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

Question

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

mikemcgarry · Answer

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 :-)

Bunuel · Answer

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

JeffTargetTestPrep · Answer

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.

Answer: C

Tonkotsu · Answer

The others have done a far greater job, but for my own sake, I'll try to explain in my own words.

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

I notice first, that the question is asking for whether n/m would produce an integer.

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

Gives us no information about m,  Not Sufficient

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

Gives us no information about n  Not Sufficient

(1) & (2)

n/m = 5*(3^k)/(3^k-1) = 5 * 3k^(k - (k - 1)) = 5 * 3k is an integer!  Sufficient

Bunuel · Answer

n = 5(3^k) means n = 5*3^k, not n = 5^3^k as you assumed.

P.S. There is no need to tag bb in quant or verbal forums. Better to tag quant/verbal experts/tutors or moderators. Thank you!

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

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GMAT Data Sufficiency (DS) Questions

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

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