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If both 5 squared and 3 cubed...

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Junior | Next Rank: 30 Posts
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by houstonrockets16 » Mon Feb 02, 2009 4:49 pm
If both 5^2 and 3^3 are factors of n x 2^5 x 6^2 x 7^3 , what is the smallest possible positive value of n?

A) 25
B) 27
C) 45
D) 75
E) 125

I am having trouble with this question....


I keep thinking it is A...

the correct answer is... D

Please help! Thanks!
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Source: — Data Sufficiency |
Junior | Next Rank: 30 Posts
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Not Relevant

by peddisetty » Mon Feb 02, 2009 4:56 pm
Hello,
Please post this question is problem solving. This is Data Sufficiency section. Anyhow answer is D.

Raj.
Raj Peddisetty
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Junior | Next Rank: 30 Posts
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by houstonrockets16 » Mon Feb 02, 2009 4:57 pm
Sorry I will move it now, is there any way you can tell me why it is the case?
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by cetmk » Mon Feb 02, 2009 4:58 pm
n x 2^5 x 6^2 x 7^3 can be written as
n x 2^5 x (3 x 2)^2 x 7^3
= n x 2^7 x 3^2 x 7^3

This should contain atleast 2 factors of 5 (5^2) and 3 factors of 3(3^3). Since the number already has 2 factors of 3, the smallest possible value of n is 5^2 x 3 = 75
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Junior | Next Rank: 30 Posts
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by peddisetty » Mon Feb 02, 2009 6:28 pm
Hi houston,
I am sorry if you were offended. I just wanted to inform you that this section is for data sufficiency only. I felt it was more appropriate not to mix questions. thats it.....take it easy....

cheers...
Raj Peddisetty
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