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# The numbers m, n, and K are all positive integers. Given that m is a

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Re: The numbers m, n, and K are all positive integers. Given that m is a [#permalink]
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This is how I did it. m and K are positive integers and m is factor of K. Hence, K/m is an integer. So, if we do K/(K/m) = m which is an integer. Hence, D.
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Re: The numbers m, n, and K are all positive integers. Given that m is a [#permalink]
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Bunuel wrote:
The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K?

A. m + n
B. mn
C. n^2/m
D. K/m
E. K/(mn)

Since m is a factor of K, we know that K/m is an integer. Since m x (K/m) = K, we see that K/m is also a factor of K.

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Re: The numbers m, n, and K are all positive integers. Given that m is a [#permalink]
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Bunuel wrote:
The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K?

A. m + n
B. mn
C. n^2/m
D. K/m
E. K/(mn)

GIVEN: m is a factor of K
This means that we can write: K = md for some integer d
If m and d are both integers, then m and d are both factors of K
Notice that, if K = md, then d = K/m, which means K/m is a factor of K

Cheers,
Brent
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Re: The numbers m, n, and K are all positive integers. Given that m is a [#permalink]
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Bunuel wrote:
The numbers m, n, and K are all positive integers. Given that m is a factor of K, that n is also a factor of K, and m < n, which of the following must also be a positive integer factor of K?

A. m + n
B. mn
C. n^2/m
D. K/m
E. K/(mn)

Different approach:

The question asks "which of the following must also be a positive integer factor of K?"
So, if we can find an answer choice that is NOT a factor of K we can ELIMINATE that answer choice.

A. m + n
If K = 12, then if COULD be the case that m = 4 and n = 6
In this case, m + n = 4 + 6 = 10, and 10 is NOT a factor of 12
ELIMINATE A

B. mn
If K = 12, then if COULD be the case that m = 4 and n = 6
In this case, mn = (4)(6) = 24, and 24 is NOT a factor of 12
ELIMINATE B

C. n²/m
If K = 12, then if COULD be the case that m = 4 and n = 6
In this case, n²/m = 6²/4 = 9, and 9 is NOT a factor of 12
ELIMINATE C

D. K/m
If K = 12, then if COULD be the case that m = 4 and n = 6
In this case, K/m = 12/4 = 3, and 3 IS a factor of 12
KEEP D (for now)

E. K/(mn)
If K = 12, then if COULD be the case that m = 4 and n = 6
In this case, K/(mn) = 12/(4)(6) = 1/2, and 1/2 is NOT a positive INTEGER factor of 12
ELIMINATE E

By the process of elimination, the correct answer is D

Cheers,
Brent
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Re: The numbers m, n, and K are all positive integers. Given that m is a [#permalink]
Opt D.

I tried using an example. Let's say K = 8
Factors - 1,2,4,8

Now look at options and we can eliminate all options except D.
Re: The numbers m, n, and K are all positive integers. Given that m is a [#permalink]
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