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Basic Permutation Question - Need Clarification

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Basic Permutation Question - Need Clarification

by Gladius » Thu Mar 24, 2011 11:39 am
I have a basic permutation question where I need some help in getting to the answer fairly quickly. Also, need to know what's the best approach to attack similar problem

Question: If P(n,3) = 210 , find value of n?

So here is what I am doing: n!/(n-3)! = 210
n x (n-1) x (n-2) = 210

I know the answer should be 7 x 6 x 5, but what's the easiest way to split 210 and get to value of n? More importantly how do you know it's 7,6&5? Any help is appreciated.

Another similar question is -

Question: If P (m+n,4) = 3024 and P(m-n,4) =120, find m & n? How would you attack this problem?
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by sjtxca » Thu Mar 24, 2011 8:32 pm
You recognized the pattern n x (n-1) x (n-2) = 210.

Now instead of going crazy with the left side. Just find the prime factorization of 210. This will yield factors: 2,5,3,7. You know that you will need 3 consecutive factors -> 7, 6 (2*3), and 5.
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by Gladius » Fri Mar 25, 2011 12:40 pm
sjtxca wrote:You recognized the pattern n x (n-1) x (n-2) = 210.

Now instead of going crazy with the left side. Just find the prime factorization of 210. This will yield factors: 2,5,3,7. You know that you will need 3 consecutive factors -> 7, 6 (2*3), and 5.
Thanks sjtxca. This explanation really helps. I just wanted to make sure there is no other way of solving it that I am not aware about.

I see that you are also getting started. Planning on writing GMAT this fall?
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by sjtxca » Fri Mar 25, 2011 1:07 pm
Yea. Just started studying this weekend actually :P. I am aiming to take the GMAT sometime late this summer or early Fall. I just found this website, it looks very resourceful.
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by Madhunara » Fri Apr 22, 2011 7:36 pm
Hi sjtxca and Gladius

I just started prep work and curious to know your prgress sofar. Have you taken any full length CAT test yet?
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