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If 15 and 4 are factors of positive integer K, and 5 and 8 a
[#permalink]
26 May 2017, 13:37

Expert Reply

2

Bookmarks

Question Stats:

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

_________________

Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a
[#permalink]
05 Jun 2017, 13:25

3

Expert Reply

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

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.

Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a
[#permalink]
15 Jun 2019, 08:55

Expert Reply

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

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

_________________

Re: If 15 and 4 are factors of positive integer K, and 5 and 8 a
[#permalink]
01 Feb 2021, 08:15

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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