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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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WE: Supply Chain Management (Energy and Utilities)
this is from one of the 'hard math' princeton pdf's and i [#permalink]

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05 Sep 2004, 22:00
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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...

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06 Sep 2004, 00:49
I agree with Princeton's answer. Why do you think it's wrong or E?

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Joined: 31 Dec 1969

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Location: Russian Federation
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

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06 Sep 2004, 07:20
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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06 Sep 2004, 10:24
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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06 Sep 2004, 10:44
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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06 Sep 2004, 10:51
Agree with E.
Same reasons as user.

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06 Sep 2004, 11:21
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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06 Sep 2004, 14:17

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

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06 Sep 2004, 14:17
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