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 →

Quant Integer Properties- Optimum Approach

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members
Location: Varanasi
Thanked: 11 times
by ankur.agrawal » Tue Aug 17, 2010 11:49 pm
k is a positive integer and 225 and 216 are both divisors of k. If k = 2a ×3b ×5c, where a, b and c are positive integers, what is the least possible value of a + b + c ?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members
Thanked: 215 times

by kvcpk » Wed Aug 18, 2010 2:15 am
ankur.agrawal wrote:k is a positive integer and 225 and 216 are both divisors of k. If k = 2a ×3b ×5c, where a, b and c are positive integers, what is the least possible value of a + b + c ?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
225 = 9*25
216=9*24
LCM of 225 and 216 is
9*25*24 =216*5(5)

There should be atleast 5 five multiples. hence answer should be greater than 5.

216 = 2a*3b
36=ab
sum of a and b should be minimum.
Hence a=b=6

I get a+b+c = 6+6+5 = 17

What am I missing?
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 98
Joined: Sat Feb 06, 2010 11:56 pm
Thanked: 5 times

by anantbhatia » Wed Aug 18, 2010 2:30 am
I presume that you meant k = 2^a X 3^b X 5^c

In that case, LCM of 225,216= 2^3 . 3^3 . 5^2

This will give us the smallest number that will be divisible by both 225 and 216. and hence the smallest value of the sum will be 8. (E)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members
Thanked: 173 times
GMAT Score:710

by gmatmachoman » Wed Aug 18, 2010 2:47 am
praveen ..u have nailed it..it has to be 17...

U can get 18 if u use a= 4, b=9,c=5

But we are looking for least so u get ur point....
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members
Location: Varanasi
Thanked: 11 times

by ankur.agrawal » Wed Aug 18, 2010 2:57 am
OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT


I meant k = 2^a X 3^b X 5^c .
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members
Thanked: 215 times

by kvcpk » Wed Aug 18, 2010 3:19 am
ankur.agrawal wrote:OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT


I meant k = 2^a X 3^b X 5^c .
Hi Ankur,

Excused :)

Request to recheck your psost after/before posting. Because I spent much time thinking what I am doing wrong.
We all do mistakes. But just wanted to let you know.

Cheers!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members
Location: Varanasi
Thanked: 11 times

by ankur.agrawal » Wed Aug 18, 2010 3:23 am
kvcpk wrote:
ankur.agrawal wrote:OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT


I meant k = 2^a X 3^b X 5^c .
Hi Ankur,

Excused :)

Request to recheck your psost after/before posting. Because I spent much time thinking what I am doing wrong.
We all do mistakes. But just wanted to let you know.

Cheers!!
I am real sorry. Wont let it happen again.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Thu Dec 31, 2009 5:54 am
Location: New York City
Thanked: 2 times

by bdevas01 » Wed Aug 18, 2010 5:43 am
Why didn't anyone post the answer?

Its 7 right?

The LCM of both numbers is 5400, which can be broken down into prime numbers: (2^2)x(3^3)x(5^2) and the values of a, b and c are 2, 3 and 2 respectively.

2 + 3 + 2 = 7, so D. 7.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members
Thanked: 215 times

by kvcpk » Wed Aug 18, 2010 6:02 am
bdevas01 wrote:Why didn't anyone post the answer?

Its 7 right?

The LCM of both numbers is 5400, which can be broken down into prime numbers: (2^2)x(3^3)x(5^2) and the values of a, b and c are 2, 3 and 2 respectively.

2 + 3 + 2 = 7, so D. 7.
5400 = 2^3*3^3*5^2
answer should be 3+3+2 = 8

HTH!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1