Which of the following is always correct?

VJesus12 wrote:Which of the following is always correct?

A. If 1/x is greater than x, x^2 is greater than x

B. If 1/x is greater than x, x is greater than x^2

C. If x^2 is greater than x, x^3 is greater than x^2

D. If x^3 is greater than x^2, x^4 is greater than x^3

E. If x^4 is greater than x^3, x^5 is greater than x^4

The OA is the option D.

I really would like to know how to solve this PS question. Could someone show me a good approach? Please.

Test numbers is prob best approach. Getting comfortable testing numbers is a BIGTIME differentiator between 600 and 700 level test-takers. I know, I love algebra too because with algebra you're PROVING the correct answer to yourself. But the GMAT is about strategy and testing numbers is sometimes flat out the best strategy. The key is choosing smart numbers. They are asking for what MUST ALWAYS BE TRUE, therefore 4 of the answers must NOT always be true. That means we should be actively picking numbers with the goal of disproving the answer. As long as you can find one case where the answer doesn't hold then you can eliminate it.

A)
x = 1/2
1/x =2
------> x^2 = 1/4 which is not greater than 1/2
----> ELIMINATE

B)
x =-2
1/x = -1/2
x^ 2 = 4
----> -2 is not greater than 4
-----> ELIMINATE

C)
x = -2
x^2 = 4
x^ 3 = -8
-------> -8 is not greater than 4
--------> ELIMINATE

D)
If x^3 > X^2 then x cannot be negative. It also cannot be between 0 & 1. Therefore x> 1
If x > 1 then x^4 > x^3. ALWAYS
-------> CORRECT ANSWER(stop here on actual test. for learning purposes I did E below)

E)
x = -2
x^4 = 16
x^3 = -8
x^5 = -32
------------> -32 is not greater than 16
------------> ELIMINATE

Answer: D

VJesus12 wrote:Which of the following is always correct?

A. If 1/x is greater than x, x^2 is greater than x

B. If 1/x is greater than x, x is greater than x^2

C. If x^2 is greater than x, x^3 is greater than x^2

D. If x^3 is greater than x^2, x^4 is greater than x^3

E. If x^4 is greater than x^3, x^5 is greater than x^4

Let’s analyze each choice.

For choices A and B, if 1/x > x, then 0 < x < 1 or x < -1. So say x = 1/2, we see that x^2 = 1/4 is not greater than x, so A is not correct. Now, say x = -2, we see that x is not greater than x^2 = 4, so B is not correct either.

For choice C, if x^2 > x, x > 1 or x < 0. If x = -1, then x^3 = -1 is not greater than x^2 = 1, so C is not correct.

For choice D, if x^3 > x^2, x > 1. If x = 2, then x^4 = 16 is greater than x^3 = 8, so D might be correct. If we can verify that E is not correct, then the answer must be D.

For choice E, if x^4 > x^3, x > 1 or x < 0. If x = -1, then x^5 = -1 is not greater than x^4 = 1, so E is not correct.

Answer: D