[jsloan01]

Originally Posted by Md. Minuddin

1. For every positive even 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

A. b/n 2 and 10
B. b/n 10 and 20
C. b/n 20 and 30
D. b/n 30 and 40
E. Greater than 40

I think in this question b/n means between.


And the answer is A. Because the smallest prime factor is 7

h(100) +1=100* 98* 96* ....*2+1

Now, 2*4*6*8*10+1=3840+1=3841 Smallest prime factor is 7
2*4*6*8*10* 12+1=46080+1=46081 Smallest prime factor is 7

And so on.................................

Here unit digit will always be 1. So is not divisible 2 or, 5. So we should check by 3 and then by 7 and if it is not factor then option is 11, 13 etc. But here it is divisible by 7. So answer is A

Minuddin and everyone else,

Thanks for the responses. I understand 2 and 3, but question 1 is a mystery. The answer is E. The question is from the GMATPrep software.

Is there a way to view an explanation to the solution? The software tells you the answer, but does not explain the answer.

Hopefully someone can figure out why it is E