If t and u are positive integers, what is the value of : GMAT Data Sufficiency (DS)
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# If t and u are positive integers, what is the value of

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If t and u are positive integers, what is the value of [#permalink]

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24 Aug 2012, 03:53
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If t and u are positive integers, what is the value of $$t^{-3}*u^{-2}$$?

(1) $$t^{-2}*u^{-3} = \frac{1}{36}$$.

(2) $$t*(u^{-1}) = \frac{1}{6}$$.
[Reveal] Spoiler: OA

Last edited by manulath on 24 Aug 2012, 23:35, edited 3 times in total.
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Re: If t and u are positive integers, what is the value of [#permalink]

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24 Aug 2012, 09:42
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If t and u are positive integers, what is the value of $$t^{-3}*u^{-2}$$?

(1) $$t^{-2}*u^{-3} = \frac{1}{36}$$ --> $$\frac{1}{t^{2}*u^{3}}=\frac{1}{36}$$ --> $$t^{2}*u^{3}=36$$ --> since $$t$$ and $$u$$ are positive integers, then only possible case is $$t^{2}*u^{3}=6^2*1^3$$ ($$u$$ cannot be any other positive integer but 1, since 36 doesn't have a prime factor in power of 3) --> $$t=6$$ and $$u=1$$. Sufficient.

(2) $$t*(u^{-1}) = \frac{1}{6}$$ --> $$\frac{t}{u}=\frac{1}{6}$$ --> infinite number of values are possible for $$t$$ and $$u$$ (1, and 6, 2 and 12, 3 and 18, ...), thus infinite number of values are possible for $$t^{-2}*u^{-3}$$. Not sufficient.

Hope it's clear.
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Kudos [?]: 95 [0], given: 14

Re: If t and u are positive integers, what is the value of [#permalink]

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24 Aug 2012, 23:34
Bunuel wrote:

If t and u are positive integers, what is the value of $$t^{-2}*u^{-3}$$?

(1) $$t^{-2}*u^{-3} = \frac{1}{36}$$ --> $$\frac{1}{t^{2}*u^{3}}=\frac{1}{36}$$ --> $$t^{2}*u^{3}=36$$ --> since $$t$$ and $$u$$ are positive integers, then only possible case is $$t^{2}*u^{3}=6^2*1^3$$ ($$u$$ cannot be any other positive integer but 1, since 36 doesn't have a prime factor in power of 3) --> $$t=6$$ and $$u=1$$. Sufficient.

(2) $$t*(u^{-1}) = \frac{1}{6}$$ --> $$\frac{t}{u}=\frac{1}{6}$$ --> infinite number of values are possible for $$t$$ and $$u$$ (1, and 6, 2 and 12, 3 and 18, ...), thus infinite number of values are possible for $$t^{-2}*u^{-3}$$. Not sufficient.

Hope it's clear.

You have corrected the error. Thanks once again.
The question now makes sense.

In the original question the answer I got was C

PS: I have edited the question again, as question stem and A have become same.
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Re: If t and u are positive integers, what is the value of [#permalink]

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27 Jan 2014, 13:21
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Re: If t and u are positive integers, what is the value of [#permalink]

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31 Oct 2016, 09:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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If t and u are positive integers, what is the value of [#permalink]

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28 Jan 2017, 18:39
Bunuel wrote:

If t and u are positive integers, what is the value of $$t^{-3}*u^{-2}$$?

(1) $$t^{-2}*u^{-3} = \frac{1}{36}$$ --> $$\frac{1}{t^{2}*u^{3}}=\frac{1}{36}$$ --> $$t^{2}*u^{3}=36$$ --> since $$t$$ and $$u$$ are positive integers, then only possible case is $$t^{2}*u^{3}=6^2*1^3$$ ($$u$$ cannot be any other positive integer but 1, since 36 doesn't have a prime factor in power of 3) --> $$t=6$$ and $$u=1$$ . Sufficient.

(2) $$t*(u^{-1}) = \frac{1}{6}$$ --> $$\frac{t}{u}=\frac{1}{6}$$ --> infinite number of values are possible for $$t$$ and $$u$$ (1, and 6, 2 and 12, 3 and 18, ...), thus infinite number of values are possible for $$t^{-2}*u^{-3}$$. Not sufficient.

Hope it's clear.

Dear Bunuel, (1) t should be 1 and u should be 6.
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Re: If t and u are positive integers, what is the value of [#permalink]

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29 Jan 2017, 02:44
ziyuenlau wrote:
Bunuel wrote:

If t and u are positive integers, what is the value of $$t^{-3}*u^{-2}$$?

(1) $$t^{-2}*u^{-3} = \frac{1}{36}$$ --> $$\frac{1}{t^{2}*u^{3}}=\frac{1}{36}$$ --> $$t^{2}*u^{3}=36$$ --> since $$t$$ and $$u$$ are positive integers, then only possible case is $$t^{2}*u^{3}=6^2*1^3$$ ($$u$$ cannot be any other positive integer but 1, since 36 doesn't have a prime factor in power of 3) --> $$t=6$$ and $$u=1$$ . Sufficient.

(2) $$t*(u^{-1}) = \frac{1}{6}$$ --> $$\frac{t}{u}=\frac{1}{6}$$ --> infinite number of values are possible for $$t$$ and $$u$$ (1, and 6, 2 and 12, 3 and 18, ...), thus infinite number of values are possible for $$t^{-2}*u^{-3}$$. Not sufficient.

Hope it's clear.

Dear Bunuel, (1) t should be 1 and u should be 6.

Everything is correct there. Notice that first statement in the original post and in your screenshot are different.

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Re: If t and u are positive integers, what is the value of   [#permalink] 29 Jan 2017, 02:44
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