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# If n is a nonzero integer, is xn < 1?

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Re: If n is a nonzero integer, is xn < 1? [#permalink]
Bunuel wrote:
If n is a nonzero integer, is x^n < 1?

(1) x > 1. If x = 2 and n = 1, then the answer is NO but if x = 2 and n = -1
, then the answer is YES.

(2) n > 0. If x = 2 and n = 1, then the answer is NO but if x = 1/2 and n = 1, then the answer is YES.

(1)+(2) x is greater than 1 and n is a positive number: any number greater than 1 in positive power is greater than 1. Sufficient.

I have just 1 query, why you have consider x as an integer only because if you assume any value non integer then ans will be no

Regards
Ls

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Re: If n is a nonzero integer, is xn < 1? [#permalink]
lastshot wrote:
Bunuel wrote:
If n is a nonzero integer, is x^n < 1?

(1) x > 1. If x = 2 and n = 1, then the answer is NO but if x = 2 and n = -1
, then the answer is YES.

(2) n > 0. If x = 2 and n = 1, then the answer is NO but if x = 1/2 and n = 1, then the answer is YES.

(1)+(2) x is greater than 1 and n is a positive number: any number greater than 1 in positive power is greater than 1. Sufficient.

I have just 1 query, why you have consider x as an integer only because if you assume any value non integer then ans will be no

Regards
Ls

Posted from my mobile device

Any number, not necessarily an integer, greater than 1 in positive power is greater than 1. Consider this: any number greater than 1 multiplied by itself n times (n > 0) must be greater than 1.
Manager
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Re: If n is a nonzero integer, is xn < 1? [#permalink]
Bunuel wrote:
lastshot wrote:
Bunuel wrote:
If n is a nonzero integer, is x^n < 1?

(1) x > 1. If x = 2 and n = 1, then the answer is NO but if x = 2 and n = -1
, then the answer is YES.

(2) n > 0. If x = 2 and n = 1, then the answer is NO but if x = 1/2 and n = 1, then the answer is YES.

(1)+(2) x is greater than 1 and n is a positive number: any number greater than 1 in positive power is greater than 1. Sufficient.

I have just 1 query, why you have consider x as an integer only because if you assume any value non integer then ans will be no

Regards
Ls

Posted from my mobile device

Any number, not necessarily an integer, greater than 1 in positive power is greater than 1. Consider this: any number greater than 1 multiplied by itself n times (n > 0) must be greater than 1.

I am doing dumbest of the mistake, my exam is on 28th of this month, & suddenly i am facing major problem with DS < Accuracy plummet to 55 % that too for easy & medium ..so you can imagine about hard >
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Re: If n is a nonzero integer, is xn < 1? [#permalink]
You are able to eliminate the answers with x as an integers to begin with. If however, you were getting 1) or 2) as the answer with x as integer only, to confirm the answer further, you would have to consider x as a rational number also.
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Re: If n is a nonzero integer, is xn < 1? [#permalink]
Quick question: Had n not been an integer the answer would be E right? Because if n was a fraction less than 1, x^n could be less than one for smaller numbers above 1
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Re: If n is a nonzero integer, is xn < 1? [#permalink]
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Re: If n is a nonzero integer, is xn < 1? [#permalink]
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