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Even Integer

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by karthikpandian19 » Fri Jan 06, 2012 2:49 pm
For every positive even integer n, the function h(n) is defined as 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

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40
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by GMATGuruNY » Fri Jan 06, 2012 2:56 pm
I posted an explanation here:

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by Anurag@Gurome » Fri Jan 06, 2012 9:51 pm
karthikpandian19 wrote:For every positive even integer n, the function h(n) is defined as 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

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
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.
Anurag Mairal, Ph.D., MBA
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