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For every positive even integer n, the function h(n)

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For every positive even integer n, the function h(n) [#permalink] New post 24 Mar 2013, 05:30
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For every positive even 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) +2, then p is?

A. between 2 and 20
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. 2
[Reveal] Spoiler: OA

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Re: For every positive even integer n, the function h(n) [#permalink] New post 24 Mar 2013, 05:38
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skamal7 wrote:
For every positive even 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) +2, then p is?

A. between 2 and 20
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. 2


h(100)+2=2*4*6*...*100+2. Notice that we can factor out 2 from h(100)+2, thus the smallest prime factor of h(100)+2 is 2: h(100)+2=2*(4*6*...*100+1).

Answer: E.

Similar question to practice: for-every-positive-even-integer-n-the-function-h-n-is-126691.html

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Re: For every positive even integer n, the function h(n) [#permalink] New post 26 Mar 2013, 13:19
skamal7 wrote:
For every positive even 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) +2, then p is?

A. between 2 and 20
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. 2


h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 10 (and 100). So h(100)+2 will have 2 in the units digit so smallest prime factor is 2.
Re: For every positive even integer n, the function h(n)   [#permalink] 26 Mar 2013, 13:19
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