prime factors problem

[akhilsaini2001]

if x and y are positive integers, is 2x/y an integer?
1. some factors of y are also factors of x.
2. all prime factors of y are also prime factors of x.

i think the answer is B BUT the answer is E, but i am not convinced by the reasoning i got for it.

the book's explaination says:-
the second statement indicates that all distinct prime factors of y are also factors of x. this means that if y has at least one of a given prime number as a factor, then x also has at least one of that prime factor. so statement 2 tells us only that at least one prime factor is shared. so we dont have an absolute yes or no.

my explaination:-
second statement says all prime factors of x are factors of y so all factors of y get cancelled with those of x. so we are left with few factors of x and 2 in numerator and nothing in denominator which makes it a integer . so B is the answer.

please help me get the correct thinking path. cos of course book cannot be wrong.

[gmatmachoman]

if x and y are positive integers, is 2x/y an integer?
1. some factors of y are also factors of x.
2. all prime factors of y are also prime factors of x.

i think the answer is B BUT the answer is E, but i am not convinced by the reasoning i got for it.

the book's explaination says:-
the second statement indicates that all distinct prime factors of y are also factors of x. this means that if y has at least one of a given prime number as a factor, then x also has at least one of that prime factor. so statement 2 tells us only that at least one prime factor is shared. so we dont have an absolute yes or no.

my explaination:-
second statement says all prime factors of x are factors of y so all factors of y get cancelled with those of x. so we are left with few factors of x and 2 in numerator and nothing in denominator which makes it a integer . so B is the answer.

please help me get the correct thinking path. cos of course book cannot be wrong.

I prefer plugging in a Number

Let X= 42 = 2*3 * 7

Y = 63 = 3^2 * 7.

Now as per st s all prime factors of Y are also prime fcators of X. But are they form a integer when 2x/y?? No

So it doesnt give a absolute yes / No.

Actually u gave thought only about the prime factors, but ignored the total number of factors of those prime numbers!

[tpr-becky]

This is a question of semantics - when it says all distinct prime factors the book does not take into account the number of them, just the identity. Therefore if y is 9 x can be 3 and thus the additional 3 on the bottom would not be cancelled out. I have never been truly convinced by their definition of all but you have to go with it becuase they write the test. The thing to learn is that all doesn't talk to the number of things, just the identity. Hope this helps.

[Patrick_GMATFix]

@akhilsaini2001,

Welcome to BTG forums

The book's explanation is right as Becky demonstrated. This question is written with an official question for template. Maybe someone else will be able to locate that question. Essentially the GMAT writers who wrote the original question (that this is based on) use slightly different language. Something closer to what's below:

(1) Every factor of p is also a factor of q

(2) Every prime factor of p is also a prime factor of q

every might have been "each". Either way, in the official version, a singular pronoun is used (instead of "all" as this question uses). Using a singular pronoun makes the question clearer by emphasizing that we're dealing with each prime (for instance 3, 5) and not all primes put together (for instance 3^2 or 5^2).

I tried to locate the question but it's taking too long. If I find it i'll edit this post.

-Patrick

[tpr-becky]

I believe the question was removed from the 12th edition but it is in the 11th edition.

[Patrick_GMATFix]

I believe the question was removed from the 12th edition but it is in the 11th edition.

Impressive memory!! The question I was referring to is #125 DS in the OG11

If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r.
(2) Every prime factor of s is also a prime factor of r.

Thanks for the tip Becky

[akhilsaini2001]

thanks guys... it was prompt help.. really appreciate...

[Patrick_GMATFix]

You're welcome.