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# If n and m are positive integers, is m a factor of n?

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Joined: 26 Mar 2013
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If n and m are positive integers, is m a factor of n?  [#permalink]

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14 Jan 2017, 11:22
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88% (01:14) correct 12% (01:27) wrong based on 158 sessions

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If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4473
Re: If n and m are positive integers, is m a factor of n?  [#permalink]

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16 Jan 2017, 17:25
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Mo2men wrote:
If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k

Dear Mo2men,

I'm happy to respond. This problem is not very challenging: it would be among the easier questions the GMAT would ask.

Either statement by itself is obviously insufficient, because with each statement we get information about only one variable and know nothing about the other, so we can't say anything meaningful about their relation.

If we consider both statements together, we note that any power of an integer is divisible by all the powers below it of that same integer. Thus, 3^(k-1) has to be a factor of 3^k, and therefore also has to be a factor of any multiple of (3^k). Thus, we get a definitive "yes" answer, and the answer to the DS question is (C).

Here's a more GMAT-like problem:
k is mult of 1440

Mike
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Mike McGarry
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Re: If n and m are positive integers, is m a factor of n?  [#permalink]

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17 Jan 2017, 01:14
1
mikemcgarry wrote:
Mo2men wrote:
If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k

Dear Mo2men,

I'm happy to respond. This problem is not very challenging: it would be among the easier questions the GMAT would ask.

Either statement by itself is obviously insufficient, because with each statement we get information about only one variable and know nothing about the other, so we can't say anything meaningful about their relation.

If we consider both statements together, we note that any power of an integer is divisible by all the powers below it of that same integer. Thus, 3^(k-1) has to be a factor of 3^k, and therefore also has to be a factor of any multiple of (3^k). Thus, we get a definitive "yes" answer, and the answer to the DS question is (C).

Here's a more GMAT-like problem:
k is mult of 1440

Mike

Thank you Mike.

If interested, here is the problem Mike is referring to: n-is-a-positive-integer-and-k-is-the-product-of-all-integer-104272.html
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Re: If n and m are positive integers, is m a factor of n?  [#permalink]

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11 Dec 2017, 12:01
Mo2men wrote:
If n and m are positive integers, is m a factor of n?

(1) n = 5(3^k), for any positive integer k
(2) m = 3^(k-1), for any positive integer k

We are given that n and m are positive integers and need to determine whether m is a factor of n, i.e., whether n/m = integer.

Statement One Alone:

n = 5(3^k), for any positive integer k

Since we do not have any information regarding m, statement one alone is not sufficient to answer the question.

Statement Two Alone:

m = 3^(k-1), for any positive integer k

Since we do not have any information regarding n, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we can create the following equation:

n/m = 5(3^k)/3^(k-1)

n/m = 5(3^k)/(3^k)(3^-1)

n/m = 5/(3^-1)

n/m = 5 x 3 = 15

Thus, n/m IS an integer.

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Re: If n and m are positive integers, is m a factor of n?  [#permalink]

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18 Jan 2019, 11:46
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Re: If n and m are positive integers, is m a factor of n?   [#permalink] 18 Jan 2019, 11:46
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