A tricky GMATprep question on functions... please help....

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Junior | Next Rank: 30 Posts
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Hello everyone, I have just taken the GMATprep 1. I have one question which I do not know how to answer, even after reviewing it. The question is:

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40

Kindly help me to solve this math problem. Thanks a lot.
Source: — Problem Solving |

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by tomhng » Sun Nov 09, 2008 6:59 am
Oops, sorry, perhaps I am not allowed to post the actual question in this forum :( I am sorry! but I really need to know how to solve it.

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by tomhng » Sun Nov 09, 2008 7:09 am
Hi beatthegmat (founder), I am sorry, I was really caught up in the problem, forgot that I must not post the real GMATprep question in this forum. I am sorry, I won't do it again.

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tomhng wrote:Hello everyone, I have just taken the GMATprep 1. I have one question which I do not know how to answer, even after reviewing it. The question is:

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40

Kindly help me to solve this math problem. Thanks a lot.
I am not sure whether you can post a GMAT question but I can help you with this question:

h(100) = 2 x 4 x 6 x 8 .... 98x100
= 2 (1) x 2 (2) x 2 ( 3) .... 2 (49 ) x 2 (50)
= 2^50 50!

so h(100) will all the prime numbers between 1-50

So, h(100)+1 will always have a remainder of 1 when divided by any of this prime numbers

Prime Number in this case > 50

E
LGTCH
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by tomhng » Mon Nov 10, 2008 6:51 am
Hello logitech, thanks a lot :D your answer is correct, it is E. After looking at how you solved it, now I believe it is solvable within 2 minutes, but I need a deep understanding on functions like yours. I am still amazed at how you derived it (at first it looked complicated). Thanks.