501 Quantitative Comparison Questions 25. a. Notice that 45% of 104 would be more than 45% of 100. Since
45% of 100 is 45, quantity A is greater than 45 which is greater than quantity B. 26. a. Simplify the exponents on the left-hand side of the equation by
multiplying. Then, since the bases are the same (c), the exponents can be set equal to each other: (c b)5 = c5 + a c5b = c5 + a 5b = 5 + a Isolate a by subtracting 5 on both sides of the equation. 5b − 5 = 5 + a − 5 5b − 5 = a The variables must be integers greater than 1 (so the smallest possible value is 2). When 2 is substituted in for b, a is equal to 5. As the value of b gets larger, so does the value of a. Quantity A is always greater than quantity B. 27. c. Multiplying by 103 moves the decimal in 16.5 three places to
the right to get 16,500 (quantity A). Multiplying by 104 moves the decimal in 1.65 four places to the right to get 16,500 (quantity B). 28. c. “Of ” means multiply. Multiply the fractions in quantity A; 3 24 8 6 4 × = 44 1 1 = 1 1 . Quantity A is equal to quantity B.
29. a. The value of x is negative. x3 is also negative because three
negatives multiply to a negative answer. The negative in front of −x3y negates the negative of x3, making the quantity positive. The value of y doesn’t matter because it is positive, making it greater than quantity B. 30. b. The possible integer factor pairs of 30 are (1,30), (2,15), (3,10),
and (5,6). Of these factor pairs, (1,30) has the largest sum; 1 + 30 = 31. 31 is not larger than 32, so quantity B is greater. 31. b. x is a positive number less than 1. The easiest way to see this
solution is to try different numbers for x. If x = 0.5, then 1x = 01.5 1 1 = = 4. Quantity B is always = 1 ÷ 0.5 = 2 and x1 2 = 0.25 (0.5)2 greater than quantity A.
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