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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: 42630

Kudos [?]: 135843 [0], given: 12715

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

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29 Sep 2017, 02:56
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Difficulty:

65% (hard)

Question Stats:

50% (01:40) correct 50% (01:25) wrong based on 28 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

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Kudos [?]: 135843 [0], given: 12715

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 625

Kudos [?]: 312 [1], given: 39

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, 03:42
1
KUDOS
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 [?]: 312 [1], given: 39

Re: If x > 1, is positive integer b a factor of positive integer a? (1) x   [#permalink] 29 Sep 2017, 03:42
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