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

[BTGModeratorVI]

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)

Answer: D
Source: Magoosh

[Brent@GMATPrepNow]

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)

Answer: D
Source: Magoosh

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

Answer: D

Cheers,
Brent

[Brent@GMATPrepNow]

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)

Answer: D
Source: Magoosh

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

[swerve]

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)

Answer: D
Source: Magoosh

If \(K\) is a positive integer and \(K\) is divided by one of its factors the result is always a factor of \(K \Rightarrow\) K/m or K/n satisfies the rule.

For example: \(K = 100 \Rightarrow\) Factors of \(K = 1, 2, 4, 5, 10, 20, 25, 50, 100\)
Let \(m = 10; n = 100\)

A. \(m + n \Rightarrow 110\) is not a factor of \(K \Large{\color{red}\chi}\)

B. \(mn \Rightarrow 1000\) is not a factor of \(K \Large{\color{red}\chi}\)

C. \(n^2/m \Rightarrow 1000\) is not a factor of \(K \Large{\color{red}\chi}\)

D. \(K/m \Rightarrow 10\) is a factor of \(K\) \(\Large{\color{green}\checkmark}\)

E. \(K/(mn) \Rightarrow 0.1\) is not an integer \(\Large{\color{red}\chi}\)

Therefore, D

[gentvenus]

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)

Answer: D
Source: Magoosh

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

I like this approach