## GRE Math Tutorial

#### Intro

A sample question similar to some that might show up on the GRE Math portion.

#### Sample Problem

If x is an integer such that x > 0, and given the following statements:

I. x – x2 > 0

II. 2x – x3 < 0

III. x-7 > 0

which of the statements are always true?

II only

III only

All are always True

I and II only

I and III only

#### Solution

Let’s go through each option, remembering that x is always a positive integer. That means x is a value from 1 to infinity.

I. Will never be true because x2 is always greater than x with the exception of x = 1. Even in the case of x = 1, the result of (I) would be 0, and the inequality is exclusive.

II. x3 will always be bigger than 2x when x is always a positive integer EXCEPT when x = 1 as in this case. While any integer value from 2 onward will make the comparison true, x = 1 will result in:

2(1) – (1)3 =
2 – 1 = 1
1 > 0

That means II is false for one case.

III. x-7 is the same as 1/x7. While you could make the argument that, as x approaches infinity, the value of x-7 is practically 0, it is not actually 0. The result is just a very small positive fraction that is still bigger than 0, and so III only is the correct answer.