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All questions of Data Sufficiency for GMAT Exam
a < b. Is a positive?
1. b = 0.
2. √a < a- a)EACH statement ALONE is sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
a < b. Is a positive?
1. b = 0.
2. √a < a
1. b = 0.
2. √a < a
a)
EACH statement ALONE is sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
 | Shivam Ghoshal answered |
In statement 1, b =0, when a < b and b = 0, it implies that a < 0, hence, a is negative and a is not positive. The statement is sufficient.
In statement 2, √a < a, the square root of a number is defined only when in √a a > 0 . Hence, the statement is sufficient. Thus, EACH statement ALONE is sufficient to answer the question asked.
In statement 2, √a < a, the square root of a number is defined only when in √a a > 0 . Hence, the statement is sufficient. Thus, EACH statement ALONE is sufficient to answer the question asked.
Determine the size of an interior angle of the polygon.
1. The ratio of its interior angle to the exterior angle is 2:1.
2. The polygon is a regular hexagon- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)EACH statement ALONE is sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'B'. Can you explain this answer?
Determine the size of an interior angle of the polygon.
1. The ratio of its interior angle to the exterior angle is 2:1.
2. The polygon is a regular hexagon
1. The ratio of its interior angle to the exterior angle is 2:1.
2. The polygon is a regular hexagon
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
EACH statement ALONE is sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Hridoy Gupta answered |
Conclusion:
Since both statements independently lead to the determination that the interior angle is 120 degrees, each statement alone is sufficient.
The correct answer is:
EACH statement ALONE is sufficient to answer the question asked.
The area of a triangle is equal to the area of the rectangle. Find the perimeter of the rectangle.
1. The perimeter of the square is 24 inches.
2. The sum of the length and the width is 13 inches.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
The area of a triangle is equal to the area of the rectangle. Find the perimeter of the rectangle.
1. The perimeter of the square is 24 inches.
2. The sum of the length and the width is 13 inches.
1. The perimeter of the square is 24 inches.
2. The sum of the length and the width is 13 inches.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Anirban Das answered |
Explanation:
Let the sides of the square be s, and the length and width of the rectangle be l and w, respectively. We need to find the perimeter of the rectangle, which is 2(l+w).
Statement 1: The perimeter of the square is 24 inches.
This means that s=6 inches. Since the area of the triangle is equal to the area of the rectangle, we have (1/2)(s^2) = lw. So, (1/2)(6^2) = lw, which means lw=18. However, we cannot determine l and w from this statement alone, so it is not sufficient.
Statement 2: The sum of the length and the width is 13 inches.
This means that l+w=13. We cannot determine the area or the perimeter of the rectangle from this statement alone, so it is not sufficient.
Using both statements together, we know that lw=18 and l+w=13. We can solve for l and w using these equations: l=9 and w=4 (or vice versa). Now we can find the perimeter of the rectangle: 2(9+4) = 26 inches. Both statements together are sufficient to answer the question.
Let the sides of the square be s, and the length and width of the rectangle be l and w, respectively. We need to find the perimeter of the rectangle, which is 2(l+w).
Statement 1: The perimeter of the square is 24 inches.
This means that s=6 inches. Since the area of the triangle is equal to the area of the rectangle, we have (1/2)(s^2) = lw. So, (1/2)(6^2) = lw, which means lw=18. However, we cannot determine l and w from this statement alone, so it is not sufficient.
Statement 2: The sum of the length and the width is 13 inches.
This means that l+w=13. We cannot determine the area or the perimeter of the rectangle from this statement alone, so it is not sufficient.
Using both statements together, we know that lw=18 and l+w=13. We can solve for l and w using these equations: l=9 and w=4 (or vice versa). Now we can find the perimeter of the rectangle: 2(9+4) = 26 inches. Both statements together are sufficient to answer the question.
Two numbers 12 and t are two positive numbers with some similar properties. What is the value of t.
1. The Least Common Multiple of the two numbers 48.
2. The Greatest Common divisor of the two numbers is 4.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
Two numbers 12 and t are two positive numbers with some similar properties. What is the value of t.
1. The Least Common Multiple of the two numbers 48.
2. The Greatest Common divisor of the two numbers is 4.
1. The Least Common Multiple of the two numbers 48.
2. The Greatest Common divisor of the two numbers is 4.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Shivam Ghoshal answered |
We consider 12 and t.
In statement 1, the Least Common multiple of 12 and t is 48 to mean that t is a factor of 48. This mean that, t can take 16, 24 and 48. Hence the statement is not sufficient.
In statement 2, the Greatest Common divisor is 4. Therefore, t can take 4, 8, 16, 28, 32, 40 among others. Thus, the statement is not sufficient.
Combining statements 1and 2, we have 16 featuring in both lists, hence it satisfies the two conditions. Therefore, t =16. Thus BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
In statement 1, the Least Common multiple of 12 and t is 48 to mean that t is a factor of 48. This mean that, t can take 16, 24 and 48. Hence the statement is not sufficient.
In statement 2, the Greatest Common divisor is 4. Therefore, t can take 4, 8, 16, 28, 32, 40 among others. Thus, the statement is not sufficient.
Combining statements 1and 2, we have 16 featuring in both lists, hence it satisfies the two conditions. Therefore, t =16. Thus BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Determine the equation of the circle passing through (-4,-2).
1. (1,-1) lies in the circle.
2. The center of the circle is the origin.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'B'. Can you explain this answer?
Determine the equation of the circle passing through (-4,-2).
1. (1,-1) lies in the circle.
2. The center of the circle is the origin.
1. (1,-1) lies in the circle.
2. The center of the circle is the origin.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
 | Avantika Sengupta answered |
Statement (2) alone is sufficient to answer the question asked.
Explanation:
For a circle passing through (-4,-2) and with the center at the origin, the equation of the circle can be written as:
(x - 0)^2 + (y - 0)^2 = r^2
where r is the radius of the circle.
Now, let's consider statement (1):
(1,-1) lies in the circle.
If we substitute this point in the equation of the circle, we get:
(1 - 0)^2 + (-1 - 0)^2 = r^2
which simplifies to:
2 = r^2
So, we know the value of r, but we still don't have the equation of the circle.
On the other hand, statement (2) tells us that the center of the circle is at the origin. This means that we can write the equation of the circle as:
x^2 + y^2 = r^2
where r is the radius of the circle that we found in statement (1).
Therefore, statement (2) alone is sufficient to answer the question asked, and the correct answer is option (B).
Explanation:
For a circle passing through (-4,-2) and with the center at the origin, the equation of the circle can be written as:
(x - 0)^2 + (y - 0)^2 = r^2
where r is the radius of the circle.
Now, let's consider statement (1):
(1,-1) lies in the circle.
If we substitute this point in the equation of the circle, we get:
(1 - 0)^2 + (-1 - 0)^2 = r^2
which simplifies to:
2 = r^2
So, we know the value of r, but we still don't have the equation of the circle.
On the other hand, statement (2) tells us that the center of the circle is at the origin. This means that we can write the equation of the circle as:
x^2 + y^2 = r^2
where r is the radius of the circle that we found in statement (1).
Therefore, statement (2) alone is sufficient to answer the question asked, and the correct answer is option (B).
Find out if t < 0.
1. |t| > t
2. t2 > 0- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
Find out if t < 0.
1. |t| > t
2. t2 > 0
1. |t| > t
2. t2 > 0
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Shivam Ghoshal answered |
In statement 1, |t| > t. But is |-t| = |t|. Hence t can be positive or negative. When |t| > t, it implies that t is a negative value, hence t < 0. The statement is sufficient.
In statement 2, t2 > 0 , but when t is negative or positive, t2 > 0 , hence the statement is not sufficient. Thus Statement (1) ALONE is sufficient but statement (2) is not sufficient.
In statement 2, t2 > 0 , but when t is negative or positive, t2 > 0 , hence the statement is not sufficient. Thus Statement (1) ALONE is sufficient but statement (2) is not sufficient.
Find the percentage change in the volume of cylinder.
1. The diameter is increased by 20%.
2. The height is increased by 21%.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Find the percentage change in the volume of cylinder.
1. The diameter is increased by 20%.
2. The height is increased by 21%.
1. The diameter is increased by 20%.
2. The height is increased by 21%.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Shivam Ghoshal answered |
The volume of the cylinder is given buy v = πr²h.
In statement 1, diameter (d) is increased by 20%, hence the radius is increased by 10%. The new radius is given by 1.1r. The new volume = π(1.1r)²h = 1.21πr²h
Percentage change in volume = (1.21πr²h - πr²h )/pr²h × 100% = 21%. The statement is sufficient.
In statement 2, height is increased by 21%, hence the new height is 1.21h. The new volume = 1.21πr²h.
Percentage change in volume = (1.21πr²h - πr²h )/πr²h × 100% = 21%. The statement is sufficient. Therefore, EACH statement ALONE is sufficient.
In statement 1, diameter (d) is increased by 20%, hence the radius is increased by 10%. The new radius is given by 1.1r. The new volume = π(1.1r)²h = 1.21πr²h
Percentage change in volume = (1.21πr²h - πr²h )/pr²h × 100% = 21%. The statement is sufficient.
In statement 2, height is increased by 21%, hence the new height is 1.21h. The new volume = 1.21πr²h.
Percentage change in volume = (1.21πr²h - πr²h )/πr²h × 100% = 21%. The statement is sufficient. Therefore, EACH statement ALONE is sufficient.
Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?
I. The maximum possible range of the set is greater than 33.
II. The median can never be an even number.
III. If y = 37, the average of the set will be greater than the median.- a)I only
- b)I and II only
- c)I, II, and III
- d)III only
Correct answer is option 'C'. Can you explain this answer?
Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?
I. The maximum possible range of the set is greater than 33.
II. The median can never be an even number.
III. If y = 37, the average of the set will be greater than the median.
I. The maximum possible range of the set is greater than 33.
II. The median can never be an even number.
III. If y = 37, the average of the set will be greater than the median.
a)
I only
b)
I and II only
c)
I, II, and III
d)
III only
 | EduRev GMAT answered |
Step 1: Key Data from the Question
Set S has 6 elements.
The elements of set S are distinct.
x and y are prime numbers. Because 2 is already an element in S, both x and y have to be odd.
0 < x < 40 and 0 < y < 40
The elements of set S are distinct.
x and y are prime numbers. Because 2 is already an element in S, both x and y have to be odd.
0 < x < 40 and 0 < y < 40
Step 2: Check Statement I
I. The maximum possible range of the set is greater than 33.
The keyword in this entire statement is maximum. We have to determine whether the maximum value possible for the range exceeds 33.
We know x and y are prime numbers. The largest prime number less than 40 is 37.
If either x or y is 37, the largest number in the set will be 37 and the smallest number is 2.
Therefore, the maximum range of the set will be 37 - 2 = 35. It is greater than 33.
The keyword in this entire statement is maximum. We have to determine whether the maximum value possible for the range exceeds 33.
We know x and y are prime numbers. The largest prime number less than 40 is 37.
If either x or y is 37, the largest number in the set will be 37 and the smallest number is 2.
Therefore, the maximum range of the set will be 37 - 2 = 35. It is greater than 33.
Statement I is true. So, eliminate choices that do not contain I.
Eliminate choice D
Eliminate choice D
Step 3: Check Statement II
II. The median can never be an even number.
There are 6 numbers in the set. Therefore, the median is the arithmetic mean of the 3rd and the 4th term when the numbers are written in ascending or descending order.
The elements are {2, 4, 6, 8, x, y}, where x and y are prime numbers.
If x and y take 3 and 5 as values, the median is 4.5
If x = 3, y = 7 or greater, the median is 5.
If x = 5, y = 7 or greater, the median is 5.5
If x = 7, y = 11 or greater, the median is 6.5
If x = 11 or greater and y = 13 or greater, the median is 7.
It is quite clear that the median is either an odd number or is not an interger. So, the median can never be an even integer.
There are 6 numbers in the set. Therefore, the median is the arithmetic mean of the 3rd and the 4th term when the numbers are written in ascending or descending order.
The elements are {2, 4, 6, 8, x, y}, where x and y are prime numbers.
If x and y take 3 and 5 as values, the median is 4.5
If x = 3, y = 7 or greater, the median is 5.
If x = 5, y = 7 or greater, the median is 5.5
If x = 7, y = 11 or greater, the median is 6.5
If x = 11 or greater and y = 13 or greater, the median is 7.
It is quite clear that the median is either an odd number or is not an interger. So, the median can never be an even integer.
Statement II is true. Eliminate choices that do not contain II.
Eliminate choices A and C as well.
Eliminate choices A and C as well.
Step 4: Check Statement III
III. If y = 37, the average of the set will be greater than the median.
If y = 37, the set will be {2, 4, 6, 8, x, 37}, where x is a prime number greater than 2 and less than 37.
The average will be 57 + x657 + x6 = 9.5 + x6x6
If x = 3, median = 5 and average = 10. Average > median.
If x = 5, median = 5.5 and average = 10.33. Average > median
If x = 7, median = 6.5 and average = 10.66. Average > medain
If x = 11 or greater, the median = 7. Average will be definitely greater than 10. So, Average > Median.
It is true that the average is greater than the median if y = 37.
If y = 37, the set will be {2, 4, 6, 8, x, 37}, where x is a prime number greater than 2 and less than 37.
The average will be 57 + x657 + x6 = 9.5 + x6x6
If x = 3, median = 5 and average = 10. Average > median.
If x = 5, median = 5.5 and average = 10.33. Average > median
If x = 7, median = 6.5 and average = 10.66. Average > medain
If x = 11 or greater, the median = 7. Average will be definitely greater than 10. So, Average > Median.
It is true that the average is greater than the median if y = 37.
Statement III is also true.
Statements I, II, and III are true.
Statements I, II, and III are true.
Choice C is the correct answer.
Determine the value of angle k.
1. Angle k and m lies on a straight line.
2. Angle m = 39° .- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
Determine the value of angle k.
1. Angle k and m lies on a straight line.
2. Angle m = 39° .
1. Angle k and m lies on a straight line.
2. Angle m = 39° .
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Navya Yadav answered |
Unfortunately, without additional information, we cannot determine the value of angle k.
Is A an obtuse angle?
1. A is more than 90°.
2. A is a supplement of an angle B, an acute triangle.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'B'. Can you explain this answer?
Is A an obtuse angle?
1. A is more than 90°.
2. A is a supplement of an angle B, an acute triangle.
1. A is more than 90°.
2. A is a supplement of an angle B, an acute triangle.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Aditya Gupta answered |
Yes, if A is more than 90 degrees, it is an obtuse angle.
Ann deposited $3000 in her bank account at the beginning of the year. Determine the amount the funds accumulated to.
1. The bank offered 4.3% interest rate.
2. The amount was deposited for a period of 5 years.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Ann deposited $3000 in her bank account at the beginning of the year. Determine the amount the funds accumulated to.
1. The bank offered 4.3% interest rate.
2. The amount was deposited for a period of 5 years.
1. The bank offered 4.3% interest rate.
2. The amount was deposited for a period of 5 years.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Prisha Mukherjee answered |
Deposit (P) = 3000.
Accumulated amount = P + (1 + R/100)n where the variables have their usual meaning for compound interest and
Accumulated amount = P + (P × r/100 × n) where the variables have their usual meaning for simple interest.
In statement 1, r = 4.3 and P = 3000 but we are not given the value of n, hence we cannot find the accumulated amount. Further more, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
In statement 2, n = 5 and P = 3000 but we are not given the value of r, hence we cannot find the accumulated amount. Furthermore, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
Combining the two statements, P = 3000, r = 4.5 and n = 5 but, the details given are not sufficient since no specific type on interest is disclosed, therefore, we cannot apply the compound or simple interest formula with accuracy. Thus Statements (1) and (2) TOGETHER are NOT sufficient.
Accumulated amount = P + (1 + R/100)n where the variables have their usual meaning for compound interest and
Accumulated amount = P + (P × r/100 × n) where the variables have their usual meaning for simple interest.
In statement 1, r = 4.3 and P = 3000 but we are not given the value of n, hence we cannot find the accumulated amount. Further more, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
In statement 2, n = 5 and P = 3000 but we are not given the value of r, hence we cannot find the accumulated amount. Furthermore, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
Combining the two statements, P = 3000, r = 4.5 and n = 5 but, the details given are not sufficient since no specific type on interest is disclosed, therefore, we cannot apply the compound or simple interest formula with accuracy. Thus Statements (1) and (2) TOGETHER are NOT sufficient.
Are the two lines L1 and L2 parallel?
1. Both lines lie in the first, second and fourth quadrants.
2. The y intercepts of the lines L1 and L2 are 8 and 4 respectively.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Are the two lines L1 and L2 parallel?
1. Both lines lie in the first, second and fourth quadrants.
2. The y intercepts of the lines L1 and L2 are 8 and 4 respectively.
1. Both lines lie in the first, second and fourth quadrants.
2. The y intercepts of the lines L1 and L2 are 8 and 4 respectively.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Shivam Ghoshal answered |
Parallel lines have equal slopes.
In statement 1, if both lines are in the first, second and fourth quadrant then they have a negative slope. This alone is not enough to prove that they are parallel or not, hence, the statement is insufficient.
In statement 2, the y intercepts are 8 and 4 to imply that the equation are of the form y = mx + 8 and y = bx + 4. But this does not enough to determine if the lines area parallel since, notheing is said about the value of m and b, hence, the statement too is insufficient.
Combining the two statements, we have equations having negative gradients, thus, y =-mx + 8 and y = -bx + 4. Since we are not sure of -m = -b, we cannot say that they are parallel on not. Therefore, Statements (1) and (2) TOGETHER are NOT sufficient.
In statement 1, if both lines are in the first, second and fourth quadrant then they have a negative slope. This alone is not enough to prove that they are parallel or not, hence, the statement is insufficient.
In statement 2, the y intercepts are 8 and 4 to imply that the equation are of the form y = mx + 8 and y = bx + 4. But this does not enough to determine if the lines area parallel since, notheing is said about the value of m and b, hence, the statement too is insufficient.
Combining the two statements, we have equations having negative gradients, thus, y =-mx + 8 and y = -bx + 4. Since we are not sure of -m = -b, we cannot say that they are parallel on not. Therefore, Statements (1) and (2) TOGETHER are NOT sufficient.
Two pipes supply waters to a cistern whose capacity of 15 cubic feet. How long does it take the two pipes to fill the cistern?
1. The first pipe supplies water at a rate (per minute) that is thrice faster than the second pipe.
2. The pipes fill 8 cubic feet of the tank in ten minute.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'B'. Can you explain this answer?
Two pipes supply waters to a cistern whose capacity of 15 cubic feet. How long does it take the two pipes to fill the cistern?
1. The first pipe supplies water at a rate (per minute) that is thrice faster than the second pipe.
2. The pipes fill 8 cubic feet of the tank in ten minute.
1. The first pipe supplies water at a rate (per minute) that is thrice faster than the second pipe.
2. The pipes fill 8 cubic feet of the tank in ten minute.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Sankar Desai answered |
Statement 1:
The first pipe supplies water at a rate (per minute) that is thrice faster than the second pipe.
This statement provides information about the relative rates of the two pipes. Let's assume that the second pipe fills the cistern in 'x' minutes. Therefore, the first pipe, which is thrice as fast, will fill the cistern in 'x/3' minutes.
Statement 2:
The pipes fill 8 cubic feet of the tank in ten minutes.
This statement provides information about the combined rate of both pipes. In ten minutes, the pipes fill 8 cubic feet of the tank.
Combined analysis:
From statement 1, we know that the first pipe fills the cistern in 'x/3' minutes, and the second pipe fills it in 'x' minutes.
In one minute, the combined rate of both pipes is (1/x + 1/(x/3)) = (1/x + 3/x) = 4/x.
From statement 2, we know that in ten minutes, the pipes fill 8 cubic feet of the tank.
Therefore, in one minute, the combined rate of both pipes is 8/10 = 4/5.
Now we have two equations:
4/x = 4/5
x = 5
Conclusion:
We can determine that it takes the second pipe 5 minutes to fill the cistern on its own. Therefore, statement 2 alone is sufficient to answer the question, but statement 1 alone is not. Hence, the correct answer is option B.
The first pipe supplies water at a rate (per minute) that is thrice faster than the second pipe.
This statement provides information about the relative rates of the two pipes. Let's assume that the second pipe fills the cistern in 'x' minutes. Therefore, the first pipe, which is thrice as fast, will fill the cistern in 'x/3' minutes.
Statement 2:
The pipes fill 8 cubic feet of the tank in ten minutes.
This statement provides information about the combined rate of both pipes. In ten minutes, the pipes fill 8 cubic feet of the tank.
Combined analysis:
From statement 1, we know that the first pipe fills the cistern in 'x/3' minutes, and the second pipe fills it in 'x' minutes.
In one minute, the combined rate of both pipes is (1/x + 1/(x/3)) = (1/x + 3/x) = 4/x.
From statement 2, we know that in ten minutes, the pipes fill 8 cubic feet of the tank.
Therefore, in one minute, the combined rate of both pipes is 8/10 = 4/5.
Now we have two equations:
4/x = 4/5
x = 5
Conclusion:
We can determine that it takes the second pipe 5 minutes to fill the cistern on its own. Therefore, statement 2 alone is sufficient to answer the question, but statement 1 alone is not. Hence, the correct answer is option B.
Determine the area of a triangle A.
1. Triangle A and B are similar with a linear scale factor of 7 : 10.
2. B is larger than A.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Determine the area of a triangle A.
1. Triangle A and B are similar with a linear scale factor of 7 : 10.
2. B is larger than A.
1. Triangle A and B are similar with a linear scale factor of 7 : 10.
2. B is larger than A.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Nilotpal Sen answered |
Statement 1: Triangle A and B are similar with a linear scale factor of 7:10.
Statement 2: B is larger than A.
To determine the area of triangle A, we need to know the specific measurements of the triangle. However, neither statement alone provides us with enough information to calculate the area of triangle A. Let's analyze each statement separately.
Statement 1: Triangle A and B are similar with a linear scale factor of 7:10.
This statement tells us that the ratio of corresponding sides of triangles A and B is 7:10. However, it doesn't provide us with any information about the specific lengths of the sides or the height of triangle A. Therefore, we cannot determine the area of triangle A based on this statement alone.
Statement 2: B is larger than A.
This statement tells us that triangle B is larger than triangle A, but it doesn't provide any information about the specific measurements of either triangle. Without knowing the measurements of triangle A, we cannot calculate its area based on this statement alone.
Both Statements Together:
When we consider both statements together, we still don't have enough information to calculate the area of triangle A. While statement 1 tells us about the similarity between the triangles, it doesn't provide any specific measurements. And statement 2 only tells us that triangle B is larger than A, but it doesn't give us any measurements either.
Therefore, the correct answer is option E: Statements (1) and (2) together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Statement 2: B is larger than A.
To determine the area of triangle A, we need to know the specific measurements of the triangle. However, neither statement alone provides us with enough information to calculate the area of triangle A. Let's analyze each statement separately.
Statement 1: Triangle A and B are similar with a linear scale factor of 7:10.
This statement tells us that the ratio of corresponding sides of triangles A and B is 7:10. However, it doesn't provide us with any information about the specific lengths of the sides or the height of triangle A. Therefore, we cannot determine the area of triangle A based on this statement alone.
Statement 2: B is larger than A.
This statement tells us that triangle B is larger than triangle A, but it doesn't provide any information about the specific measurements of either triangle. Without knowing the measurements of triangle A, we cannot calculate its area based on this statement alone.
Both Statements Together:
When we consider both statements together, we still don't have enough information to calculate the area of triangle A. While statement 1 tells us about the similarity between the triangles, it doesn't provide any specific measurements. And statement 2 only tells us that triangle B is larger than A, but it doesn't give us any measurements either.
Therefore, the correct answer is option E: Statements (1) and (2) together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Find the equation of a line.
1. Its x and y intercept is 2 and -2 respectively.
2. The slope of the line is 1.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
Find the equation of a line.
1. Its x and y intercept is 2 and -2 respectively.
2. The slope of the line is 1.
1. Its x and y intercept is 2 and -2 respectively.
2. The slope of the line is 1.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Shivam Ghoshal answered |
In statement 1, the x and y intercept is 2 and -2 respectively, hence the line passes through (2,0) and (0,-2). The slope is
(-2 - 0)/(2 - 0) = -1.
The equation is y/(x - 2) = -1 hence x = -x + 2.
The statement is sufficient.
In statement 2, the slope is 1. Since we are not given any point where the line is passing, the statement is insufficient. Thus, Statement (1) ALONE is sufficient but statement (2) is not sufficient.
(-2 - 0)/(2 - 0) = -1.
The equation is y/(x - 2) = -1 hence x = -x + 2.
The statement is sufficient.
In statement 2, the slope is 1. Since we are not given any point where the line is passing, the statement is insufficient. Thus, Statement (1) ALONE is sufficient but statement (2) is not sufficient.
The ratio of water to alcohol in a 14 cup container is 2:5. Determine the new volume of the liquid in the container.
1. Water is increased by 14%.
2. Mixture whose ratio of water to alcohol is 4:5 is added to that in the container.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
The ratio of water to alcohol in a 14 cup container is 2:5. Determine the new volume of the liquid in the container.
1. Water is increased by 14%.
2. Mixture whose ratio of water to alcohol is 4:5 is added to that in the container.
1. Water is increased by 14%.
2. Mixture whose ratio of water to alcohol is 4:5 is added to that in the container.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Aditya Gupta answered |
Ratio water : alcohol = 2 : 5.
To imply that water = 2/7 × 14 = 4 cups
Alcohol = 14 - 4 = 10 cups.
If water is increased by 14%, we have
new capacity of water =114/100 × 4 = 4.56 cups.
The new volume of the liquid is 10 + 4.56 cups. Hence the statement is sufficient.
In statement 2, ratio of water : alcohol = 4 : 5 but we are not told the quantity of the liquid added or the quantity of water or alcohol added, hence, the statement is not sufficient.
To imply that water = 2/7 × 14 = 4 cups
Alcohol = 14 - 4 = 10 cups.
If water is increased by 14%, we have
new capacity of water =114/100 × 4 = 4.56 cups.
The new volume of the liquid is 10 + 4.56 cups. Hence the statement is sufficient.
In statement 2, ratio of water : alcohol = 4 : 5 but we are not told the quantity of the liquid added or the quantity of water or alcohol added, hence, the statement is not sufficient.
Is 2x + 1 > 0.
1. x is an integer
2. |x| < 1.5- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Is 2x + 1 > 0.
1. x is an integer
2. |x| < 1.5
1. x is an integer
2. |x| < 1.5
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Parth Singh answered |
2x + 1 > 0
In statement 1, a is an integer, when x = -2, 2x + 1 = -3 < 0. When x = 2, 2x + 1 = 5 > 0, hence the statement is not sufficient.
In statement 2, |x| < 1.5 implies that -1.5 < x < 1.5.
When x = 1.4, 2x + 1 = 3.8 > 0. When x = -1.4, 2x + 1 = -1.8 < 0.
Hence, the statement is not sufficient.
Combining the two statements, we have, x, an integer and -1.5 < x < 1.5, considering the more strict condition, -1.5 < x < 1.5, we find that 2x + 1 < 0, when x = -1.4 and 2x + 1 > 0 when x = 1.4.
Therefore, Statements (1) and (2) TOGETHER are NOT sufficient.
In statement 1, a is an integer, when x = -2, 2x + 1 = -3 < 0. When x = 2, 2x + 1 = 5 > 0, hence the statement is not sufficient.
In statement 2, |x| < 1.5 implies that -1.5 < x < 1.5.
When x = 1.4, 2x + 1 = 3.8 > 0. When x = -1.4, 2x + 1 = -1.8 < 0.
Hence, the statement is not sufficient.
Combining the two statements, we have, x, an integer and -1.5 < x < 1.5, considering the more strict condition, -1.5 < x < 1.5, we find that 2x + 1 < 0, when x = -1.4 and 2x + 1 > 0 when x = 1.4.
Therefore, Statements (1) and (2) TOGETHER are NOT sufficient.
Find the direction in which the parabola y = ax2 + bx - 2 is facing.
1. a = b
2. a < 0- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'B'. Can you explain this answer?
Find the direction in which the parabola y = ax2 + bx - 2 is facing.
1. a = b
2. a < 0
1. a = b
2. a < 0
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Abhishek Kapoor answered |
The parabola y = ax2 + bx - 2 faces upwards when a > 0 and downwards when a < 0.
In statement 1, a = b, this does not give the numerical equivalent to a, hence it is not sufficient.
In statement 2, a < 0, hence the parabola faces downwards. Thus the statement is sufficient.
In statement 1, a = b, this does not give the numerical equivalent to a, hence it is not sufficient.
In statement 2, a < 0, hence the parabola faces downwards. Thus the statement is sufficient.
Stephenson, a businessman bought an Iron box for $80. Determine his profit.
1. He made a 30% profit.
2. His selling price was $104.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Stephenson, a businessman bought an Iron box for $80. Determine his profit.
1. He made a 30% profit.
2. His selling price was $104.
1. He made a 30% profit.
2. His selling price was $104.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Geetika Sarkar answered |
Cost price = $80 is equivalent to 100%.
In statement 1, profit = 30%
= 30/100 × 80 = $24.
Profit = 104 - 80 = $24. The statement is sufficient.
In statement 2, selling price = 104.
selling price = cost price + profit; hence, profit =104 - 80 = $24. The statement is sufficient.
In statement 1, profit = 30%
= 30/100 × 80 = $24.
Profit = 104 - 80 = $24. The statement is sufficient.
In statement 2, selling price = 104.
selling price = cost price + profit; hence, profit =104 - 80 = $24. The statement is sufficient.
Determine the price of two type A footballs if the total cost of a type A and a type B football is $500.
1. Type B football costs $200.
2. Two type A and three type B footballs costs $1200.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Determine the price of two type A footballs if the total cost of a type A and a type B football is $500.
1. Type B football costs $200.
2. Two type A and three type B footballs costs $1200.
1. Type B football costs $200.
2. Two type A and three type B footballs costs $1200.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Maya Khanna answered |
Let A and B represent the number of type A and Type B footballs respectively. Then A + B = 500.
In statement 1, B = 200, hence, from A + B = 500, A = 500 - B = 500 - 200 = $300. Thus 2A = $600. The statement is sufficient.
In statement 2, 2A + 3B = 1200, from A + B = 500,multiplying it by 3, we have 3A + 3B = 1500. Subtracting 2A + 3B = 1200 from 3A + 3B = 1500, we have A = 300; thus 2A = $600. The statement too is sufficient.
In statement 1, B = 200, hence, from A + B = 500, A = 500 - B = 500 - 200 = $300. Thus 2A = $600. The statement is sufficient.
In statement 2, 2A + 3B = 1200, from A + B = 500,multiplying it by 3, we have 3A + 3B = 1500. Subtracting 2A + 3B = 1200 from 3A + 3B = 1500, we have A = 300; thus 2A = $600. The statement too is sufficient.
A straight line L passes through (2,8) and the origin. Find the equation of a line perpendicular to L.
1. The line passes through the origin.
2. The line passes through (2,-0.5).- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
A straight line L passes through (2,8) and the origin. Find the equation of a line perpendicular to L.
1. The line passes through the origin.
2. The line passes through (2,-0.5).
1. The line passes through the origin.
2. The line passes through (2,-0.5).
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Shivam Ghoshal answered |
The line L passes through (2,8) and (0,0) hence its slope is
slope = (8 - 0)/(2 - 0) = 4.
Since L is perpendicular to the line in question, the product of their slope is -1. Therefore, the slope of the line in question is -1/4.
In statement 1, the line passes the origin, (0,0) and its slope is -1/4 hence its equation is y = -x/4. The statement is sufficient.
In statement 2, line passes through the (2,0.5) and its slope is -1/4. Thus we have (y + 0.5)/(x - 2) = -1/4
y + 1/2 = -x/4 + 1/2
thus y = -x/4. The statement is sufficient too.
Thus, EACH statement ALONE is sufficient.
slope = (8 - 0)/(2 - 0) = 4.
Since L is perpendicular to the line in question, the product of their slope is -1. Therefore, the slope of the line in question is -1/4.
In statement 1, the line passes the origin, (0,0) and its slope is -1/4 hence its equation is y = -x/4. The statement is sufficient.
In statement 2, line passes through the (2,0.5) and its slope is -1/4. Thus we have (y + 0.5)/(x - 2) = -1/4
y + 1/2 = -x/4 + 1/2
thus y = -x/4. The statement is sufficient too.
Thus, EACH statement ALONE is sufficient.
Determine the volume of a cuboids.
1. The length is twice the width and the height is 4 inches.
2. The length is 6 inches.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
Determine the volume of a cuboids.
1. The length is twice the width and the height is 4 inches.
2. The length is 6 inches.
1. The length is twice the width and the height is 4 inches.
2. The length is 6 inches.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Maya Khanna answered |
Volume = length × width × height
In statement 1, let width be x, length = 2x and height = 4
Volume = x × 2x × 4 = 8x² cubic inches. Since it is in terms of unknown value, x, it is insufficient.
In statement 2, length = 6 inches but the width and height is unknown hence it is not sufficient to determine the volume.
Combining the two statements, length = 2x = 6 hence x = 3 inches.
width = 3 inches and height = 4 inches.
Volume = 3 × 4 × 6 = 72 cubic inches. Thus , BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
In statement 1, let width be x, length = 2x and height = 4
Volume = x × 2x × 4 = 8x² cubic inches. Since it is in terms of unknown value, x, it is insufficient.
In statement 2, length = 6 inches but the width and height is unknown hence it is not sufficient to determine the volume.
Combining the two statements, length = 2x = 6 hence x = 3 inches.
width = 3 inches and height = 4 inches.
Volume = 3 × 4 × 6 = 72 cubic inches. Thus , BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Find the value of r if 4r + 2t = 14.
1. t = 2.
2. r > t.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
Find the value of r if 4r + 2t = 14.
1. t = 2.
2. r > t.
1. t = 2.
2. r > t.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Aditya Sharma answered |
4r + 2t = 14
In statement 1, t = 2, substituting for t in 4r + 2t = 14, we have
4r + 4 = 14; 4r = 10; r = 2 1/2. The statement is sufficient.
In statement 2, r > t , thus none of this is assigned a numeric value. Thisa implies that the solution of r in 4r + 2t = 14 will be a set of values. This implies that the statement is not sufficient.
In statement 1, t = 2, substituting for t in 4r + 2t = 14, we have
4r + 4 = 14; 4r = 10; r = 2 1/2. The statement is sufficient.
In statement 2, r > t , thus none of this is assigned a numeric value. Thisa implies that the solution of r in 4r + 2t = 14 will be a set of values. This implies that the statement is not sufficient.
A particle moving in air increases its speed within 30 minutes. Find its acceleration.
1. Its initial velocity is 20miles per hour and its final velocity is 25 miles per hour.
2. The particle increases its speed by 5 miles per hour.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
A particle moving in air increases its speed within 30 minutes. Find its acceleration.
1. Its initial velocity is 20miles per hour and its final velocity is 25 miles per hour.
2. The particle increases its speed by 5 miles per hour.
1. Its initial velocity is 20miles per hour and its final velocity is 25 miles per hour.
2. The particle increases its speed by 5 miles per hour.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Hridoy Desai answered |
Time taken = change in time = 30 minutes = 1/2 hours
In statement 1, Initial velocity (v1) = 20 miles per hour and change in time = 0.5 hours (given)
Final velocity (v2) = 25 miles per hour.
Acceleration = (v2 - v1)/ change in time = (25 - 20)/ 0.5 = 10 miles per hour per hour. Therefore, the statement is sufficient.
In statement 2, Change in velocity = 5 miles per hour and change in time = 0.5 hours (given).
Acceleration = Change in velocity/change in time = 5/0.5 =10 miles per hour per hour. Therefore, the statement is sufficient.
Therefore, EACH statement ALONE is sufficient.
In statement 1, Initial velocity (v1) = 20 miles per hour and change in time = 0.5 hours (given)
Final velocity (v2) = 25 miles per hour.
Acceleration = (v2 - v1)/ change in time = (25 - 20)/ 0.5 = 10 miles per hour per hour. Therefore, the statement is sufficient.
In statement 2, Change in velocity = 5 miles per hour and change in time = 0.5 hours (given).
Acceleration = Change in velocity/change in time = 5/0.5 =10 miles per hour per hour. Therefore, the statement is sufficient.
Therefore, EACH statement ALONE is sufficient.
What is the cost of one pen?1. The cost of 3 pens and 2 pencils is ₹80.2. The cost of 2 pens and 2 pencils is ₹70, and each pencil costs ₹10.- 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.
Correct answer is option 'C'. Can you explain this answer?
What is the cost of one pen?
1. The cost of 3 pens and 2 pencils is ₹80.
2. The cost of 2 pens and 2 pencils is ₹70, and each pencil costs ₹10.
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.
| | EduRev GMAT answered |
Let cost of pen = P, pencil = Q.
From (1): 3P + 2Q = 80 — (i)
From (2): 2P + 2Q = 70 and Q = 10
Substitute Q = 10 into both equations:
From (2): 2P + 20 = 70 → 2P = 50 → P = 25
From (1): 3P + 20 = 80 → 3P = 60 → P = 20
Conflict in values shows contradiction → So both are needed to cross-verify.
From (1): 3P + 2Q = 80 — (i)
From (2): 2P + 2Q = 70 and Q = 10
Substitute Q = 10 into both equations:
From (2): 2P + 20 = 70 → 2P = 50 → P = 25
From (1): 3P + 20 = 80 → 3P = 60 → P = 20
Conflict in values shows contradiction → So both are needed to cross-verify.
s,p and q are interior angles of an Isosceles triangle. Find the value of q.
1. s = 72°.
2. p and q are base angles of the triangle.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
s,p and q are interior angles of an Isosceles triangle. Find the value of q.
1. s = 72°.
2. p and q are base angles of the triangle.
1. s = 72°.
2. p and q are base angles of the triangle.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Shivam Ghoshal answered |
Since s, p and q are interior angles of Isosceles triangle, s + p + q = 180°.
In statement 1, If s = 72°, then p + q + 72 = 180° and
p + q = 180°.
Since we have two unknowns in one equation and we are not sure which angles are base angles, we cannot determine the value of q, hence the statement is not sufficient.
In statement 2, p and q are base angles of the triangle, hence from s + p + q = 180°, we have s + 2q = 180°, but p = q.
But the statement is not sufficient since it does not have any information about s.
Combining the two, we have s + 2q = 180° and s = 72°, we have
72° + 2q = 180°; 2q = 180 - 72 = 108°. q = 54°.
Therefore, BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
In statement 1, If s = 72°, then p + q + 72 = 180° and
p + q = 180°.
Since we have two unknowns in one equation and we are not sure which angles are base angles, we cannot determine the value of q, hence the statement is not sufficient.
In statement 2, p and q are base angles of the triangle, hence from s + p + q = 180°, we have s + 2q = 180°, but p = q.
But the statement is not sufficient since it does not have any information about s.
Combining the two, we have s + 2q = 180° and s = 72°, we have
72° + 2q = 180°; 2q = 180 - 72 = 108°. q = 54°.
Therefore, BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Determine the value of t.
1. 2t + 6s = 8
2. t/2 - 2 = - 3s/4- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Determine the value of t.
1. 2t + 6s = 8
2. t/2 - 2 = - 3s/4
1. 2t + 6s = 8
2. t/2 - 2 = - 3s/4
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Abhishek Kapoor answered |
In statement 1, 2t + 6s = 8 is one equation is two unknowns, hence we cannot determine the value of t. The statement is insufficient.
In statement 2, t/2 - 2 = -3s/4 can be transformed to t - 4 = -6s/2. But this is an equation with two unknowns hence we cannot determine the value of t. The statement is insufficient.
Combining the two statements, we have 2, t/2 - 2 = -3s/4 which can be transformed to t - 4 = -6s/2 then to 2t - 8 = -6s but this is equal to the equation 2t + 6s = 8, hence we have an equation with two unknowns. Thus, we cannot determine the value of t; the statements (1) and (2) TOGETHER are NOT sufficient.
In statement 2, t/2 - 2 = -3s/4 can be transformed to t - 4 = -6s/2. But this is an equation with two unknowns hence we cannot determine the value of t. The statement is insufficient.
Combining the two statements, we have 2, t/2 - 2 = -3s/4 which can be transformed to t - 4 = -6s/2 then to 2t - 8 = -6s but this is equal to the equation 2t + 6s = 8, hence we have an equation with two unknowns. Thus, we cannot determine the value of t; the statements (1) and (2) TOGETHER are NOT sufficient.
Is the number a prime number?
1. The number is divisible by a prime factor.
2. The number is positive- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Is the number a prime number?
1. The number is divisible by a prime factor.
2. The number is positive
1. The number is divisible by a prime factor.
2. The number is positive
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Bhavana Kulkarni answered |
In statement 1, the number is divisible by a prime factor, hence the number can be 2, 4, 6, -2, -4, -6, 8 , 9 . . . . Hence the statement is insufficient.
In statement 2, the number is positive. But there are infinitely many numbers that are positive but not prime, hence, the statement is not sufficient.
Combining the two statements, we have the numbers being positive, thus, 2,4,6,8,9,10,. . . . The numbers are infinitely many, hence Statements (1) and (2) TOGETHER are NOT sufficient.
In statement 2, the number is positive. But there are infinitely many numbers that are positive but not prime, hence, the statement is not sufficient.
Combining the two statements, we have the numbers being positive, thus, 2,4,6,8,9,10,. . . . The numbers are infinitely many, hence Statements (1) and (2) TOGETHER are NOT sufficient.
Find the area of a right angle triangle whose base is 12 inches.
1. The hypotenuse is 13 inches.
2. The perpendicular height of the triangle is one less than half its base.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Find the area of a right angle triangle whose base is 12 inches.
1. The hypotenuse is 13 inches.
2. The perpendicular height of the triangle is one less than half its base.
1. The hypotenuse is 13 inches.
2. The perpendicular height of the triangle is one less than half its base.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Sanskriti Ahuja answered |
Statement 1: The hypotenuse is 13 inches.
Statement 2: The perpendicular height of the triangle is one less than half its base.
To find the area of a right-angled triangle, we need to know the length of the base and the height (perpendicular to the base). Let's evaluate each statement separately:
Statement 1: The hypotenuse is 13 inches.
Knowing the length of the hypotenuse alone is not enough to determine the area of the triangle. The hypotenuse only provides information about the length of the sides, not the height or the angles of the triangle. Therefore, statement 1 alone is not sufficient.
Statement 2: The perpendicular height of the triangle is one less than half its base.
Let's denote the base of the triangle as 'b' inches. According to statement 2, the height of the triangle is (1/2)b - 1 inches.
To calculate the area of the triangle, we need both the base and the height. Therefore, statement 2 alone is sufficient to determine the area of the triangle.
Using both statements:
Now, if we consider both statements together, we have the length of the base (12 inches) from statement 2 and the length of the hypotenuse (13 inches) from statement 1.
We can use the Pythagorean theorem to find the height of the triangle, which is the missing piece of information needed to calculate the area.
By the Pythagorean theorem:
base^2 + height^2 = hypotenuse^2
12^2 + height^2 = 13^2
144 + height^2 = 169
height^2 = 169 - 144
height^2 = 25
height = 5
Now, we have the base (12 inches) and the height (5 inches), so we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Therefore, both statements together are sufficient to determine the area of the triangle.
Hence, the answer is option C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Statement 2: The perpendicular height of the triangle is one less than half its base.
To find the area of a right-angled triangle, we need to know the length of the base and the height (perpendicular to the base). Let's evaluate each statement separately:
Statement 1: The hypotenuse is 13 inches.
Knowing the length of the hypotenuse alone is not enough to determine the area of the triangle. The hypotenuse only provides information about the length of the sides, not the height or the angles of the triangle. Therefore, statement 1 alone is not sufficient.
Statement 2: The perpendicular height of the triangle is one less than half its base.
Let's denote the base of the triangle as 'b' inches. According to statement 2, the height of the triangle is (1/2)b - 1 inches.
To calculate the area of the triangle, we need both the base and the height. Therefore, statement 2 alone is sufficient to determine the area of the triangle.
Using both statements:
Now, if we consider both statements together, we have the length of the base (12 inches) from statement 2 and the length of the hypotenuse (13 inches) from statement 1.
We can use the Pythagorean theorem to find the height of the triangle, which is the missing piece of information needed to calculate the area.
By the Pythagorean theorem:
base^2 + height^2 = hypotenuse^2
12^2 + height^2 = 13^2
144 + height^2 = 169
height^2 = 169 - 144
height^2 = 25
height = 5
Now, we have the base (12 inches) and the height (5 inches), so we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Therefore, both statements together are sufficient to determine the area of the triangle.
Hence, the answer is option C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
What is the value of the positive number, p?
1. One of its divisors is 7.
2. p is divisible by two positive numbers only- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
What is the value of the positive number, p?
1. One of its divisors is 7.
2. p is divisible by two positive numbers only
1. One of its divisors is 7.
2. p is divisible by two positive numbers only
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Aditya Gupta answered |
In statement 1, since one of the divisor is 7, it implies that the number is a multiple of 7. This allows us to have infinitely many numbers, hence the statement is not sufficient.
In statement 2, the number is divisible by two numbers only. This implies that p is prime since a prime number is divisible by two positive numbers. Since there are infinitely many prime numbers, the statement is not sufficient.
Combining the two statements, we have p a prime number being divisible by 7, hence p must be 7. Therefore, both statements together are sufficient but neither statement alone is sufficient.
In statement 2, the number is divisible by two numbers only. This implies that p is prime since a prime number is divisible by two positive numbers. Since there are infinitely many prime numbers, the statement is not sufficient.
Combining the two statements, we have p a prime number being divisible by 7, hence p must be 7. Therefore, both statements together are sufficient but neither statement alone is sufficient.
Find the common difference of the arithmetic sequence.
1. The third term of the sequence is 1.428.
2. The first and the fifth terms of the sequence is 1 and 1.856.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'B'. Can you explain this answer?
Find the common difference of the arithmetic sequence.
1. The third term of the sequence is 1.428.
2. The first and the fifth terms of the sequence is 1 and 1.856.
1. The third term of the sequence is 1.428.
2. The first and the fifth terms of the sequence is 1 and 1.856.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
| | Tanishq Choudhury answered |
an = a + (n - 1)d
In statement 1, third term, a3 = a + (3 - 1)d = 1.428; a + 2d =1.428.
This is one equation with two unknowns hence we cannot determine the value of d. The statement is not sufficient.
In statement 2, a = 1 and a5 = a + (5 - 1)d = 1.856
Substituting for a, we have 1 + 4d = 1.856; d = 0.214.
The common difference is 0.214, therefore, the statement is sufficient.
In statement 1, third term, a3 = a + (3 - 1)d = 1.428; a + 2d =1.428.
This is one equation with two unknowns hence we cannot determine the value of d. The statement is not sufficient.
In statement 2, a = 1 and a5 = a + (5 - 1)d = 1.856
Substituting for a, we have 1 + 4d = 1.856; d = 0.214.
The common difference is 0.214, therefore, the statement is sufficient.
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