Is x^n/x^n+1 > x^n+1/x^n? (1) x < 0 (2) n < 0

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Is x^n/x^n+1 > x^n+1/x^n? (1) x < 0 (2) n < 0 [#permalink]

27 Sep 2009, 22:29

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Is x^n/x^(n+1)>x^(n+1)/x^n?

(1) x < 0

(2) n < 0

[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Jan 2012, 11:31, edited 1 time in total.

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Re: is it greater? [#permalink]

28 Sep 2009, 00:38

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The expression can be rephrased as : Is 1/x > x ?
stmt 1. The expression is true for x < 0 except x=-1. But there is no restriction on x. So insuff.
stmt 2. Value of n does not matter.

combining , still the same question, can x be -1 ( and also be < 0 )?
Hence E.

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Re: is it greater? [#permalink]

01 Oct 2009, 04:25

can you please explain it in detail?

Economist wrote:

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Re: is it greater? [#permalink]

01 Oct 2009, 06:28

x^(n+1) = x^n.x

Now, while reducing the given inequality we need to take care of the inequality sign. ONLY if a -ve value is multiplied/divided on BOTH sides of the equation we need to reverse the inequality.

But, in this case we are not multiplying or dividing each side. We are just canceling out the same factor(-ve or +ve) from each side. So the inequality will remain the same.

In other words, x^n/x^n = 1, regardless of the sign of x^n. So, basically we are just multiplying each side by 1

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Re: is it greater? [#permalink]

23 Oct 2009, 16:26

Economist wrote:

Is it only for x= -1 or for the range -1<x<0?

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Re: Is x^n/x^n+1 > x^n+1/x^n? (1) x < 0 (2) n < 0 [#permalink]

26 Jan 2012, 07:17

+1 E

When we simplify the original inequality, using exponents theory, we get 1/x > x.

So both statements are insufficient.
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Re: Is x^n/x^n+1 > x^n+1/x^n? (1) x < 0 (2) n < 0 [#permalink]

26 Jan 2012, 11:31

Ranges in above solutions are not correct.

Is \frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}?

First of all realistic GMAT question would mention that x\neq{0}.

Anyway: is \frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}? --> is x^{n-n-1}<x^{n+1-n}? --> is \frac{1}{x}<x? --> is x-\frac{1}{x}>0? --> is \frac{x^2-1}{x}>0? --> is \frac{(x-1)(x+1)}{x}>0? So the question basically asks is -1<x<0 or x>1. (For more on this check: i-have-been-trying-to-understand-inequalities-by-reading-110917.html or range-for-variable-x-in-a-given-inequality-109468.html) Also noitce that the value of n is irrelevant to answer the question.

(1) x < 0. Not sufficient.

(2) n < 0. Not sufficient.

(1)+(2) Still can not answer the question. Not sufficient.

Answer: E.
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Re: Is x^n/x^n+1 > x^n+1/x^n? (1) x < 0 (2) n < 0 [#permalink] 26 Jan 2012, 11:31

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Is x^n/x^n+1 > x^n+1/x^n? (1) x < 0 (2) n < 0

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