Quantitative Comparison Test Preparation for GRE

Compare the two quantities and choose the best answer from four choices given.

1.

Diagram is illustrative and is not drawn to scale.
Quantity A = Measure of angle 1 + Measure of angle 4
Quantity B = 90^o - Measure of angle 2^o

A Quantity A is greater
B Quantity B is greater
C The two quantities are equal
D The relationship cannot be determined from the information given

2. Quantity A = (27 - 13) (296 + 534) Quantity B = (27 + 13) (534 + 296)

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

3. y² + z² = 34 and yz = 15
Quantity A = y² + 2yz + z²
Quantity B = (y + z)²

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

4. Quantity A = (y + 5)² Quantity B = (y - 5)²

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

5. Quantity A = (1/25)^1/2 + (1/144)^1/2 Quantity B = [(1/25) + (1/144)]^1/2

A. Quantity A is greater
B. Quantity B is greater
C The two quantities are equal
D. The relationship cannot be determined from the information given

6. Quantity A = Time to travel 95 miles at 50 miles per hour
Quantity B = Time to travel 125 miles at 60 miles per hour

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

7. Quantity A = 4 / 100 Quantity B = 0.012 / 3

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

8. Quantity A = 1.1 Quantity B = 12.1^1/2

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

9. Quantity A = (9/13)² Quantity B = (9/13)^1/2

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

10. Quantity A = 0.83 Quantity B = 0.81/3

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

11. Quantity A = (3 x 4 x 17) / (121 x 100)
Quantity B = (4 x 5 x 19) / (1000 x 121)

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

12. 100 < y < 200 and 100 < z < 210
Quantity A = y Quantity B = z

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

13. Consider a triangle PQR.
Quantity A = length of PQ + length of QR
Quantity B = length of PR

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

14. Consider a rectangle. The length of its shorter side is 8, and the length of its diagonal is 16.
Quantity A = 30^o
Quantity B = measure of angle formed by diagonal and shorter side

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

15. Quantity A = Percentage increase from 10 ft to 13 ft
Quantity B = Percentage increase from 13 ft to 16 ft

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

16. Quantity A = Time elapsed from 6:47 a.m. to 10.13 the same morning
Quantity B = 3 hours 25 minutes

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

17. Quantity A = Volume of a cube in which the length of a side is 5
Quantity B = Volume of a cube in which the length of a diagonal of a face is 6 (2)^1/2

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

18. Quantity A = Average of (2y + 3z + 127) and (4y + 5z + 73)
Quantity B = Average of (3y + 4z + 173) and (3y + 4z + 73)

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

19. A task is done by y women in 45 hours.
The same task is done by (y + 2) women in z hours.
Quantity A = 45 Quantity B = z

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

20.

Diagram is illustrative and is not drawn to scale.
AB is the diameter of the circle.
Angle BAC = 30o
Quantity A = Length of side AB
Quantity B = 2 (Length of side BC)

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

ANSWERS and EXPLANATIONS

1. A
Quantity A is greater
In the figure, angles 3 and 4 are vertically opposite angles and are equal.
Also the sum of the three angles of a triangle is 180o.
Hence angle 1 + angle 2 + angle 4 = 180o or
angle 1 + angle 4 = 180o - angle 2.

2. B
Quantity B is greater
Let y = 296 + 534.
Then, Quantity A = 14y and Quantity B = 40y. Now, 14y < 40y.
Note that you save time by not calculating the exact values of Quantity A and Quantity B.

3. C
The two quantities are equal
It is worth remembering that
(y + z)² = (y + z) (y + z) = y² + 2yz + z²

Note that it is not meaningful to solve the equations simultaneously and determine y and z equal +3 or -3 and +5 or -5.

4. D
The relationship cannot be determined from the information given
For y = 0, (y + 5)² = (y - 5)² = 25
For y < 0, (y + 5)²< (y - 5)²
For y > 0, (y + 5)² > (y - 5)²

5. A
Quantity A is greater
(1/25)^1/2 + (1/144)^1/2 = (1/5) + (1/12) = 17/60.
[(1/25) + (1/144)]^1/2 = [(144+25) / (25 x 144)]^1/2 = [169/(25 x 144)]^1/2 = 13/60.

6. B
Quantity B is greater
Time = Distance / Speed
Time to travel 95 miles at 50 miles per hour = 95/50 < 2 hours.
Time to travel 125 miles at 60 miles per hour = 125/60 > 2 hours.
Note that you save time by not calculating the exact values of Quantity A and Quantity B.

7. A
Quantity A is greater
4/100 = 0.04 and 0.012/3 = 0.004. Note that 0.04 > 0.004

8. B
Quantity B is greater
Now 9^1/2 = 3 and 16^1/2 = 4.
So, 12.1^1/2 lies between 3 and 4. Therefore, it is greater than 1.1
Note that you save time by not calculating the exact values of Quantity A and Quantity B.
Also, note that 1.12 = 1.1 x 1.1 = 1.21 (and not 12.1).

9. B
Quantity B is greater
A tricky problem.
Let y = 9/13. However, it is not meaningful to try to manually calculate y² or y^1/2 in this case. The relationship is not indeterminate because the
uantities are given numbers. It is also clear that Quantity A does not equal Quantity B here.
So, we need to ascertain whether y² is greater than or less than y^1/2
when 0 < y < 1.
Note y²< y when 0 < y < 1.
Also y^1/2 > y when 0 < y < 1.
Therefore, y^1/2 > y² when 0 < y < 1... worth remembering!

10. B
Quantity B is greater
A tricky problem.
Let y = 0.8 ; however, it is not meaningful to try to manually calculate y³ or y^1/3 in this case. The relationship is not indeterminate because the quantities are given numbers. It is also clear that Quantity A does not equal Quantity B here.
So, we need to ascertain whether y³ is greater than or less than y^1/3
when 0 < y < 1.
Note y³< y when 0 < y < 1.
Also y^1/3> y when 0 < y < 1.
Therefore, y^1/3> y³ when 0 < y < 1... worth remembering!

11. A
Quantity A is greater
Let y = 4/121.
Then, Quantity A = (3 x 17)/(100 y) = 0.51 y and
Quantity B = (5 x 19)/(1000 y) = 0.095 y. Now, 0.51 y > 0.095 y.
Note that you save time by not calculating the exact values of Quantity A and Quantity B.

12. D
The relationship cannot be determined from the information given
The relationship is clearly indeterminate because y can take any value between 100 and 200, whereas z can take any value between 100 and 210.
hus, y = z, y < z or y > z.

13. A
Quantity A is greater
With some visualization, it is clear than PQ + QR can never be less than or equal to PR. In fact, the sum of the lengths of two sides (PQ + QR) is
ecessarily greater than the length of the third side PR.

14. B
Quantity B is greater
A rough sketch will help in visualizing the solution.
The diagonal with the two sides of the rectangle forms a right triangle.
The measure of the angle formed by the diagonal and the shorter side is 60^o because cos 60^o = 1/2 = 8/16. So, Quantity B = 60^o

15. A
Quantity A is greater
Quantity A = (3/10) x 100 and Quantity B = (3/13) x 100. Now, 3/10 > 3/13.
Note that you save time by not calculating the exact values of Quantity A and Quantity B.

16.A
Quantity A is greater
Quantity A = 3 hours 26 minutes (on adding up
13 minutes from 6.47 a.m. to 7 a.m.,
3 hours from 7 a.m. to 10 a.m., and again
13 minutes from 10 a.m. to 10.13 a.m.)

17.B
Quantity B is greater
If side = 5, then volume of cube = 5³ = 125.
If side = a, then diagonal of a face = (a2 + a2)^1/2 = (2)^1/2 a.
If diagonal of a face = 6 (2)^1/2, then side = 6 and volume = 6³ = 216.
Note that you may save time by not calculating the volumes. If the side of the cube is greater in length, then its volume must be greater.

18. B
Quantity B is greater
Quantity A = (2y + 4y + 3z + 5z + 127 + 73)/2
= (6y + 8z + 200)/2 = 3y + 4z + 100.
Quantity B = (3y + 3y + 4z + 4z + 173 + 73)/2
= (6y + 8z + 246)/2 = 3y + 4z + 123.

19.A
Quantity A is greater
If the number of women is increased, then the task is done in fewer hours.
So, z < 45.

20. C
The two quantities are equal
Angle subtended by the diameter on the circumference = 90o.
So, ABC is a right triangle.
sin BAC = opposite side / hypotenuse = BC / AB.
sin BAC = sin 30o = 0.5
So, BC / AB = 0.5 or AB = 2 BC.

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