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

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Manager
Joined: 02 Sep 2012
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For every positive even integer n, the function h(n) [#permalink]

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24 Mar 2013, 06:30
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Question Stats:

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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]

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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: $$h(100)+2=2*(4*6*...*100+1)$$.

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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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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05 Oct 2015, 11:59
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Re: For every positive even integer n, the function h(n) [#permalink]

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24 Jan 2017, 07:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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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] 03 Apr 2017, 10:45
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