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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 15 and 4 are factors of positive integer K, and 5 and 8 a
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26 May 2017, 13:37
26 May 2017, 13:37
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Question Stats:
38% (01:31) correct
61% (02:05) wrong based on 86 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
A) 34
B) 44
C) 54
D) 70
E) 83
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a
[#permalink]
05 Jun 2017, 13:25
05 Jun 2017, 13:25
3
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
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
Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a
[#permalink]
15 Jun 2019, 08:46
15 Jun 2019, 08:46
1
Bookmarks
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
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.
