From 1: q/2 can be any integer value >/1
so pq/10 we can say
let q= 2 so now p has to be 5 to be valid so yes p/5 is an integer
let q=10, so now p has to be 1 , so p/5 is not an integer
In suficient

From 2:
P is a prime no. it can be ,3,2,7,, so again we would get yes at 5 and no at other no. in sufficient

Again when combining let p =3 and q= 10 so pq/10 is an integer and 3/5 "p/5" is not an integer and
at p=5, q=2 , p/5 is an integer hence E ....

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.

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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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)