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If a, b, k, and m are positive integers, is a^k a factor of

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If a, b, k, and m are positive integers, is a^k a factor of [#permalink]

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New post 04 Jan 2009, 18:55
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If a, b, k, and m are positive integers, is a^k a factor of b^m?

(1) a is a factor of b
(2) k <= m

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Re: DS: Factor [#permalink]

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New post 04 Jan 2009, 19:40
IMO C.

a^k a factor of b^m means => b^m = X * a^k , where X is a non zero integer

1 ) a is a factor of b = > not sufficient as we do not know about m and k.

2 ) k <= m => not sufficient alone as we do not know about b and a.

together, a is a factor of b , so a <=b .also as and k<=m , a^k <= b^m and as a,b,k and m are integers, a^k should be a factor of b^m

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Re: DS: Factor [#permalink]

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New post 04 Jan 2009, 19:45
bigfernhead wrote:
If a, b, k, and m are positive integers, is a^k a factor of b^m?

(1) a is a factor of b
(2) k <= m


Need to answer the question whether (b^m)/(a^k) is integer.
(1) says (b/a) is integer. b^k/a^k or b^m/a^m is integer.
(2) m-k>=0. Hence, b^m/a^k = b^k/a^k*b^(m-k) is integer.

Both are together sufficient. Hence, C.

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Re: DS: Factor [#permalink]

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New post 05 Jan 2009, 09:14
Isn't A) always true regardless of what k and m are?

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Re: DS: Factor [#permalink]

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New post 05 Jan 2009, 09:24
i think the answer should be A
what is the OA

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Re: DS: Factor [#permalink]

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New post 05 Jan 2009, 12:23
I think just A is not enough, because if k is larger then m then there is a possibility that a^k will be larger than b^m and in that case a^k will not be a factor of b^m.

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Re: DS: Factor [#permalink]

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New post 05 Jan 2009, 14:27
Please derive b^m/a^k = integer based on b/a=integer. I am not sure if it can be derived; hence, (I) alone is not sufficient.

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New post 05 Jan 2009, 14:43
Correct! The answer is C) Thanks for the explanations.

smarinov wrote:
I think just A is not enough, because if k is larger then m then there is a possibility that a^k will be larger than b^m and in that case a^k will not be a factor of b^m.

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Re: DS: Factor   [#permalink] 05 Jan 2009, 14:43
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If a, b, k, and m are positive integers, is a^k a factor of

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