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If 15 and 4 are factors of positive integer K, and 5 and 8 are not

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If 15 and 4 are factors of positive integer K, and 5 and 8 are not  [#permalink]

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New post 18 May 2017, 07:00
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Question Stats:

60% (02:02) correct 40% (02:05) wrong based on 154 sessions

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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

*kudos for all correct solutions

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Re: If 15 and 4 are factors of positive integer K, and 5 and 8 are not  [#permalink]

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New post 18 May 2017, 07:59
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GMATPrepNow 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

*kudos for all correct solutions


k is a multiple of 5 and M is NOT a multiple of 5

hence K-M can never be a multiple of 5

Answer: Option D
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Re: If 15 and 4 are factors of positive integer K, and 5 and 8 are not  [#permalink]

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New post 26 May 2017, 14:36
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GMATPrepNow 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:

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If 15 and 4 are factors of positive integer K, and 5 and 8 are not  [#permalink]

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New post 24 Aug 2018, 18:19
GMATPrepNow 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

*kudos for all correct solutions


picking a number,
if K=120,
then K-M cannot equal 120-50=70,
as 50 is a multiple of 5
D
GMAT Club Bot
If 15 and 4 are factors of positive integer K, and 5 and 8 are not   [#permalink] 24 Aug 2018, 18:19
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If 15 and 4 are factors of positive integer K, and 5 and 8 are not

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