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

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

by BTGModeratorVI » Sun Sep 27, 2020 7:07 am

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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)

Source: Magoosh

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

by [email protected] » Mon Sep 28, 2020 12:02 pm
BTGModeratorVI wrote:
Sun Sep 27, 2020 7:07 am
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)

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

Cheers,
Brent

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

by [email protected] » Mon Sep 28, 2020 12:02 pm
BTGModeratorVI wrote:
Sun Sep 27, 2020 7:07 am
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)

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

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

by swerve » Tue Sep 29, 2020 12:39 pm
BTGModeratorVI wrote:
Sun Sep 27, 2020 7:07 am
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)

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

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

by gentvenus » Tue Sep 29, 2020 6:24 pm
[email protected] wrote:
Mon Sep 28, 2020 12:02 pm
BTGModeratorVI wrote:
Sun Sep 27, 2020 7:07 am
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)

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

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