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M is a positive integer, what is the greatest common factor of M and 64? (1) No two different factors of M sum to a

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by BTGmoderatorDC » Mon Feb 17, 2020 6:22 pm
M is a positive integer, what is the greatest common factor of M and 64?

(1) No two different factors of M sum to a prime number.

(2) The greatest common factor of M and 2,310 is 165.



OA D

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Re: M is a positive integer, what is the greatest common factor of M and 64? (1) No two different factors of M sum to

by Jay@ManhattanReview » Mon Feb 17, 2020 10:07 pm
BTGmoderatorDC wrote: ↑
Mon Feb 17, 2020 6:22 pm
 M is a positive integer, what is the greatest common factor of M and 64?

(1) No two different factors of M sum to a prime number.

(2) The greatest common factor of M and 2,310 is 165.

OA D

Source: Manhattan Prep
Let's take each statement one by one.

(1) No two different factors of M sum to a prime number.

Note that 1 is a factor to every number. Since no two different factors of M sum to a prime number, '2' cannot be a factor of M because if were, 1 + 2 = 3, a prime number.

Again, since '2' is not a factor of M, M must be an odd number.

Since M, an odd number and 64, an even number cannot have a common factor, other than 1. The GCF of M and 64 is 1. Sufficient.

(2) The greatest common factor of M and 2,310 is 165.

Since 2,310 is an even number and GCF = 165 is an odd number, M must NOT be an even number; had it been an even number, the GCF must also be an even number.

So, M is an odd number.

As discussed in Statement 1, since M, an odd number and 64, an even number cannot have a common factor, other than 1. The GCF of M and 64 is 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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