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

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

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27 Apr 2016, 11:00
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Difficulty:

65% (hard)

Question Stats:

62% (01:50) correct 38% (01:33) wrong based on 177 sessions

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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)

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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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28 Apr 2016, 23:45
1
If K is a positive integer and K is divided by one of its factors the result is always a factor of K. --> K/m or K/n satisfies the rule.

For ex: K = 100 --> Factors of K = 1, 2, 4, 5, 10, 20, 25, 50, 100
Let m = 10; n = 100

A. m + n --> 110 is not a factor of K
B. mn --> 1000 is not a factor of K
C. n^2/m --> 1000 is not a factor of K
D. K/m --> 10 is a factor of K
E. K/(mn) --> 0.1 is not an integer

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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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28 Dec 2016, 09:58
Great Question.
Here is what i did in this Question =>

k=mx=ny
here, x and y air integers.

Lets use brute Force here ->

Option 1=>
k=10
m=1
n=2
m+n=3 which is not a factor of 10
WRONG
Option 2->
k=10
m=5
n=10
mn=50 which is not a factor of 10
WRONG
option 3->
k=18
m=2
n=3
n^2/m = 9/2 which can never be a factor of any integer
WRONG
option->4
k/m = mx/m = x
BINGO..!!

Just to be sure
Option E->
k/mn =>
k=10
m=5
n= 10
k/mn = 10/50
WRONG

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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15 Jan 2017, 01:07
1
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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21 Jan 2019, 18:54
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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25 Jan 2019, 05:44
Top Contributor
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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25 Jan 2019, 05:45
Top Contributor
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] 25 Jan 2019, 05:45
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