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 →

Function/Prime Number Problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 11
Joined: Tue Sep 15, 2009 6:01 am
Location: Lagos
by Onigbogi Tosin » Tue Sep 15, 2009 6:14 am
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 &10

b. Between 10 & 20

c. Between 20 & 30

d. Between 30 & 40

e. Greater than 40
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Thu Jan 08, 2009 6:24 pmFollowed by: 4 members
Thanked: 1 times

by sakurle » Tue Sep 15, 2009 9:37 am
If we plug in values. h(6) = 48
h(6) + 1 = 49, smallest factor = 7.

similarly h(8) = 384
h(8)+1 = 385

again smallest factor is between 2 & 10

Therefor IMO A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 189
Joined: Thu Apr 03, 2008 2:03 pm
Location: USA
Thanked: 21 times

by rohan_vus » Tue Sep 15, 2009 9:47 am
the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive

h(100) = 2*4*6*..100 = 2^50*(1*2*3..*50) ==> (2^50)*50!

Thus all numbers from 1 to 50 are factors of h(100) as 50! = 1*2*3*4*5*6*..50 .

But when we add 1 to h(100) all factors of h(100) will give remainder as 1 ( except factor 1) . So we can say h(100) + 1 is not divisible by any factor from integer 2 to integer 50 . So any prime factor got to be more than 50 which from he list of options is E . So IMO E
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 11
Joined: Tue Sep 15, 2009 6:01 am
Location: Lagos

by Onigbogi Tosin » Wed Sep 16, 2009 5:35 am
Please, I'm not yet clear about the solution to this problem. I still need more clarification.Thanks
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 157
Joined: Tue Oct 07, 2008 5:47 am
Thanked: 3 times

by PussInBoots » Wed Sep 16, 2009 12:09 pm
2*4*6*8*..*100 = 1*2 * 2*2 * 3*2 * 4*2 *... * 50*2 = 50! * 2^50

50! is divisible by any positive integer less or equal to 50, just like 4! is divisible by 1, 2, 3, 4. Hence 50! * 2^50 is divisible by any positive integer less or equal to 50. If you add 1, then the new number is not divisible by any number less or equal to 50. Hence smallest prime number > 40.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1