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Prime Numbers -GMAT ques

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Prime Numbers -GMAT ques

by geet_ge » Tue Feb 07, 2012 1:31 am
For every positive integer n , the function h(n)is defined to be the product of all even integers from 2 to n inclusive. If p is the smallest prime factor of h(100)+1, then p is

1)between 2 and 10
2)between 10 and 20
3)between 20 and 30
4)between 30 and 40
5)greater than 40

Answer: greater than 40
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by neelgandham » Tue Feb 07, 2012 3:10 am
Hey geet_ge,

Please find my solution here -> https://www.beatthegmat.com/gmat-prep-t97536.html
Please find Mitch's solution here -> https://www.beatthegmat.com/tough-prime- ... 25475.html
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by ronnie1985 » Tue Feb 07, 2012 3:28 am
The product is too big it is 2^102 + 1. Hence the largest prime factor must be greater than 40
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by Anurag@Gurome » Tue Feb 07, 2012 3:49 am
geet_ge wrote:For every positive integer n , the function h(n)is defined to be the product of all even integers from 2 to n inclusive. If p is the smallest prime factor of h(100)+1, then p is

1)between 2 and 10
2)between 10 and 20
3)between 20 and 30
4)between 30 and 40
5)greater than 40

Answer: greater than 40

h(100) = 2 * 4 * 6 * ... * 100
= (2 * 1) * (2 * 2) * (2 * 3) * ... * (2 * 50)
= 2^(50) * (1 * 2 * 3 ... * 50)
Then h(100) + 1 = 2^(50) * (1 * 2 * 3 ... * 50) + 1
Now, h(100) + 1 cannot have any prime factors 50 or below, because dividing this value by any of these prime numbers will give a remainder of 1.

The correct answer is E.
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