Factor problem

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chdn20: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Dec 27, 2009 6:02 am

by chdn20 » Mon May 10, 2010 8:15 am

Any help in solving this problem would be great:

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

25
27
45
75
125

Thanks,

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Source: Beat The GMAT — Problem Solving | Mon May 10, 2010 8:15 am

liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Mon May 10, 2010 8:17 am

n x 2^5 x 6^2 x 7^3=k*5^2*3^3..where k is an integer

or n x 2^5 x 2^2x3^2 x 7^3=k*5^2*3^3

so smallest possible value of n is 5^2*3or 75

Ans option D

"If you don't know where you are going, any road will get you there."
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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 11, 2010 2:09 am

chdn20 wrote:Any help in solving this problem would be great:

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

25
27
45
75
125

Thanks,

5^2 is a factor of n x 2^5 x 6^2 x 7^3, no 5 is appearing in the split, 5^2 must be hidden as a factor in n, and also that 3^3 is a factor of n x 2^5 x 2^2 Ã— 3^2 x 7^3, only 3^2 is appearing in the split, the left over 3 must be hidden as a factor in n. For the smallest possible positive value of n, we must not supply anything other than 5^2 Ã— 3 to construct the n in question. This n must be [spoiler]25 Ã— 3 = 75.

D in your order[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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