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Additional resources for 501 Quantitative Comparison Questions: Master This Specialized Math Skill and Score Higher!
C. ᎏ3ᎏx + ᎏ3ᎏx + ᎏ3ᎏx = 1x; therefore, x = 9. The quantities are equal. 104. a. Since the bases are the same (b) and b > 1, the exponents can be compared. a + 1 > a since a is positive. 105. b. Simplify both fractions by canceling the x’s. The fractions then become just −y and y. y is positive, so −y is negative. Any positive number is greater than any negative number. 21 501 Quantitative Comparison Questions 106. b. Quantity A is less than 1 and quantity B is greater than 1. This is easily seen by the fact that ᎏ31ᎏ0 is being taken from 1, which brings the value below 1 for quantity A.
Both quantities are equivalent to m18. m18; ͙m ෆ 119. c. Divide both terms in the numerator of quantity A by 5. This yields x − 7, which is equivalent to quantity B. 120. c. The only prime divisible by 7 is 7. It is the same for 11—the only prime divisible by 11 is 11. If any other number was divisible by 7 or 11, it would not be prime. 121. a. 0989. 122. c. When multiplying by 105, move the decimal 5 places to the right to get 425,000. When dividing by 102, move the decimal 2 places to the left to get 425,000.
C. Add the numbers inside the parentheses. (84 + 12)(15 + 91) = (96)(106) and (74 + 22)(20 + 86) = (96)(106). 56. c. 5. 57. a. Since the bases are equal, just compare the exponents to compare the expressions. 3 > ᎏ13ᎏ. 58. c. 4x is an even number because any multiple of 4 is even. The remainder when an even number is divided by 2 is 0. 59. b. ͙4 ෆ = 2, so ͙5 ෆ > 2. 60. a. ͙17 ෆ > 4 and ͙5 ෆ > 2, therefore, ͙17 ෆ + ͙5 ෆ > 6. Since ͙25 ෆ = 5, ͙22 ෆ < 5. Quantity A is greater. a b a 4 9 36 36 61. a.