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

Last edited by manulath on 25 Aug 2012, 00:35, edited 3 times in total.

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

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The question should read:

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

Answer: A.

Hope it's clear.
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Re: If t and u are positive integers, what is the value of [#permalink]

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New post 25 Aug 2012, 00:34
Bunuel wrote:
The question should read:

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.

Answer: A.

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

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

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New post 28 Jan 2017, 19:39
Bunuel wrote:
The question should read:

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.

Answer: A.

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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New post 29 Jan 2017, 03:44
ziyuenlau wrote:
Bunuel wrote:
The question should read:

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.

Answer: A.

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]

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New post 29 May 2017, 17:29
manulath wrote:
If t and u are positive integers, what is the value of \(t^{-3}*u^{-2}\)?

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

(2) \(t*(u^{-1}) = \frac{1}{6}\).



This problem is a classic C-trap. The goal is to find the value of t^-2*u^-3. It should be a distinct value.

Statement 1) t^-3*u^-2 = 1/36

We should take the reciprocal here to make the math easier.

t^3*u^2 = 36

There is only one possible value here that satisfies this relationship:

t = 1, u = 6.

Sufficient.

Statement 2) t/u = 1/6

6t = u. We cannot infer anything beyond this ratio. Insufficient.

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

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I got A and that wasn't difficult for me, however, doesn't the second statement contradict the first statement which wouldn't happen in DS questions?

For the 2nd statement, assuming you knew what you did from the 1st statement, you would have the values of t and u be reversed.

Can someone please clarify that that is correct?

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

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New post 13 Jun 2017, 06:26
laxpro2001 wrote:
I got A and that wasn't difficult for me, however, doesn't the second statement contradict the first statement which wouldn't happen in DS questions?

For the 2nd statement, assuming you knew what you did from the 1st statement, you would have the values of t and u be reversed.

Can someone please clarify that that is correct?


You are right. Edited the second statement to fix this issue. Thank you.
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Re: If t and u are positive integers, what is the value of [#permalink]

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New post 13 Jun 2017, 10:00
Thank you for the quick response, Bunuel.

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Re: If t and u are positive integers, what is the value of   [#permalink] 13 Jun 2017, 10:00
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