• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Reach higher with Artificial Intelligence. Guaranteed
Now free for 30 days

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

## Problem involving prime factors

This topic has 6 member replies
wlvoh Newbie | Next Rank: 10 Posts
Joined
07 Feb 2007
Posted:
8 messages
1

#### Problem involving prime factors

Sat Feb 10, 2007 12:23 pm
The following is a doozy of a PS problem from a practice test on the Official GMAT Prep Software from GMAC. If anyone can help explain how to solve this one, I'd greatly appreciate it.

"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) + 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

(highlight to see the OA)

Thanks.

wlvoh

wlvoh Newbie | Next Rank: 10 Posts
Joined
07 Feb 2007
Posted:
8 messages
1
Mon Feb 12, 2007 5:16 am
jayhawk2001 wrote:
I posted this on an earlier thread. Hope this helps.

h(100) + 1
= 2 * 4 * ... * 100 + 1
= 2*50! + 1

2*50! can be expressed as a multiple of X (2 <= X <= 50) and so
(2*50! + 1) cannot be a multiple of of that same number X.

Since p is a factor of h(100) +1, p should be > X and so option
"E" looks like the correct answer.
Thanks for the help. But, in your explanation, one thing isn't quite right. The product 2*4*6*...*100 cannot be expressed as 2*50! It isn't a sum, so you can't simply factor out a single 2. Instead, you must factor out 2 from each element in the sum. So, actually, 2*4*6*...*100 is equal to:

(2^50) * 50!

I'm not sure if this makes any difference in the reasoning. Any thoughts?

Thanks.

wlvoh

jayhawk2001 Community Manager
Joined
28 Jan 2007
Posted:
789 messages
Followed by:
1 members
30
Tue Feb 13, 2007 10:36 pm
wlvoh, Yes, that is correct. The value is (2^50 * 50!) not 2*50!.

In anycase, the element to focus on is 50! and the rest of the logic should

Thanks.

aim-wsc Legendary Member
Joined
20 Apr 2006
Posted:
2470 messages
Followed by:
14 members
85
Target GMAT Score:
801-
Sat Feb 10, 2007 1:12 pm
difficult indeed.
or maybe i lost number properties basics.

_________________
Getting started @BTG?

Please do not PM me, (not active anymore) contact Eric.

jayhawk2001 Community Manager
Joined
28 Jan 2007
Posted:
789 messages
Followed by:
1 members
30
Sat Feb 10, 2007 1:20 pm
I posted this on an earlier thread. Hope this helps.

h(100) + 1
= 2 * 4 * ... * 100 + 1
= 2*50! + 1

2*50! can be expressed as a multiple of X (2 <= X <= 50) and so
(2*50! + 1) cannot be a multiple of of that same number X.

Since p is a factor of h(100) +1, p should be > X and so option
"E" looks like the correct answer.

aim-wsc Legendary Member
Joined
20 Apr 2006
Posted:
2470 messages
Followed by:
14 members
85
Target GMAT Score:
801-
Sat Feb 10, 2007 1:36 pm
yeah thanks for the quick reply.
i knew that answer is E.

but i started thinking of the value of p
yeah! now thats really a wrong approach for GMAT i know... & i still fall in the trap.
it doesnt expect the value but the answer choice.... same applies for DS....

thanks once again.
the value of p by the way would be far much higher than 40 for sure.

_________________
Getting started @BTG?

Please do not PM me, (not active anymore) contact Eric.

Mark Dabral Guest
Sat Feb 10, 2007 8:26 pm

### Best Conversation Starters

1 lheiannie07 76 topics
2 LUANDATO 59 topics
3 ardz24 52 topics
4 AAPL 46 topics
5 M7MBA 45 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Jeff@TargetTestPrep

Target Test Prep

141 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

136 posts
3 GMATGuruNY

The Princeton Review Teacher

134 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

129 posts
5 Scott@TargetTestPrep

Target Test Prep

110 posts
See More Top Beat The GMAT Experts