For every positive integer n, the function h(n) is defined t

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imane81: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Wed Jan 13, 2010 7:17 pmFollowed by: 1 member; Thanked: 1 times

by imane81 » Wed Feb 17, 2010 12:04 pm

Thank you for your input on this one

For every positive 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)+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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komal: Legendary Member; Posts: 777; Joined: Fri Jan 01, 2010 4:02 amFollowed by: 47 members; Location: Mumbai, India; Thanked: 117 times

by komal » Wed Feb 17, 2010 12:15 pm

imane81 wrote:Thank you for your input on this one

For every positive 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)+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

source : testmagic
h(100)= 2*4*6............100
h(100)+1=2*4*6............100 +1
2(1*2*3.......50)+1

so when h(100)+1 is divided by any of the nos between 2 and 50 will leave a remainder 1.

2*50!+1 will not be divisible by any no <50

answer E

https://www.e-gmat.com/

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 3:01 pm

komal wrote:
imane81 wrote:Thank you for your input on this one

For every positive 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)+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
source : testmagic
h(100)= 2*4*6............100
h(100)+1=2*4*6............100 +1
2(1*2*3.......50)+1

so when h(100)+1 is divided by any of the nos between 2 and 50 will leave a remainder 1.

2*50!+1 will not be divisible by any no <50

answer E

Hey komal,
I didn't get this :-2*50!+1 will not be divisible by any no <50
Even if we take 50 or 51 how can we confidently say that 2*50!+1 will be divisible by it.The remainder 1 will be there then also.
Kindly clarify.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu Feb 18, 2010 7:00 pm

imane81 wrote:Thank you for your input on this one

For every positive 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)+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

This is probably the most asked question on this site (or close to it); do a search on "h(100)" and you'll see lots of explanations.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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vicksikand: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Fri Nov 13, 2009 6:05 am

by vicksikand » Sun Oct 17, 2010 10:30 am

harsh.champ wrote:
komal wrote:
imane81 wrote:Thank you for your input on this one

For every positive 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)+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
source : testmagic
h(100)= 2*4*6............100
h(100)+1=2*4*6............100 +1
2(1*2*3.......50)+1

so when h(100)+1 is divided by any of the nos between 2 and 50 will leave a remainder 1.

2*50!+1 will not be divisible by any no <50

answer E
Hey komal,
I didn't get this :-2*50!+1 will not be divisible by any no <50
Even if we take 50 or 51 how can we confidently say that 2*50!+1 will be divisible by it.The remainder 1 will be there then also.
Kindly clarify.

Just FYI:
h(100) = 2^50.50! and not 2.50!

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