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# If c and d are positive, is d an integer ?

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Intern
Joined: 12 Jun 2011
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If c and d are positive, is d an integer ? [#permalink]

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22 Jul 2012, 18:17
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If c and d are positive, is d an integer ?

(1) c=d^3
(2) $$d=\sqrt{c}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jul 2012, 01:40, edited 2 times in total.
Edited the question.
Senior Manager
Joined: 11 May 2011
Posts: 361
Location: US
Re: If c & d are positive, is d an integer? [#permalink]

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22 Jul 2012, 20:26
pathakshashi wrote:
If c & d are positive, is d an integer ?
i) c=d^3
ii) d=\sqrt{c}

My answer is C and below is the explanation.
i) c=d^3 -> c & d can have multiple fraction values to satisfy this equation. Hence Insuff.
ii) d=\sqrt{c} -> Here as well, c & d can have multiple fraction values to satisfy this equation. Hence Insuff.

Putting together -> d = square_root (d^3) and this equation can have only one value, which is d =1. Hence C is the answer.

Cheers!
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Joined: 02 Sep 2009
Posts: 39702
Re: If c and d are positive, is d an integer ? [#permalink]

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23 Jul 2012, 01:50
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If c and d are positive, is d an integer ?

(1) c=d^3. If $$c$$ is a perfect cube (for example 1^3=1, 2^3=8, 3^3=27, ...), then the answer is YES but if $$c$$ is NOT a perfect cube (for xample if $$c=2$$), then the answer is NO. Not sufficient.

(2) $$d=\sqrt{c}$$ --> $$c=d^2$$. The same here: if $$c$$ is a perfect square (for example 1^2=1, 2^3=4, 3^2=9, ...), then the answer is YES but if $$c$$ is NOT a perfect square (for xample if $$c=2$$), then the answer is NO. Not sufficient.

(1)+(2) From above we have that $$d^3=d^2$$ --> $$d^3-d^2=0$$ --> $$d^2(d-1)=0$$ --> $$d=0$$ (not a valid solution since we are told that $$d$$ must be positive) or $$d=1=integer$$. Sufficient.

Hope it's clear.
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Re: If c and d are positive, is d an integer ? [#permalink]

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09 Nov 2015, 23:06
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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Re: If c and d are positive, is d an integer ?   [#permalink] 09 Nov 2015, 23:06
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