If pq/10 is an integer, is p/5 an integer?


(1) q/2 is an integer

(2) p is a prime number
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pq/10 can also be written as p/5 * q/2: this product is given to be an integer. We have to determine whether p/5 is an integer or not.

(1) q/2 is an integer. And product of this integer q/2 with p/5 is also an integer. Now in this case p/5 could be integer or it could be not.
Eg, say q/2 is 4, and p/5 is 1, then the product 4*1 is an integer. Or say q/2 is 4 and p/5 is 0.5, here also the product 4*0.5 is an integer.
So we cannot be sure whether p/5 is an integer or not.
Not sufficient.

(2) This is definitely not sufficient. Eg if p is 5, then p/5 is an integer. But if p is 2, then p/5 is not an integer. '
Not sufficient.

Combining the two statements, p is a prime number, q/2 is an integer, and the product of q/2 * p/5 is also integer.
So lets say, q/2 = 4, p=5. Here the product 4*5 is an integer, p is a prime number and p/5 is an integer.
Now lets say, q/2 = 5, p=2. Here the product 5*2 is an integer, p is a prime number BUT p/5 is NOT an integer.

Not sufficient. Hence E answer.

pq/10=integer… factors(p and/or q) may contain any multiples of 10

(1) q/2 is an integer: insufic.

q=2*anything;
q=2, p=5*anything, p/5=integer;
q=10, p=anything, p/5=anything;

(2) p is a prime number: insufic.

p=prime;
p=5, p/5=integer;
p=3, p/5≠integer;

(1 & 2): insufic.

q=10, p=3, p/5≠integer;
q=10, p=5, p/5=integer;

Answer (E)