Tricky math factoring problem

[Magic_Man]

Need some help with this problem from the GMATs:

For each positive integer n, the function h(n) is defined as the product of all even numbers from 2 to n inclusive.

Let p = 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) Over 40

Not sure what to do here...I think I need to do some kind of tricky factoring:
2*4*6*...*100 + 1 = ?

Anyone have any ideas? Thanks!

~MagicMan

[51cards]

Over 40 ftw


explination to follow

[Sooga]

i'm probably missing something here, but i'd go with e) over 40.

2 * 4 * 6 * ... * 100 you can think of as 2 * (2*2) * (2*3) * (2*4) * ... * (2*50). So basically any whole number from 2 to 50 cannot not be a factor of h(100) + 1, since you'll always have 1 as a remainder.

So I think the smallest possible factor of h(100) + 1 is 53. Is that right? I'm just spitballin here.

[51cards]

There really isn't that much to it.

h(100) = 2*(1*2*3*4*5...50)

So h(100) is divisible by every number between 1 and 49 (and a whole lot more)

Any number that divides h(100) cannot divide h(100) + 1

So there are no numbers, let alone prime numbers, that are below 49 and divide h(100) + 1.

edited: meh, details.

[Magic_Man]

Ugh, that was easy. I have to go sulk in the corner now.

::sulks::

~MagicMan

PS Thanks!

[felson]

OP, change location pls! that is embarrassing.

[Magic_Man]

Meh, I'm in engineering. We can't bother ourselves with these trifling math exercises /images/graemlins/wink.gif

~MagicMan

[thylacine]

[ QUOTE ]
Meh, I'm in engineering. We can't bother ourselves with these trifling math exercises /images/graemlins/wink.gif
~MagicMan

[/ QUOTE ]

Tacoma bridge, etc.

[HeavilyArmed]

[ QUOTE ]
h(100) = 2*(1*2*3*4*5...50)

[/ QUOTE ]

h(100) = 2^50*(1*2*3*4*5...50)

I had to look at it twice to get that part right.

I looked at the possible answers and decided that >40 had to be the best guess. This is an ability most intelligent test taker have in many situations. This is a very poor question for a multiple guess test.

[felson]

[ QUOTE ]
Meh, I'm applying for business school. We can't bother ourselves with these trifling math exercises /images/graemlins/wink.gif

[/ QUOTE ]