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