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If 15 and 4 are factors of positive integer K, and 5 and 8 a

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GreenlightTestPrep
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If 15 and 4 are factors of positive integer K, and 5 and 8 a [#permalink] New post   26 May 2017, 13:37
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If 15 and 4 are factors of positive integer K, and 5 and 8 are not factors of positive integer M, then K – M CANNOT equal

A) 34
B) 44
C) 54
D) 70
E) 83
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D
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Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a [#permalink] New post   05 Jun 2017, 13:25
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GreenlightTestPrep wrote:
If 15 and 4 are factors of positive integer K, and 5 and 8 are not factors of positive integer M, then K – M CANNOT equal

A) 34
B) 44
C) 54
D) 70
E) 83


RULE #1: If d is a divisor/factor of x, but d is NOT a divisor/factor of y, then d is NOT a divisor/factor of x+y
RULE #2: If d is a divisor/factor of x, but d is NOT a divisor/factor of y, then d is NOT a divisor/factor of x-y


If 15 is a factor of K, then we can also be certain that 5 is a factor of K.
So, we know that 5 is a factor of K AND we know that 5 is not a factor of M
By RULE #2, we know that 5 is not a factor of K - M
So, K-M cannot equal 70

Answer:
Show: ::
D
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Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a [#permalink] New post   15 Jun 2019, 08:46
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GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
If 15 and 4 are factors of positive integer K, and 5 and 8 are not factors of positive integer M, then K – M CANNOT equal

A) 34
B) 44
C) 54
D) 70
E) 83


RULE #1: If d is a divisor/factor of x, but d is NOT a divisor/factor of y, then d is NOT a divisor/factor of x+y
RULE #2: If d is a divisor/factor of x, but d is NOT a divisor/factor of y, then d is NOT a divisor/factor of x-y


If 15 is a factor of K, then we can also be certain that 5 is a factor of K.
So, we know that 5 is a factor of K AND we know that 5 is not a factor of M
By RULE #2, we know that 5 is not a factor of K - M
So, K-M cannot equal 70

Answer:
Show: ::
D



as both 15 and 4 are the factors of K, then K =60x , where x a positive integer greater than or equal to 1.
Therefore, K-M when equal 70
we get, 120-M=70 [ say, K equal 60*2]
M=120-70=50 which is NOT possible, because M is not a MULTIPLE of 5 and 8.
But, elimination of other options need little elucidation .
pls do it, if possible.
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Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a [#permalink] New post   15 Jun 2019, 08:55
GreenlightTestPrep wrote:
If 15 and 4 are factors of positive integer K, and 5 and 8 are not factors of positive integer M, then K – M CANNOT equal

A) 34
B) 44
C) 54
D) 70
E) 83


Another approach is to eliminate 4 of the 5 answer choices by showing that K - M CAN equal those values.

A) 34
If K = 60 and M = 26, then K - M = 34
ELIMINATE A

B) 44
If K = 120 and M = 76, then K - M = 44
ELIMINATE B

C) 54
If K = 60 and M = 6, then K - M = 54
ELIMINATE C

E) 83
If K = 120 and M = 37, then K - M = 83
ELIMINATE E

By the process of elimination, the correct answer is D

Cheers,
Brent
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rainer85
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Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a [#permalink] New post   04 Sep 2022, 19:28
Just wanted to throw out there that any factor of both 15 and 4 has to end in the number 0 which is the case for K.

M is not divisible by 5 so it therefore cannot end in the numbers 5 or 0. Thus, no matter what K and M actually are subtracting K-M cannot yield a result where the ending digit is 0 thus 70 (D) is the correct answer choice.
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gmatclubot
Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a [#permalink]
04 Sep 2022, 19:28
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