The Quantitative Comparison section emphasizes shortcuts, insight, and quick techniques. Long and/or involved mathematical computation is unnecessary and is contrary to the purpose of this section.
Remember that your answers will conform to the following:
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if the quantity in Column A is greater;
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if the quantity in Column B is greater;
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if the two quantities are equal;
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if the comparison cannot be determined from the information given.
Sample 1
| Column A |
Column B |
| (.9)8 |
(1.01)4 |
In Column A, a fractional value (a value less than 1) is multiplied by itself many times. So its value becomes increasingly smaller. (For example, 1⁄2 x 1⁄2 = 1⁄4; 1⁄4 x 1⁄2 = 1⁄8, and so forth.) In Column B, a number greater than 1 is multiplied by itself; its value grows larger. So Column B is greater.
The correct answer is B.
Sample 2
| Column A |
Column B |
| (-10)100 |
(-10)101 |
A negative number multiplied an even number of times will yield a positive product. A negative number multiplied an odd number of times will yield a negative product. Since Column A will be positive and Column B will be negative, A is greater.
The correct answer is A.
Sample 3
| Column A |
Column B |
| .05 - .125 |
.1 |
Subtracting in Column A, you get .05 - .125 = -.075. Our difference is a negative number. Thus, the positive value in Column B must be greater.
The correct answer is B.
Sample 4
| Column A |
Column B |
| a, b, c, all greater than 0 |
| a(b + c) |
ab + ac |
Using the distributive property on Column A to simplify gives ab and ac; therefore, the columns are equal.
The correct answer is C.
Sample 5
| Column A |
Column B |
a > 0
b > 0
c > 0 |
| (3a)(3b)(3c) |
3abc |
Multiplying column A gives (3a)(3b)(3c) = 27abc. Because a, b, and c are all positive values, 9abc will always be greater than 3abc.
The correct answer is A.
Sample 6
| Column A |
Column B |
| Number of prime numbers between 3 and 19 |
5 |
The prime numbers between 3 and 19 are 5, 7, 11, 13, and 17. The correct answer is C, since there are 5 primes.