that 'x' take when y = 0
So, the roots of the quadratic equation are the points where the parabola cuts the x-axis.
The question mentions that the curve described by the equation cuts the x-axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic equation.
For quadratic equations of the form ax2 + bx + c = 0, the sum of the roots =
The sum of the roots of this equation is
Note : Higher the value of 'b', i.e., higher the sum of the roots of this quadratic equation, lower the value of b.
The roots of the quadratic equation are computed by equating the quadratic expression to 0. i.e., the roots are the values that 'x' take when y = 0
So, the roots of the quadratic equation are the points where the parabola cuts the x-axis.
The question mentions that the curve described by the equation cuts the x-axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic equation.
For quadratic equations of the form ax2 + bx + c = 0, the sum of the roots =
The sum of the roots of this equation is
Note : Higher the value of 'b', i.e., higher the sum of the roots of this quadratic equation, lower the value of b.
For quadratic equations of the form ax2 + bx + c = 0, the product of roots = c/a.
Therefore, the product of the roots of this equation = 256/1 = 256.
i.e., h × k = 256 h and k are both integers.
So, h and k are both integral factors of 256.
Therefore, the product of the roots of this equation = 256/1 = 256.
i.e., h × k = 256 h and k are both integers.
So, h and k are both integral factors of 256.
Step 2: List possible values of h and k and find the least value of ‘b’
This is the step in which number properties concepts kick in. 256 can be expressed as product of two numbers in the following ways:
1 × 256
2 × 128
4 × 64
8 × 32
16 × 16
1 × 256
2 × 128
4 × 64
8 × 32
16 × 16
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.
∴ The least value possible for b is -257.
∴ The least value possible for b is -257.
Choice D is the correct answer.
How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?- a)6
- b)7
- c)5
- d)8
- e)18
Correct answer is option 'B'. Can you explain this answer?
How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?
a)
6
b)
7
c)
5
d)
8
e)
18
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|
Nandita Chauhan answered |
Understanding the Problem
To find the different positive integers between 106 and 107 whose sum of digits is equal to 2, we need to analyze and determine the possible numbers that satisfy this condition.
Identifying the Numbers
- The numbers between 106 and 107 are 107, 106.
- To find the sum of digits equal to 2, the possible numbers are 107, 106, 17.
Calculating the Sum of Digits
- For the number 107: 1 + 0 + 7 = 8 (Not equal to 2)
- For the number 106: 1 + 0 + 6 = 7 (Not equal to 2)
- For the number 17: 1 + 7 = 8 (Not equal to 2)
Determining the Correct Answer
After analyzing the possible numbers between 106 and 107 and checking their sum of digits, we can see that there are 2 numbers (106 and 17) whose sum of digits is equal to 2.
Therefore, the correct answer is option B) 7.
To find the different positive integers between 106 and 107 whose sum of digits is equal to 2, we need to analyze and determine the possible numbers that satisfy this condition.
Identifying the Numbers
- The numbers between 106 and 107 are 107, 106.
- To find the sum of digits equal to 2, the possible numbers are 107, 106, 17.
Calculating the Sum of Digits
- For the number 107: 1 + 0 + 7 = 8 (Not equal to 2)
- For the number 106: 1 + 0 + 6 = 7 (Not equal to 2)
- For the number 17: 1 + 7 = 8 (Not equal to 2)
Determining the Correct Answer
After analyzing the possible numbers between 106 and 107 and checking their sum of digits, we can see that there are 2 numbers (106 and 17) whose sum of digits is equal to 2.
Therefore, the correct answer is option B) 7.
By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What % profit will the merchant make if the article is sold at 95% of its marked price?- a)5% profit
- b)1% loss
- c)10% profit
- d)5.5% profit
- e)4.5% profit
Correct answer is option 'E'. Can you explain this answer?
By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What % profit will the merchant make if the article is sold at 95% of its marked price?
a)
5% profit
b)
1% loss
c)
10% profit
d)
5.5% profit
e)
4.5% profit
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EduRev GMAT answered |
Approach: Assume cost price to be $100
Let the marked price be S and the cost price of the article be $100.
Let the marked price be S and the cost price of the article be $100.
When the article is sold at 80% of its marked price, selling price is 0.8S.
Selling the article at 0.8S results in a loss of 12% of the cost price.
Therefore, the loss incurred when selling at 0.8S = 12% of 100 = $12.
Hence, when selling at 80% of the marked price, the article is sold at 100 − 12 = $88.
i.e., 0.8S = $88.
or S = 88/0.8 = $110.
If the merchant sells at 95% of the marked price, then the new selling price of the article is 95% of $110 = $104.5
Selling the article at 0.8S results in a loss of 12% of the cost price.
Therefore, the loss incurred when selling at 0.8S = 12% of 100 = $12.
Hence, when selling at 80% of the marked price, the article is sold at 100 − 12 = $88.
i.e., 0.8S = $88.
or S = 88/0.8 = $110.
If the merchant sells at 95% of the marked price, then the new selling price of the article is 95% of $110 = $104.5
The profit made = 95% of Selling Price − Cost Price = 104.5 − 100 = $4.5.
% Profit = profit/cost price = 4.5/100 = 4.5%
The merchant made 4.5% profit
% Profit = profit/cost price = 4.5/100 = 4.5%
The merchant made 4.5% profit
Choice E is the correct answer.
Window 1: First Analyst
The Widget world has grown from a niche interest of teenage and college boys to a multi-billion dollar industry attracting men and women of all ages. In particular, Next Widget Corporation has had great success, increasing its revenues almost threefold ovcr the past decade, and boasting six of the ten most popular products in the market.Yet investors have become jittery recently, fearing that widget sales will decline—as gizmo sales did last year—and knocked Next Widget’s stock price down 33% from its peak of $113.17 in late 2011. These fears are misguided. Unlike the gizmo industry, the widget industry should continuc to grow, as more consumers switch from higher-priced Gizmos to more affordable Widgets. Next Widget should also get a boost in revenues from its upcoming expansion into South America.For now, Next Widget’s stock remains a buy.
Window 2: Second Analyst
Next Widget’s stock has skyrocketed over the past decade, reaching its all-time high of $113.17 per share on December 19, 2011—a 415% increase over its initial public offering share price in 2002—as the company’s revenues increased from $570 million in 2002 to $1.62 billion in 2011.This run cannot continue. The revenue gains came mostly prior to 2009: The increases in the company’s top line of $210 million and $193 million in 2010 and 2011, respectively, were the smallest of the past decade. This trend is likely to continue in 2012, at least in the domestic market, given increased competition from the up-and-coming Widgitainers, Inc.Furthermore, Next Widget’s planned expansion into South America may be trickier than expected. Even if successful in the long term, it will certainly contribute a loss in the near term, thus putting a strain on the company’s operating margins.Now is a good time to sell your Next Widget stock.Q: On the day of the first analyst’s report, Next Widget’s stock price was approximately what percent of its stock price at its initial public offering?- a)245 %
- b)278 %
- c)345 %
- d)382 %
- e)482 %
Correct answer is option 'C'. Can you explain this answer?
Window 1: First Analyst
The Widget world has grown from a niche interest of teenage and college boys to a multi-billion dollar industry attracting men and women of all ages. In particular, Next Widget Corporation has had great success, increasing its revenues almost threefold ovcr the past decade, and boasting six of the ten most popular products in the market.
The Widget world has grown from a niche interest of teenage and college boys to a multi-billion dollar industry attracting men and women of all ages. In particular, Next Widget Corporation has had great success, increasing its revenues almost threefold ovcr the past decade, and boasting six of the ten most popular products in the market.
Yet investors have become jittery recently, fearing that widget sales will decline—as gizmo sales did last year—and knocked Next Widget’s stock price down 33% from its peak of $113.17 in late 2011. These fears are misguided. Unlike the gizmo industry, the widget industry should continuc to grow, as more consumers switch from higher-priced Gizmos to more affordable Widgets. Next Widget should also get a boost in revenues from its upcoming expansion into South America.
For now, Next Widget’s stock remains a buy.
Window 2: Second Analyst
Next Widget’s stock has skyrocketed over the past decade, reaching its all-time high of $113.17 per share on December 19, 2011—a 415% increase over its initial public offering share price in 2002—as the company’s revenues increased from $570 million in 2002 to $1.62 billion in 2011.
This run cannot continue. The revenue gains came mostly prior to 2009: The increases in the company’s top line of $210 million and $193 million in 2010 and 2011, respectively, were the smallest of the past decade. This trend is likely to continue in 2012, at least in the domestic market, given increased competition from the up-and-coming Widgitainers, Inc.
Furthermore, Next Widget’s planned expansion into South America may be trickier than expected. Even if successful in the long term, it will certainly contribute a loss in the near term, thus putting a strain on the company’s operating margins.
Now is a good time to sell your Next Widget stock.
Q: On the day of the first analyst’s report, Next Widget’s stock price was approximately what percent of its stock price at its initial public offering?
a)
245 %
b)
278 %
c)
345 %
d)
382 %
e)
482 %
|
|
Kiran Chauhan answered |
Calculation of Next Widget's stock price on the day of the first analyst's report:
Given data:
- All-time high stock price on December 19, 2011: $113.17 per share
- Initial public offering share price in 2002
- Current stock price on the day of the first analyst's report
Calculation:
1. Calculate the percentage increase from the initial public offering to the all-time high stock price:
Percentage increase = ((All-time high price - IPO price) / IPO price) x 100
= (($113.17 - IPO price) / IPO price) x 100
Given that the stock price increased by 415% from the IPO price to the all-time high price.
2. Determine the stock price on the day of the first analyst's report:
Given that the stock price decreased by 33% from its peak of $113.17 in late 2011.
3. Compare the stock price on the day of the first analyst's report to the IPO price to find the percentage relation.
Therefore, the stock price on the day of the first analyst's report was approximately 345% of its stock price at the initial public offering.
Given data:
- All-time high stock price on December 19, 2011: $113.17 per share
- Initial public offering share price in 2002
- Current stock price on the day of the first analyst's report
Calculation:
1. Calculate the percentage increase from the initial public offering to the all-time high stock price:
Percentage increase = ((All-time high price - IPO price) / IPO price) x 100
= (($113.17 - IPO price) / IPO price) x 100
Given that the stock price increased by 415% from the IPO price to the all-time high price.
2. Determine the stock price on the day of the first analyst's report:
Given that the stock price decreased by 33% from its peak of $113.17 in late 2011.
3. Compare the stock price on the day of the first analyst's report to the IPO price to find the percentage relation.
Therefore, the stock price on the day of the first analyst's report was approximately 345% of its stock price at the initial public offering.
Eggplants are always purple. John bought a purple vegetable. Therefore, it was an eggplant. Q. Which of the following arguments contains reasoning most similar to the flawed reasoning in the above argument?- a)Jenny always eats healthy. Salmon is a healthy food. Therefore, she eats salmon.
- b)Gambling is a risky hobby. Jamie likes taking risks. Therefore, she likes to gamble.
- c)Except for 2, prime numbers are always odd. The number 13 is odd. Therefore, it is prime.
- d)Rabbits are fast creatures. A fast creature ran by. Therefore, it may have been a rabbit.
- e)Bluebirds are not always blue. A brown bird was outside the window. Therefore, it may or may not have been a blue bird.
Correct answer is option 'C'. Can you explain this answer?
Eggplants are always purple. John bought a purple vegetable. Therefore, it was an eggplant.
Q. Which of the following arguments contains reasoning most similar to the flawed reasoning in the above argument?
a)
Jenny always eats healthy. Salmon is a healthy food. Therefore, she eats salmon.
b)
Gambling is a risky hobby. Jamie likes taking risks. Therefore, she likes to gamble.
c)
Except for 2, prime numbers are always odd. The number 13 is odd. Therefore, it is prime.
d)
Rabbits are fast creatures. A fast creature ran by. Therefore, it may have been a rabbit.
e)
Bluebirds are not always blue. A brown bird was outside the window. Therefore, it may or may not have been a blue bird.
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EduRev GMAT answered |
In this argument, the flaw is framed in the following way:
X is always Y. A is Y. Therefore, A is X.
(Just because X is always Y does NOT mean that Y is always X.)
The flawed argument is therefore most like:
Except for 2, prime numbers are always odd. The number 13 is odd. Therefore, it is prime.
Here
x = prime numbers
Y = odd
A = 13
The structure of this argument is the same as the structure argument in:
Eggplants are always purple. John bought a purple vegetable. Therefore, it was an eggplant.
X= eggplants
Y = purple
A = purple vegetable
Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 80% more than Bert had in savings, and separately, the same price was also 20% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
- a)1 : 4
- b)4 : 1
- c)3 : 4
- d)3 : 2
- e)2 : 3
Correct answer is option 'E'. Can you explain this answer?
Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 80% more than Bert had in savings, and separately, the same price was also 20% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.
a)
1 : 4
b)
4 : 1
c)
3 : 4
d)
3 : 2
e)
2 : 3
|
|
Palak Yadav answered |
Given Information:
Bert's savings = x
Rebecca's savings = y
Price of condominium = 80% more than Bert's savings = 1.8x
Price of condominium = 20% more than Rebecca's savings = 1.2y
Calculation:
1.8x = 1.2y
1.8/1.2 = y/x
1.5 = y/x
Ratio of Bert's savings to Rebecca's savings:
Therefore, the ratio of what Bert has in savings to what Rebecca has in savings is 3:2. So, the correct answer is option E.
If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > a
II. a + b + c + d = 0- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
- c)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient
- e)Statements (1) and (2) TOGETHER are NOT sufficient
Correct answer is option 'A'. Can you explain this answer?
If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?
I. m > a
II. a + b + c + d = 0
II. a + b + c + d = 0
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
c)
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient
e)
Statements (1) and (2) TOGETHER are NOT sufficient
|
|
Mihir Nambiar answered |
Understanding the Problem
We need to determine if the standard deviation (s) of integers a, b, c, and d is greater than 0. The average (m) is given by the formula:
m = (a + b + c + d) / 4
The standard deviation is 0 only if all values are identical; otherwise, it is greater than 0.
Analyzing the Statements
Statement I: m > a
- If m > a, it implies that the average of a, b, c, and d is greater than the value of a.
- For the average to be greater than a, at least one of the other integers (b, c, or d) must be greater than a, which means they cannot all be the same.
- Hence, different values exist among a, b, c, and d, indicating that the standard deviation s must be greater than 0.
Statement II: a + b + c + d = 0
- This equation implies that the sum of the four integers equals zero.
- It is possible for these integers to be equal, for example, if a = b = c = d = 0, then s = 0.
- Thus, this statement alone does not guarantee that s > 0, as it allows for the possibility of no variation among the integers.
Conclusion
- Statement I alone is sufficient to conclude that s > 0.
- Statement II does not provide enough information to make this conclusion.
Thus, the correct answer is option 'A': Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
We need to determine if the standard deviation (s) of integers a, b, c, and d is greater than 0. The average (m) is given by the formula:
m = (a + b + c + d) / 4
The standard deviation is 0 only if all values are identical; otherwise, it is greater than 0.
Analyzing the Statements
Statement I: m > a
- If m > a, it implies that the average of a, b, c, and d is greater than the value of a.
- For the average to be greater than a, at least one of the other integers (b, c, or d) must be greater than a, which means they cannot all be the same.
- Hence, different values exist among a, b, c, and d, indicating that the standard deviation s must be greater than 0.
Statement II: a + b + c + d = 0
- This equation implies that the sum of the four integers equals zero.
- It is possible for these integers to be equal, for example, if a = b = c = d = 0, then s = 0.
- Thus, this statement alone does not guarantee that s > 0, as it allows for the possibility of no variation among the integers.
Conclusion
- Statement I alone is sufficient to conclude that s > 0.
- Statement II does not provide enough information to make this conclusion.
Thus, the correct answer is option 'A': Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
There are two sets of letters, and you are going to pick exactly one letter from each set.Set #1 = {A, B, C, D, E}Set #2 = {K, L, M, N, O, P}What is the probability of picking a C and an M?- a)1/30
- b)1/15
- c)1/6
- d)1/5
- e)1/3
Correct answer is option 'A'. Can you explain this answer?
There are two sets of letters, and you are going to pick exactly one letter from each set.
Set #1 = {A, B, C, D, E}
Set #2 = {K, L, M, N, O, P}
What is the probability of picking a C and an M?
a)
1/30
b)
1/15
c)
1/6
d)
1/5
e)
1/3
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|
EduRev GMAT answered |
Whatever we pick from the first set is independent with whatever we pick from the second set, so we can use the simplified AND rule.
P(first pick = C) = 1/5
P(second pick = M) = 1/6
P(C and M) = P(C)*P(M) = (1/5)*(1/6) = 1/30
A certain school has three performing arts extracurricular activities: Band, Chorus, or Drama. Students must participate in at least one, and may participate in two or even in all three. There are 120 students in the school. There are 70 students in Band, 73 in the Chorus, and 45 in the Drama. Furthermore, 37 students are in both the Band and Chorus, 20 are in both the Band and the Drama, and 8 students are in all three groups. Twenty-five students are just in the chorus, not in anything else. How many students participate in only the drama?- a)11
- b)12
- c)14
- d)17
- e)21
Correct answer is option 'C'. Can you explain this answer?
A certain school has three performing arts extracurricular activities: Band, Chorus, or Drama. Students must participate in at least one, and may participate in two or even in all three. There are 120 students in the school. There are 70 students in Band, 73 in the Chorus, and 45 in the Drama. Furthermore, 37 students are in both the Band and Chorus, 20 are in both the Band and the Drama, and 8 students are in all three groups. Twenty-five students are just in the chorus, not in anything else. How many students participate in only the drama?
a)
11
b)
12
c)
14
d)
17
e)
21
|
|
Abhishek Choudhury answered |
Analysis:
To find out how many students participate in only the Drama extracurricular activity, we need to subtract the students who participate in multiple activities from the total number of Drama participants.
Given Information:
- Total number of students = 120
- Number of students in Band = 70
- Number of students in Chorus = 73
- Number of students in Drama = 45
- Number of students in Band and Chorus = 37
- Number of students in Band and Drama = 20
- Number of students in all three groups = 8
- Number of students in only Chorus = 25
Calculation:
First, we need to calculate the number of students who participate in multiple activities:
- Number of students in both Band and Chorus = 37
- Number of students in both Band and Drama = 20
- Number of students in all three groups = 8
Total number of students in multiple activities = 37 + 20 + 8 = 65
Now, we find the total number of students who participate in at least one activity:
Total number of students in at least one activity = Number of students in Band + Number of students in Chorus + Number of students in Drama - Total number of students in multiple activities
Total number of students in at least one activity = 70 + 73 + 45 - 65 = 123
Now, we find the number of students who participate in only the Drama extracurricular activity:
Number of students in only Drama = Number of students in Drama - Number of students in multiple activities
Number of students in only Drama = 45 - 65 = 14
Therefore, the number of students who participate in only the Drama extracurricular activity is 14, option c.
To find out how many students participate in only the Drama extracurricular activity, we need to subtract the students who participate in multiple activities from the total number of Drama participants.
Given Information:
- Total number of students = 120
- Number of students in Band = 70
- Number of students in Chorus = 73
- Number of students in Drama = 45
- Number of students in Band and Chorus = 37
- Number of students in Band and Drama = 20
- Number of students in all three groups = 8
- Number of students in only Chorus = 25
Calculation:
First, we need to calculate the number of students who participate in multiple activities:
- Number of students in both Band and Chorus = 37
- Number of students in both Band and Drama = 20
- Number of students in all three groups = 8
Total number of students in multiple activities = 37 + 20 + 8 = 65
Now, we find the total number of students who participate in at least one activity:
Total number of students in at least one activity = Number of students in Band + Number of students in Chorus + Number of students in Drama - Total number of students in multiple activities
Total number of students in at least one activity = 70 + 73 + 45 - 65 = 123
Now, we find the number of students who participate in only the Drama extracurricular activity:
Number of students in only Drama = Number of students in Drama - Number of students in multiple activities
Number of students in only Drama = 45 - 65 = 14
Therefore, the number of students who participate in only the Drama extracurricular activity is 14, option c.
Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?- a)5
- b)2
- c)9
- d)3
- e)7
Correct answer is option 'D'. Can you explain this answer?
Susan invited 13 of her friends for her birthday party and created return gift hampers comprising one each of $3, $4, and $5 gift certificates. One of her friends did not turn up and Susan decided to rework her gift hampers such that each of the 12 friends who turned up got $13 worth gift certificates. How many gift hampers did not contain $5 gift certificates in the new configuration?
a)
5
b)
2
c)
9
d)
3
e)
7
|
|
Nandita Chauhan answered |
Given information:
- 13 friends were invited to Susan's birthday party.
- Each return gift hamper originally contained $3, $4, and $5 gift certificates.
- One friend did not turn up, so Susan reworked the gift hampers for the 12 friends who attended.
- Each of the 12 friends who turned up received $13 worth of gift certificates in the new configuration.
Solution:
- Original Configuration:
- Total value of each gift hamper = $3 + $4 + $5 = $12
- Total value of 13 gift hampers = 13 * $12 = $156
- New Configuration:
- Total value of each gift hamper = $13
- Total value of 12 gift hampers = 12 * $13 = $156
- Calculating the number of $5 gift certificates in the new configuration:
- Each gift hamper in the new configuration has a total value of $13, which includes $3 and $4 gift certificates.
- Therefore, the number of $5 gift certificates in each gift hamper is calculated as: $13 - $3 - $4 = $6
- Number of gift hampers that did not contain $5 gift certificates = $6/$5 = 1.2
- Since we cannot have a fraction of a gift certificate, the number of gift hampers that did not contain $5 gift certificates is 1.
- Conclusion:
- The number of gift hampers that did not contain $5 gift certificates in the new configuration is 1.
Therefore, the correct answer is option D
A cost-effective solution to the problem of airport congestion is to provide high-speed ground transportation between major cities lying 200 to 500 miles apart. The successful implementation of this plan would cost far less than expanding existing airports and would also reduce the number of airplanes clogging both airports and airways.Q. Which of the following, if true, could be proponents of the plan above most appropriately cite as a piece of evidence for the soundness of their plan?- a)An effective high-speed ground-transportation system would require major repairs to many highways and mass-transit improvements.
- b)One-half of all departing flights in the nation's busiest airport head for a destination in a major city 225 miles away.
- c)The majority of travelers departing from rural airports are flying to destinations in cities over 600 miles away.
- d)Many new airports are being built in areas that are presently served by high-speed ground-transportation systems.
- e)A large proportion of air travelers are vacationers who are taking long-distance flights.
Correct answer is option 'B'. Can you explain this answer?
A cost-effective solution to the problem of airport congestion is to provide high-speed ground transportation between major cities lying 200 to 500 miles apart. The successful implementation of this plan would cost far less than expanding existing airports and would also reduce the number of airplanes clogging both airports and airways.
Q. Which of the following, if true, could be proponents of the plan above most appropriately cite as a piece of evidence for the soundness of their plan?
a)
An effective high-speed ground-transportation system would require major repairs to many highways and mass-transit improvements.
b)
One-half of all departing flights in the nation's busiest airport head for a destination in a major city 225 miles away.
c)
The majority of travelers departing from rural airports are flying to destinations in cities over 600 miles away.
d)
Many new airports are being built in areas that are presently served by high-speed ground-transportation systems.
e)
A large proportion of air travelers are vacationers who are taking long-distance flights.
|
|
EduRev GMAT answered |
The plan proposes that high-speed ground transportation would be a less expensive solution to airport congestion than would airport expansion. B indicates that between the cities to be served by the plan there is substantial air travel to which ground transportation would represent an alternative. Therefore, B is the best answer. No other choice could be cited appropriately. A and D both provide some evidence against the plan. A by emphasizing the likely costs of providing high-speed ground transportation is not by itself a solution to airport congestion. D by indicating that such an alternative is not by itself a solution to airport congestion. C and E say that there are many travelers for whom the proposed system would actually provide no alternative.
The average life expectancy for the United States population as a whole is 73.9 years, but children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7 years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their children would be expected to live longer than would be the case if the family remained in
Louisiana.
Q. Which of the following, if true, would most seriously weaken the conclusion drawn in the passage?- a)Insurance company statisticians do not believe that moving to Hawaii will significantly lengthen the average Louisianan's life.
- b)The governor of Louisiana has falsely alleged that statistics for his state are inaccurate.
- c)The longevity ascribed to Hawaii's current population is attributable mostly to genetically determined factors.
- d)Thirty percent of all Louisianans can expect to live longer than 77 years.
- e)Most of the Hawaiian Islands have levels of air pollution well below the national average for the United States.
Correct answer is option 'C'. Can you explain this answer?
The average life expectancy for the United States population as a whole is 73.9 years, but children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7 years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their children would be expected to live longer than would be the case if the family remained in
Louisiana.
Q. Which of the following, if true, would most seriously weaken the conclusion drawn in the passage?
Louisiana.
Q. Which of the following, if true, would most seriously weaken the conclusion drawn in the passage?
a)
Insurance company statisticians do not believe that moving to Hawaii will significantly lengthen the average Louisianan's life.
b)
The governor of Louisiana has falsely alleged that statistics for his state are inaccurate.
c)
The longevity ascribed to Hawaii's current population is attributable mostly to genetically determined factors.
d)
Thirty percent of all Louisianans can expect to live longer than 77 years.
e)
Most of the Hawaiian Islands have levels of air pollution well below the national average for the United States.
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EduRev GMAT answered |
This choice suggests that a significant proportion of Hawaii's population is genetically predisposed to be long lived. Since Louisianans are not necessarily so predisposed, and since the Louisianans' children will acquire their genetic characteristics from their parents, not from their birthplace, this choice presents a reason to doubt that Hawaiian born children of native Louisianans will have an increased life expectancy. Therefore, this choice is the best answer. Because the conclusion concerns people born in Hawaii, not the average Louisianan, A does not weaken the conclusion. Because the governor's allegation is false, it cannot affect the conclusion. D fails to weaken the conclusion because it is consistent with the information given and the conclusion about life expectancy. By suggesting that Hawaii's environment is in one respect particularly healthy, E supports the conclusion.
If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?
- a)1
- b)0
- c)2
- d)4
- e)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?
a)
1
b)
0
c)
2
d)
4
e)
Cannot be determined
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Gitanjali Kumar answered |
Given Information:
The given equations are:
1. y = |2 + x| - |2 - x|
2. |2x - 15| <>
Solution:
Analysis of Equation 1:
The expression y = |2 + x| - |2 - x| can be simplified as follows:
When x ≥ -2,
y = (2 + x) - (2 - x) = 2 + x - 2 + x = 2x
When x <>
y = -(2 + x) - (2 - x) = -2 - x - 2 + x = -4
So, the possible values of y are 2x and -4.
Analysis of Equation 2:
|2x - 15| <>
-2 < 2x="" -="" 15=""><>
13 < 2x=""><>
6.5 < x=""><>
The possible integer values for x are 7 and 8.
Combining the Results:
When x = 7, y = 2(7) = 14
When x = 8, y = 2(8) = 16
Therefore, the only possible integer values for y are 14 and 16. Hence, the correct answer is option 'A', which is 0 integer values for y.
The given equations are:
1. y = |2 + x| - |2 - x|
2. |2x - 15| <>
Solution:
Analysis of Equation 1:
The expression y = |2 + x| - |2 - x| can be simplified as follows:
When x ≥ -2,
y = (2 + x) - (2 - x) = 2 + x - 2 + x = 2x
When x <>
y = -(2 + x) - (2 - x) = -2 - x - 2 + x = -4
So, the possible values of y are 2x and -4.
Analysis of Equation 2:
|2x - 15| <>
-2 < 2x="" -="" 15=""><>
13 < 2x=""><>
6.5 < x=""><>
The possible integer values for x are 7 and 8.
Combining the Results:
When x = 7, y = 2(7) = 14
When x = 8, y = 2(8) = 16
Therefore, the only possible integer values for y are 14 and 16. Hence, the correct answer is option 'A', which is 0 integer values for y.
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