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this is from one of the 'hard math' princeton pdf's and i

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Joined: 31 Dec 1969
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Concentration: Marketing, Other
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this is from one of the 'hard math' princeton pdf's and i [#permalink] New post 05 Sep 2004, 21:00
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this is from one of the 'hard math' princeton pdf's and i think their answer is wrong.


18. If x , y , and z are integers, is x / ( yz ) an integer?
(1) y is a factor of x more than once.
(2) All of the prime factors of z are also
factors of y .

My answer and theirs are below, PAGE DOWN a few times to see...





















***********I'd*go*with*E*their*answer*is*C************
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 [#permalink] New post 05 Sep 2004, 23:49
I agree with Princeton's answer. Why do you think it's wrong or E?
Joined: 31 Dec 1969
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 [#permalink] New post 06 Sep 2004, 06:20
y = 2 ^ 2 * 3 = 12
z = 2 * 3 ^ 3 = 54

x = y * y = 2916
y * z = 648

and yet, (zy) does not divide x, 2916 / 648 is not an integer.

the way i am reading it is, all the prime factors of z are factors of y. so 2 and 3 are factors of y, but not necessarily 3 ^ 3.
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 [#permalink] New post 06 Sep 2004, 09:24
user wrote:
y = 2 ^ 2 * 3 = 12
z = 2 * 3 ^ 3 = 54

x = y * y = 2916
y * z = 648

and yet, (zy) does not divide x, 2916 / 648 is not an integer.

the way i am reading it is, all the prime factors of z are factors of y. so 2 and 3 are factors of y, but not necessarily 3 ^ 3.


The way I read the question, I get that ALL the prime factors of z have to be factors of y. Therefore, if 3 happens to occur twice in z, then it must occur twice in y.
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 [#permalink] New post 06 Sep 2004, 09:44
I think user is correct in the assumption on Prime factors. Otherwise, they would just be called factors. I support E too.
Btw, user, you might have meant, x = y * y = 144

The ans for the above example, x=144 y=12 z=54, is "No, x/yz is not an integet"
The ans for another example, x=25 y=5 z=5, is " "Yes, x/yz is an integer".
Hence, E.
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 [#permalink] New post 06 Sep 2004, 09:51
Agree with E.
Same reasons as user.
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 [#permalink] New post 06 Sep 2004, 10:21
hardworker_indian wrote:
I think user is correct in the assumption on Prime factors. Otherwise, they would just be called factors.


The reason they use prime factors in case of z and just factors in case of y is that if you don't do that, you'll be explicitly stating that y and z are the same numbers.

It's just a matter of semantics. Questions on the actual GMAT are usually not this ambigious.
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 [#permalink] New post 06 Sep 2004, 13:17
This question has already been solved in another thread...

http://www.gmatclub.com/phpbb/viewtopic.php?t=9471

Btw answer is C
  [#permalink] 06 Sep 2004, 13:17
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this is from one of the 'hard math' princeton pdf's and i

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