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

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Joined: 02 Sep 2009
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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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New post 29 Sep 2017, 02:56
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Question Stats:

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

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

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Joined: 25 Feb 2013
Posts: 625

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

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

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New post 29 Sep 2017, 03:42
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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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