With GRE Quantitative Comparisons look for savvy methods for comparison to avoid unnecessary calculation. In this case note the number of negative values created in each quantity.
Quote:
A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4)
Quantity A |
Quantity B |
f(2.5) |
f(3.5) |
Now for Quantity A: x - 1 and x - 2 are each > 0 | x - 3 and x - 4 are each < 0 --> Positive x Positive x Negative x Negative will result in a product > 0
Now for Quantity B: x - 1 is the only value > 0 --> Positive x Negative x Negative x Negative will result in a product < 0
Therefore, Quantity A will always be greater and the correct choice is A.
In quantity B, x-1, x-2 and x-3 all are positive, only x-4 is negative.