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If a,b,k, and m are positive integers, is a^k a factor of [#permalink]
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07 Apr 2011, 23:32
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Re: If a,b,k, and m are positive integers, is a^k a factor of [#permalink]
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07 Apr 2011, 23:54
Baten80 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
I don't know OA. we need to find out if \(\frac{b^m}{a^k}\) is an integer. Statement 1 says a is a factor of b so \(b = na\) where n is an integer. So \(\frac{b^m}{a^k}\) = \(\frac{(na)^m}{a^k}\) = \(\frac{(n^m*a^m)}{a^k}\) This will be integer if \(a^m \geq a^k\) which will happen only if \(k \leq m\)which is not given in statement 1, so insufficient Statement 2 doesnt say anything about a and b so insufficient Combining statement 1 and 2 we can answer the question in affirmative, hence sufficient and Answer is C.



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Re: If a,b,k, and m are positive integers, is a^k a factor of [#permalink]
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08 Apr 2011, 00:33
Is b^m = r *a^k ? (where p is as an integer) (1) b = p * a (where p is as an integer) so b^k = p^k * a^k but we don't know the relationship between m and k, so insufficient. e.g. a = 3, b = 6 so 6^2/3^3 is not an integer. (2) No information about a and b, so insufficient. (1) and (2) => b^m = p^k * a^k or, b^m/a^k = p^k (an integer), so sufficient Answer  C
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Re: If a,b,k, and m are positive integers, is a^k a factor of [#permalink]
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08 Apr 2011, 18:22
My Answer is C too.
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Re: If a,b,k, and m are positive integers, is a^k a factor of [#permalink]
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08 Apr 2011, 20:22
Take a = 2, b = 6 =>2^k and 6^m =>2^k and 2^m x 3^m If k<=m, for any positive value of k and m, 2^k is always a factor of 2^m So C
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Re: If a,b,k, and m are positive integers, is a^k a factor of [#permalink]
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12 Sep 2016, 11:48
Baten80 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
I don't know OA. 1) b^m = a^k * n. Since a is factor of B, let a =2, b=8 so 2^3m = 2^k * n. 2^k can only be a factor of 2^3m if the exponents of 2^k is less than 2^3m for all k and m. So not sufficient 2)k <= m, not sufficient because a and b relationship not given. If a = 3, b = 5, can be yes or no for a^k a factor of b^m 1+2) given a is a factor of b and the exponent of a will be smaller than or equal to the exponent of b, a^k is then a factor of b^m. C



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Re: If a,b,k, and m are positive integers, is a^k a factor of [#permalink]
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14 Aug 2017, 06:25
Baten80 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
I don't know OA. Question: is \(a^k\) a factor of \(b^m\) > \(a^kx=b^m\), where \(x\) is an integer? > \(x=\frac{b^m}{a^k}\). So basically the question is: Is \(x\) an integer \(>0\)? (1) \(a\) is a factor of \(b\) > \(ay=b\) > \(x=\frac{a^my^m}{a^k}\) > \(x=a^{mk}y^m\). Now if \(m<k\) and \(a\) is not a factor of \(y\), then \(x\) will not be an integer. Not sufficient. Or even without any algebra: if a and b are equal to say 3 and m<k (there are less b's than a's) then a^k won't be a factor of b^m. Though if k<=m then even if a and b are not equal still a^k will be a factor of b^m as there will be enough b's for a's. (2) \(k\leq{m}\), not sufficient on it's own. (1)+(2) \(x=a^{mk}y^m\) and \(k<m\), hence \(x\) is an integer. Sufficient. (Or again as there are more b's then a's (enough b's for a) then a^k is a factor of b^m, for example (bbb)/(aa)) Answer: C. OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/ifabkand ... 88503.html
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Re: If a,b,k, and m are positive integers, is a^k a factor of
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