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When x and n are positive integers, if x^{2n}>(3x)^n, whi

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by Max@Math Revolution » Mon Jun 04, 2018 11:26 am

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[GMAT math practice question]

When x and n are positive integers, if x^{2n}>(3x)^n, which of the following must be true?

A. x>3
B. n>1
C. x=3
D. n=3
E. x=n
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by GMATGuruNY » Mon Jun 04, 2018 1:06 pm
Max@Math Revolution wrote:[GMAT math practice question]

When x and n are positive integers, if x^{2n}>(3x)^n, which of the following must be true?

A. x>3
B. n>1
C. x=3
D. n=3
E. x=n
x^(2n) > (3x)^n
(x^n)² > (3^n)(x^n)
(x^n)(x^n) > (3^x)(x^n)
x^n > 3^n.
Since each side of the resulting inequality has the same exponent, the left side will be greater than the right side only if x > 3.

The correct answer is A.
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by Brent@GMATPrepNow » Mon Jun 04, 2018 1:08 pm
Max@Math Revolution wrote:[GMAT math practice question]

When x and n are positive integers, if x^{2n} > (3x)^n, which of the following must be true?

A. x>3
B. n>1
C. x=3
D. n=3
E. x=n
Let's find some values that satisfy the given condition that x^{2n} > (3x)^n
How about x = 4 and n = 1.
When we plug in these values we get: 4^2 > 12^1, which simplifies to 16 > 12.
PERFECT.

Which of the following must be true?
A. x>3 One possible solution is n = 4. This works. KEEP
B. n>1 We just showed that one possible solution is n = 1 ELIMINATE.
C. x=3 We just showed that one possible solution is x = 4. ELIMINATE.
D. n=3 We just showed that one possible solution is n = 1. ELIMINATE.
E. x=n We just showed that one possible solution is x = 4 and n = 1. ELIMINATE.

Answer: A

Cheers,
Brent
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by Max@Math Revolution » Wed Jun 06, 2018 7:17 am
=>

x^{2n}>(3x)^n
=> x^{2n} > 3^nx^n
=> x^n > 3^n
=> x > 3

Therefore, A is the answer.
Answer: A
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