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 →

prime factorization

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 324
Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member
Thanked: 17 times
by rahul.s » Tue Feb 23, 2010 1:35 am
If K is a positive integer, how many different prime numbers are factors of the expression K^2?

(1) Three different prime numbers are factors of 4K^4
(2) Three different prime numbers are factors of 4K

OA: E
Source: Knewton

i was stunned after reading the statements. i didn't know how to approach them. how do i simplify the statements? what's the approach?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members
Location: Arabian Sea
Thanked: 125 times

by ajith » Tue Feb 23, 2010 1:41 am
rahul.s wrote:If K is a positive integer, how many different prime numbers are factors of the expression K^2?

(1) Three different prime numbers are factors of 4K^4
(2) Three different prime numbers are factors of 4K

OA: E
Source: Knewton

i was stunned after reading the statements. i didn't know how to approach them. how do i simplify the statements? what's the approach?
K, K^2, K^4, K^n where n is an integer, all have equal no of prime factors.

1) Three prime factors are there for 4K^4
Insufficient to determine how many prime factors are there for K^4 since 2 may or may not be a prime factor of K^4
thus K^4 and thus K will have either 2 or 3 prime numbers as factors

2) Same is the case, we do not know whether 2 is a factor of K, Insufficient

Combined also insufficient, E
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 40
Joined: Thu Mar 26, 2009 3:02 pm
Thanked: 3 times
GMAT Score:410

by Pedros » Tue Feb 23, 2010 3:49 am
ajith wrote:
rahul.s wrote:If K is a positive integer, how many different prime numbers are factors of the expression K^2?

(1) Three different prime numbers are factors of 4K^4
(2) Three different prime numbers are factors of 4K

OA: E
Source: Knewton

i was stunned after reading the statements. i didn't know how to approach them. how do i simplify the statements? what's the approach?
K, K^2, K^4, K^n where n is an integer, all have equal no of prime factors.
2 could be a factor of K as it is for 4 , Good catch.....

1-You mean equal number of distinct prime factors, right ?
2- how hard you guys rate this question?

Thanks
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 59
Joined: Mon Jan 25, 2010 10:11 pm
Location: United States
Thanked: 4 times

by chaya009 » Tue Feb 23, 2010 1:55 pm
Good explanation ajith, thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members
Location: Arabian Sea
Thanked: 125 times

by ajith » Wed Feb 24, 2010 4:53 am
Pedros wrote: 2 could be a factor of K as it is for 4 , Good catch.....

1-You mean equal number of distinct prime factors, right ?
2- how hard you guys rate this question?

Thanks
1. Yes I do mean distinct prime factors
2. It is a question which is not very difficult when you know the concept. Yet, it is a bit tricky
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1