Statement 1: The greatest common divisor of z and 140 is 7.canbtg wrote:If z is an integer, is z prime?
1. The greatest common divisor of z and 140 is 7.
2. The sum of the distinct factors of z is less than 10.
OA C
It's possible that z=7, since the greatest integer that divides into both z=7 and 140 is 7.
In this case, z is prime.
It's possible that z=21, since the greatest integer that divides into both z=21 and 140 is 7.
In this case, z is not prime.
INSUFFICIENT.
Statement 2: The sum of the distinct factors of z is less than 10.
It's possible that z=7, since the sum of the distinct factors of 7 = 1+7 = 8, which is less than 10.
In this case, z is prime.
It's possible that z=4, since the sum of the distinct factors of 4 = 1+2+4 = 7, which is less than 10.
In this case, z is not prime.
INSUFFICIENT.
Statements combined:
The smallest value that satisfies both statements is z=7.
The next smallest value that satisfies statement 1 is z=21, but this value does not satisfy statement 2, since the sum of the distinct factors of 21 = 1+3+7+21 = 32, which is greater than 10.
Implication:
The ONLY value small enough to satisfy both statements is z=7, implying that z must be prime.
SUFFICIENT.
The correct answer is C.
