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How Many m and n's? -From your challenge series

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rhoeta
 Post subject: How Many m and n's? -From your challenge series
 Post Posted: Tue Oct 23, 2007 5:00 am 
04/03/06
Question
What is the positive integer n?

(1) For every positive integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16

(2) n2 - 9n + 20 = 0

Its not clear to me in your OE why n =4 for 1) is not acceptable all the time. I tried a few +ve integers at it turns out the 4 works.
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StaceyKoprince
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 Post Posted: Mon Oct 29, 2007 9:21 pm 
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Posts: 6077
Location: San Francisco
When n=4, we have m(m + 1)(m + 2)(m + 3)(m + 4).

If m = 1, then we have 1*2*3*4*5, which has only three 2's as factors. 2*2*2 = 8, not 16. So this number is not divisible by 16.
If m = 2, then we have 2*3*4*5*6, which has four 2's as factors. 2*2*2*2 = 16. So this number is divisible by 16.

Trying numbers is often a very good technique, but when a question says something must be true for "every" value, you have to be careful - if you happen not to try the right numbers, you might miss the right answer.

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Stacey Koprince
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yousuf_azim
 Post subject: Re: How Many m and n's? -From your challenge series
 Post Posted: Sun Nov 20, 2011 10:39 am 
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Students


Posts: 45
What is the ans?

BR

Farid
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jnelson0612
 Post subject: Re: How Many m and n's? -From your challenge series
 Post Posted: Sat Dec 10, 2011 9:46 pm 
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ManhattanGMAT Staff


Posts: 1857
yousuf_azim wrote:
What is the ans?

BR

Farid


The answer should be C.

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Jamie Nelson
ManhattanGMAT Instructor
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matthewwhchu
 Post subject: Re: How Many m and n's? -From your challenge series
 Post Posted: Sun Jan 08, 2012 4:56 am 
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Posts: 1
As from your explanation, 1) is not always true (for example, if m = 1). Therefore, could we conclude the answer should be E? Since 1) is not always true and 2) comes to either n = 4 or n = 5, which is not sufficient to have the result where n is.
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tim
 Post subject: Re: How Many m and n's? -From your challenge series
 Post Posted: Sun Jan 15, 2012 4:39 pm 
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Posts: 2242
Location: Southwest Airlines, seat 21C
it's not correct to say that (1) is not always true. when the GMAT gives you a statement, you take it as always true, and accept whatever consequences flow from that. as shown in the example, (1) is not true when n=4 and m=1. what this means is that n cannot be 4 because it creates a situation that contradicts (1)..

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Tim Sanders
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