Problem Solving

GRE Math Tutorial

Problem Solving


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?

I and II only

I and III only

III only

All are always True

II only


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.

About The Author

Math, Computer Science, And Writing Tutor
Hello! My name is Jesson and my tutoring experience extends over 5 years, with several subjects at nearly all levels of education. I have over 3 years experience as mentor for elementary school students (K-5) in after school programs in Oakland and San Francisco, tutoring primarily with English writ...
11 Subjects
KnowRo Tutor
5 Tutorials
Vallejo, CA
Get Tutoring Info

Suggested Tutors for GRE Math Help

Siddarth C

Vienna, VA

All Subjects

Greg L

Vienna, VA

Government And History Expert

Luke N

Bethesda, MD

SAT Instructor And Humanities, Biology

Sophia G

Washington, DC

General Tutor