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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]

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New post 24 Mar 2013, 06:30
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A
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E

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84% (00:50) correct 16% (00:58) wrong based on 407 sessions

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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

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Re: For every positive even integer n, the function h(n)  [#permalink]

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New post 24 Mar 2013, 06:38
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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

Hope it helps.
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Re: For every positive even integer n, the function h(n)  [#permalink]

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New post 26 Mar 2013, 14:19
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.
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Re: For every positive even integer n, the function h(n)  [#permalink]

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New post 03 Apr 2017, 10:45
The answer will be even and thus the SMALLEST prime factor would be 2 (even).
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Re: For every positive even integer n, the function h(n)  [#permalink]

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New post 07 Sep 2018, 12:11
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Re: For every positive even integer n, the function h(n) &nbs [#permalink] 07 Sep 2018, 12:11
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