If x and y are two distinct positive integers, is x/y an int

Question

If x and y are two distinct positive integers, is x/y an integer?

(1) y is the product of 2 and another integer.
(2) There is only 1 pair of positive integers whose product equals x.

Source: 4gmat

BrushMyQuant · Answer

STAT1
says, y is even
Doesn't talk about x
So, INSUFFICIENT

STAT2
Says, x is prime, But does not talk about y.
If y is 1 then x/y is integer.
If y is not 1 then x/y will not be an integer
SO, INSUFFICIENT

STAT1 and STAT2 together
Y is even and x is prime and both are different integers so
X/y can never be an integer
So, SUFFICIENT

Answer will be C

hope it helps!

Bunuel · Answer

If x and y are two distinct positive integers, is x/y an integer?

(1) y is the product of 2 and another integer. This statement implies that y is even. No info about x. Not sufficient.

(2) There is only 1 pair of positive integers whose product equals x. This statement implies that x is prime. No info about y. Not sufficient.

(1)+(2) y is even and x is a prime different from y, thus y is even and x is an odd prime --> x/y = odd/even, which cannot be an integer OR y is even number greater than 2 and x = 2 = prime --> x/y = 2/(greater than 2), not an integer. Sufficient.

Answer: C.

alphonsa · Answer

Hi Bunuel, ' x is a prime different from y' . So you've considered it to be an odd prime But the question does not mention either. Please clarify

pqhai · Answer

Hello.

There is only one even prime number that is 2. Other prime numbers are odd. Because y = 2*integer. Thus, y is even. 
We have:
(1) x and y are distinct numbers 
(2) x is prime 
(2) y is even.
Thus, x must be odd.

Hope it's clear.

WoundedTiger · Answer

Since x has only 1 pair of positive integers whose product equals X therefore X is prime.
Consider Prime nos 3= 1*3,5=1*5,7=1*7....If x =2 then 1*2 and so on

Remember 2 is the only even prime number and all other Primes numbers are odd and St1 tells us that y is 2*(Some Integer, I) or 2I

Therefore on Combining two statements you get that x/y is never an integer because  \frac{x(Odd Prime)}{y (2I)} =\frac{Odd}{Even}  never result in a integer

Hope it helps

alphonsa · Answer

Sorry to ask such a stupid question

Distinct , i thought implies that the two numbers are differentl.
But from what is mentioned, does it mean that distinct implies 2 nos. belong to different categories itself.
Why can't x=2 and y=6 . They are distinct right?

Sorry if the question is very stupid

Bunuel · Answer

Yes, one case was missing there: y is even number greater than 2 and x = 2 = prime --> x/y = 2/(greater than 2), not an integer.

alphonsa · Answer

But 'y' can be 2* (1) = 2. Because they haven't mentioned that y is greater than 2. So should the answer be E?

Bunuel · Answer

If x = 2 = prime, then y cannot be 2 because we are told that x and y are distinct. So, if x = 2 = prime, then y must be even number greater than 2: 4, 6, 8, ... So, even in this case x/y won't be an integer.

IanStewart · Answer

If x and y are positive integers, the question "is x/y an integer" means "is x divisible by y?", or "is y a divisor of x?"

Neither statement is sufficient alone, since we need information about both letters. Using both statements, we know x is prime, so the question becomes "is y a divisor of the prime number x". But the prime number x has only two divisors: 1 and itself. The only way y could be a divisor of x is if y=1 or if y=x. We know y is not 1, from Statement 1, and we know y is not x, since they are distinct. So y can't be a divisor of x, and the two statements are sufficient together.

If x and y are two distinct positive integers, is x/y an int

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If x and y are two distinct positive integers, is x/y an int

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