Hide all answers
Hide all answers
View all answers
View all answers
Print
Try the Quiz
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} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity A is greaterIn the figure, angles 3 and 4 are vertically opposite angles and are equal. Also the sum of the three angles of a triangle is 180^{o}. Hence angle 1 + angle 2 + angle 4 = 180^{o} or angle 1 + angle 4 = 180^{o}  angle 2.
2. Quantity A = (27  13) (296 + 534) Quantity B = (27 + 13) (534 + 296) • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterLet 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. y^{2} + z^{2} = 34 and yz = 15 Quantity A = y^{2} + 2yz + z^{2} Quantity B = (y + z)^{2} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: The two quantities are equalIt is worth remembering that (y + z)^{2} = (y + z) (y + z) = y^{2} + 2yz + z^{2}
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. Quantity A = (y + 5)^{2} Quantity B = (y  5)^{2} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: The relationship cannot be determined from the information givenFor 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. Quantity A = (1/25)^{1/2} + (1/144)^{1/2 }Quantity B = [(1/25) + (1/144)]^{1/2} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: 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. Quantity A = Time to travel 95 miles at 50 miles per hour Quantity B = Time to travel 125 miles at 60 miles per hour • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterTime = 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. Quantity A = 4 / 100 Quantity B = 0.012 / 3 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity A is greater4/100 = 0.04 and 0.012/3 = 0.004. Note that 0.04 > 0.004
8. Quantity A = 1.1 Quantity B = 12.1^{1/2} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterNow 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 1.1^{2} = 1.1 x 1.1 = 1.21 (and not 12.1).
9. Quantity A = (9/13)^{2} Quantity B = (9/13)^{1/2} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterA tricky problem. Let y = 9/13. However, it is not meaningful to try to manually calculate y^{2} 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 y^{2} is greater than or less than y^{1/2} when 0 < y < 1. Note y^{2} < y when 0 < y < 1. Also y^{1/2} > y when 0 < y < 1. Therefore, y^{1/2} > y^{2} when 0 < y < 1... worth remembering!
10. Quantity A = 0.8^{3} Quantity B = 0.8^{1/3} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterA tricky problem. Let y = 0.8 ; however, it is not meaningful to try to manually calculate y^{3} or y^{1/3} 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 y^{3} is greater than or less than y^{1/3} when 0 < y < 1. Note y^{3} < y when 0 < y < 1. Also y^{1/3} > y when 0 < y < 1. Therefore, y^{1/3} > y^{3} when 0 < y < 1... worth remembering!
11. Quantity A = (3 x 4 x 17) / (121 x 100) Quantity B = (4 x 5 x 19) / (1000 x 121) • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity A is greaterLet 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. 100 < y < 200 and 100 < z < 210 Quantity A = y Quantity B = z • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: The relationship cannot be determined from the information givenThe 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. Consider a triangle PQR. Quantity A = length of PQ + length of QR Quantity B = length of PR • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity A is greaterWith 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. 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 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterA 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. Quantity A = Percentage increase from 10 ft to 13 ft Quantity B = Percentage increase from 13 ft to 16 ft • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity A is greaterQuantity 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. Quantity A = Time elapsed from 6:47 a.m. to 10.13 the same morning Quantity B = 3 hours 25 minutes • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity A is greaterQuantity 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. 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} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterIf side = 5, then volume of cube = 5^{3} = 125. If side = a, then diagonal of a face = (a^{2} + a^{2})^{1/2} = (2)^{1/2} a. If diagonal of a face = 6 (2)^{1/2}, then side = 6 and volume = 6^{3} = 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. Quantity A = Average of (2y + 3z + 127) and (4y + 5z + 73) Quantity B = Average of (3y + 4z + 173) and (3y + 4z + 73) • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity B is greaterQuantity 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 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 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: Quantity A is greaterIf the number of women is increased, then the task is done in fewer hours. So, z < 45.
20. Diagram is illustrative and is not drawn to scale. AB is the diameter of the circle. Angle BAC = 30^{o} Quantity A = Length of side AB Quantity B = 2 (Length of side BC) • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer: The two quantities are equalAngle subtended by the diameter on the circumference = 90^{o}. So, ABC is a right triangle. sin BAC = opposite side / hypotenuse = BC / AB. sin BAC = sin 30^{o} = 0.5 So, BC / AB = 0.5 or AB = 2 BC.
Try the Quiz : GRE Test Prep : Quantitative Comparison I
