BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Factor problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Mon Nov 12, 2012 11:12 amFollowed by: 2 members
Thanked: 8 times
by Anindya Madhudor » Mon Nov 12, 2012 11:57 am
Can anyone please help me show how to solve the following?

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 435
Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member
Thanked: 32 times

by eaakbari » Mon Nov 12, 2012 12:04 pm
*Please post in the right designated forum*


IMO A

Use strategy of picking numbers,

If you pick 4 as n,

then h(4) + 1 = 9 which makes 3 the only prime factor

Since the function is true for all n, the answer must be A, as its the only answer choice whose range includes 3.

Hence A
Last edited by eaakbari on Tue Nov 13, 2012 7:07 am, edited 1 time in total.
Whether you think you can or can't, you're right.
- Henry Ford
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Mon Nov 12, 2012 11:12 amFollowed by: 2 members
Thanked: 8 times

by Anindya Madhudor » Mon Nov 12, 2012 1:44 pm
The question is specifically asking for factor of h(100)+1. It is not asking for factor of all h(n)+1.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Mon Nov 12, 2012 11:12 amFollowed by: 2 members
Thanked: 8 times

by Anindya Madhudor » Mon Nov 12, 2012 3:37 pm
Sorry about posting in the wrong area. I am new to this.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 435
Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member
Thanked: 32 times

by eaakbari » Tue Nov 13, 2012 8:57 am
Anindya Madhudor wrote:The question is specifically asking for factor of h(100)+1. It is not asking for factor of all h(n)+1.
Yes, I misread the question and stand corrected.

By taking 2 as common, we can rewrite h(100) as

2^50x(1x2x3x...x50).

Hence every number from 1 to 50 is a factor of 100

So every h(100) + 1 will not be a factor and will leave remainder as one (including primes).

Hence the smallest prime will be above 50.

Answer E seems to fit the description.

Hence E

P.S. Whats the source of the question.
Whether you think you can or can't, you're right.
- Henry Ford
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Mon Nov 12, 2012 11:12 amFollowed by: 2 members
Thanked: 8 times

by Anindya Madhudor » Tue Nov 13, 2012 9:49 am
It came up in one of the two sample tests provided by official GMAC.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1