If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer

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

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)

Hi..
Can any please tell me where Im doing this wrong.
Given pq/10 is an integer.
So, pq = 10 k,where k is an integer
= 2 * 5 * k
St. (1) q/2 is an integer
So, q = 2 * k1, where k1 is an integer
Substituting value of q,
p * 2 * k1 = 2 * 5 * k
p = 5 * (k/k1)
Thus for p/5 to be an integer, (k/k1) needs to be an integer.
So, its not sufficient.

St. (2) clearly not sufficient.

Combining st. 1 and st. 2 we have
p = 5 * (k/k1) and p is a prime number.
So only possible case is p = 5
Hence, option C

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Hi Papai21. I believe your mistake is on this line: "Thus for p/5 to be an integer, (k/k1) needs to be an integer."

We can't assume that p/5 is an integer, nor that k/k1 is an integer.

From the stem, all we know is that pq = 2*5*k. We don't know anything else about what is or isn't an integer. Assuming that something is an integer is a common mistake — we must proactively check our assumptions to prevent these traps.

Let's pick some numbers to illustrate, looking at both statements together:

Case A: p = 2, q = 10. This gives us a "NO" answer to "is p/5 an integer?"

Case B: p = 5, q = 2. This gives us a "YES" answer to "is p/5 an integer?"

Therefore, Insufficient together. Answer is E.

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