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Which of the following is always correct?

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Which of the following is always correct?

by VJesus12 » Wed Jun 20, 2018 2:53 am

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C

D

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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.
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answer

by arosman » Wed Jun 20, 2018 11:00 am
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
Adam Rosman, MD
University of Chicago Booth School of Business, Class of 2020
[email protected]

Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock.
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by Jeff@TargetTestPrep » Thu Jun 21, 2018 4:14 pm
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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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