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# Properties

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# Properties

by garuhape » Sat Mar 26, 2011 8:21 am
Hey guys, this one really is difficult. I've no clue how to solve it! Can someone help me please!!!

For every positive 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 50
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by HSPA » Sat Mar 26, 2011 8:38 am
Only prime numbers shall have 1 and itself as factors, All other numbers can be represented using numbers btw 2 to 10 exclusive

2 is excluded as P(100)+1 = 2*(50!) +1 = 2n+1 odd number

2(50!)+1 is not in options so it "MAY" not prime

I am going with A...


What is the OA and source??
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by garuhape » Sat Mar 26, 2011 8:49 am
It's a question from MBAhelp.com and the OA is d but they do not provide an explanation!
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by force5 » Sat Mar 26, 2011 10:51 am
Good question what is the source....?? but here is my explanation

As per definition

h(100) = 2 x 4 x 6 x 8 x ....... x 100

can be written as-

h(100) = 2 x [1 x 2 x 3 x .......50] = 2 x 50!

now every number from 1 to 50 is a factor of 50!. the largest prime factor will be 47.

now since the question is asking h(100)+1 that means that the next number will be greater than 50 ( since 2*50!+1 becomes an odd number)
hence i go with E.....
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by manpsingh87 » Sat Mar 26, 2011 11:23 am
garuhape wrote:Hey guys, this one really is difficult. I've no clue how to solve it! Can someone help me please!!!

For every positive 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 50

hi this question has already been discussed at the following post, please go through it...!!!!
https://www.beatthegmat.com/prime-factor-t76145.html
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
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