6 or 8?

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realanoop: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sun Dec 14, 2008 12:04 pm

by realanoop » Tue Dec 30, 2008 11:57 am

k is a positive integer and 225 and 216 are both divisors of k. If k=2^a*3^b*5^c, where a, b and care positive integers, what is the least possible value of a+ b+ c?
(A) 4(B) 5(C) 6(D) 7(E) 8

ans is 6 or 8?

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Source: Beat The GMAT — Problem Solving | Tue Dec 30, 2008 11:57 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: 6 or 8?

by Ian Stewart » Tue Dec 30, 2008 12:03 pm

realanoop wrote:k is a positive integer and 225 and 216 are both divisors of k. If k=2^a*3^b*5^c, where a, b and care positive integers, what is the least possible value of a+ b+ c?
(A) 4(B) 5(C) 6(D) 7(E) 8

ans is 6 or 8?

In a question that mentions divisors, you'll almost always want to prime factorize:

225 = 15^2 = 3^2 * 5^2
216 = 6^3 = 2^3 * 3^3

So we know k is divisible by 2^3 * 3^3 * 5^2. The answer is thus 8. Note that this question is really just asking about the Least Common Multiple of 225 and 216, which is what we found.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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rajataga: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Tue Dec 23, 2008 11:06 pm; Thanked: 2 times

by rajataga » Tue Dec 30, 2008 12:52 pm

I found the LCM 5400, and then broke it up into

2^3
3^3
5^2

However, Ian's solution is quicker.

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Wed Dec 31, 2008 4:48 am

thanks Ian for the explanation.

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