Smallest positive factor PS. Help.

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aman88: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sat Oct 20, 2012 3:31 amFollowed by: 3 members; Location: New Delhi; Thanked: 20 times

by aman88 » Wed Dec 26, 2012 12:13 am

Both 52 and 33 are factors of n Ã— 25 Ã— 62 Ã— 73 where n is a positive integer. What is the smallest possible positive value of n?

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

OA D

Can someone please explain this problem.

Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Dec 26, 2012 12:13 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Dec 26, 2012 12:25 am

Please check your source.
I think the original question is as follows...

Both 5^2 and 3^3 are factors of n Ã— 2^5 Ã— 6^2 Ã— 7^3 where n is a positive integer. What is the smallest possible positive value of n?

Say, N = n Ã— 2^5 Ã— 6^2 Ã— 7^3

If 5^2 and 3^3 are factors of N, then N must contain two 5s and three 3s.

Now, 2^5 Ã— 6^2 Ã— 7^3 does not contain any 5. But it does contain two 3s in 6^2 = (2*3)^2

Hence, the missing two 5s and one 3 must be a factor of n.
Hence, minimum possible value of n is (5^2)*3 = 3*25 = 75

The correct answer is D.

PS : According to the question you have posted, following the similar logic the minimum possible value of n should be 33*(52/2) = 33*26

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aman88: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sat Oct 20, 2012 3:31 amFollowed by: 3 members; Location: New Delhi; Thanked: 20 times

by aman88 » Wed Dec 26, 2012 12:40 am

Yes, you are right sir. I posted the question incorrectly. Sorry for that.

The original question is what you've mentioned as:
"Quote:
Both 5^2 and 3^3 are factors of n X 2^5 X 6^2 X 7^3 where n is a positive integer. What is the smallest possible positive value of n?"

**I have one question though.
What if the question asked the largest possible value of n?

Thanks.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Dec 26, 2012 9:58 pm

aman88 wrote:What if the question asked the largest possible value of n?

There is no definite answer to this question. As our requirement is n must have two 5s and one 3, we can find the minimum positive value for n. But the maximum value of n can be the largest possible positive multiple of 75 which we cannot definitely determine.

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