Solutions and detailed explanations to questions and problems similar to the quantitative comparison GRE questions in sample 1.
When solving quantitative comparison questions, you asked to compare two quantities – Quantity A and Quantity B – and then determine which of the following statements describes the comparison: (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.
Solution to Questions 1
A: 2(3 + 4)2 + 10 = 2(7)2 + 10 = 2(49) + 10 = 108 B: 2 + (3 + 4)2 + 10 = 2 + 49 + 10 = 61 Quantity A is greater than quantity B Answer (A) Solution to Questions 2
A: 2×310 + 2×310 + 2×310 = 2× ( 310 + 310 + 310 ) = 2× ( 3×310 ) = 2×311 B: 3×310 = 311 Quantity A is greater than quantity B Answer (A)
Solution to Questions 3
A: 25% of 300 = (25/100)×300 = 25 × 300 / 100 = 75 B: Three quarters of 200 = (3/4) × 200 = 150 Quantity B is greater than quantity A Answer (B) Solution to Questions 4ABC is a triangle such that the measure of angle A is 45°. The measure of angle C is twice the measure of angle B.
C = 2 B The sum of the measures of the three angles A, B and C of the triangles is 180° A + B + C = 180 Substitute A by 45 and C by 2B in the above equation 45 + B + 2B = 180 Solve for B 3 B = 135 B = 135 / 3 = 45° The measures of angle A and B are equal Answer (C) Solution to Questions 5
x = 0 A: x2 + 1 = 02 + 1 = 1 B: 100x + 1 = 100(0) + 1 = 1 x = 1 A: x2 + 1 = 12 + 1 = 2 B: 100x + 1 = 100(1) + 1 = 101 We have tried two values of x 0 and 1 and they gave different conclusions. Therefore the relationship between the quantities in A and B cannot be determined from the information given. Answer (D) Solution to Questions 6
Answer (D) Solution to Questions 7
A: x3 = (- 10-2)3 = (-1)3(10-2)3 = - 10-6 B: x2 = (- 10-2)2 = (-1)2(10-2)2 = 10-4 Quantity B is greater than quantity A Answer (B) Solution to Questions 8
A: radius 1 cm , length = 100 m = 100 * 100 cm = 104 cm B: radius 10 cm , length = 10 m = 10 * 100 cm = 103 cm We now calculate the volume using the formula for the volume of a cylindrical tube: Pi * radius2 * height. A: Pi * 12 * 104 = 104 Pi B: Pi * 102 * 103 = 105 Pi The volume in B is greater than the volume in A. Answer (B) Solution to Questions 9
0*x < x*x < 1*x Which simplifies to 0 < x2 < x Again since x is positive, the inequality x2 < x gives an inequality of the reciprocals as follows 1 / x2 > 1 / x Quantity A is greater than quantity B Answer (A) Solution to Questions 10A bag contains green, blue and yellow balls. The ratio of green to blue balls is 2:7. The ratio of green to yellow balls is 3:5.
g / b = 2 / 7 and g / y = 3 / 5 The first fraction gives b / g = 7 / 2 We now evaluate the product of fractions g / y and b / g as follows (g / y) * (b / g) = (3 / 5) * (7 / 2) Note that (g / y) * (b / g) simplifies to b / y, hence b / y = 21 / 10 The above fraction indicates that the number of blue balls (A) is greater than the number of yellow balls (B). Answer (A)
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