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

Question

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

(1) q/2 is an integer

(2) p is a prime number

M36-123

Bunuel · Accepted Answer

Official Solution:

If  p  and  q  are integers and  \frac{pq}{10}  is an integer, is  \frac{p}{5}  an integer? ​ 
 
(1)  \frac{q}{2}  is an integer.
 
The above means that  q  is even.
 
Can  p  be a multiple of 5? Certainly. Consider  p=5  and  q=2=even ;
 
Can  p  NOT be a multiple of 5? Certainly. Consider  p=1  and  q=10=even . 
 
Not sufficient.
 
(2)  p  is a prime number
 
Can  p  be a multiple of 5? Certainly. Consider  p=5=prime  and  q=2 ;
 
Can  p  NOT be a multiple of 5? Certainly. Consider  p=3=prime  and  q=10 . 
 
Not sufficient.
 
(1)+(2) Examples used for (2) are also valid for (1) (because we consider even values of  q  there). So, even taken together we cannot answer the question. Not sufficient.

Answer: E

Archit3110 · Answer

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 ....

amanvermagmat · Answer

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 .

Bunuel · Answer

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

exc4libur · 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)

Papai21 · Answer

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

Posted from my mobile device

GMATCoachBen · Answer

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.

bumpbot · Answer

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

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

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