manik11 wrote:If n is an integer, is the sum of all of n's divisors, which are not equal to n or equal to one, greater than 100?
(1) 3 and 96 are divisors of n that are neither equal to n nor equal to one.
(2) 3 and 97 are divisors of n that are neither equal to n nor equal to one.
OA : A
Source : BellCurves
Statement 1:
Any integer divisible by 96 will also be divisible by 3.
Since 96 is a factor of n that is not EQUAL to n, n must be a multiple of 96 such that n > 96:
192, 288...
If n is equal to any value in this list, its factors will include 2, 4 and 96, so the sum of its factors between 1 and n will be GREATER THAN 100.
SUFFICIENT.
Statement 2:
Since 3 and 97 are both prime, n must be a multiple of 3 and 97:
291, 582...
If n=291, then the sum of its factors between 1 and n = 3+97 = 100.
In this case, the answer to the question stem is NO.
If n=582, then its factors include 2, 3 and 97, so the sum of its factors between 1 and n will be GREATER THAN 100.
In this case, the answer to the question stem is YES.
INSUFFICIENT.
The correct answer is
A.
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