If p and q are positive integers, is every factor of p a factor of q?
(1) The product of the prime factors of p is a factor of q.
(2) p is a factor of q.
a. statement 1 and 2 are sufficient
b. Both are not sufficient
c. statement 1 is sufficient while statement 2 is not sufficient
d. statement 1 is not sufficient while statement 2 is sufficient
e. statement 1 is sufficient
OA is d
why is statement not sufficient and how do you arrive at this?
Number properties
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The correct answer is B.Roland2rule wrote:If p and q are positive integers, is every factor of p a factor of q?
(1) The product of the prime factors of p is a factor of q.
(2) p is a factor of q.
OA is d
why is statement not sufficient and how do you arrive at this?
Statement 1: The product of the prime factors of p is a factor of q.
Case 1: Say p = 6 and q = 6
Prime factors of p are 2 and 3. The product of 2 and 3 = 6 is a factor of q and all the factors of p are factors of p. The answer is Yes.
Case 2: Say p = 12 and q = 6
Prime factors of p are 2 and 3. The product of 2 and 3 = 6 is a factor of q, but not all factors of p are factors of q (12 is not a factor of q). The answer is No. Insufficient.
Statement 2: p is a factor of q.
Since p is a factor of q , q/p = integer, thus every factor of p will be a factor of q. Sufficient.
The correct answer: B
Hope this helps!
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