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16 Jun 2006, 10:30
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Question:
For every positive even interger 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
For every positive even interger 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
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16 Jun 2006, 10:38
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fireboll
This question has been posted before but I could not find it for you, so here is the soln.
Ans. E---greater than 40
h(100)+1 = 2*4*6*8*....100 + 1
= 2^50(1*2*...50) + 1
= 2^50(50!) + 1
50! = 50*49*48*47*46...
Ans: 47
16 Jun 2006, 12:28
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tapan22
I agree that answer should be E but how did you arrived at 47. IMO this will even be greater than 50.
Lets assume that h(100) = x
x is a multiple of 47. How x +1 can be a multiple of 47?
Also x includes all the numbers from 1 to 50. So no number could between 1 and 50 divide x +1.
