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# If x > 1, is positive integer b a factor of positive integer a? (1) x

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Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128688 [0], given: 12182

If x > 1, is positive integer b a factor of positive integer a? (1) x [#permalink]

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29 Sep 2017, 03:56
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Question Stats:

63% (01:29) correct 37% (01:00) wrong based on 19 sessions

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If x > 1, is positive integer b a factor of positive integer a?

(1) $$x^{(a + b)} = x^{(ab)}$$

(2) $$x^{(\frac{a}{b})} = x^{(\frac{a}{2})}$$
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128688 [0], given: 12182

Senior Manager
Joined: 25 Feb 2013
Posts: 392

Kudos [?]: 166 [0], given: 31

Location: India
GPA: 3.82
Re: If x > 1, is positive integer b a factor of positive integer a? (1) x [#permalink]

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29 Sep 2017, 04:42
Bunuel wrote:
If x > 1, is positive integer b a factor of positive integer a?

(1) $$x^{(a + b)} = x^{(ab)}$$

(2) $$x^{(\frac{a}{b})} = x^{(\frac{a}{2})}$$

The question stem implies that whether $$a=b*Integer$$

Statement 1: this implies $$ab=a+b$$ or $$ab-b=a$$

Hence $$a=b*(a-1)= b*Integer$$ as $$a$$ & $$b$$ are integers, hence $$a$$ is a multiple of $$b$$ or $$b$$ is a factor of $$a$$. Sufficient

Statement 2: implies $$\frac{a}{b}=\frac{a}{2}$$ or $$b =2$$. But we cannot find the value of $$a$$. Hence Insufficient

Option A

Kudos [?]: 166 [0], given: 31

Re: If x > 1, is positive integer b a factor of positive integer a? (1) x   [#permalink] 29 Sep 2017, 04:42
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