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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