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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach Starts Oct 17
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Chris Peckover, 100th-Percentile GMAT Scorer

Oct 17 · Chris Peckover
Sat · 11:00 AM to 2:00 PM ET
Oct 20 · Chris Peckover
Tue, Thu · 8:00 to 10:00 PM ET
Oct 25 · Josh Braslow
Sun · 1:00 to 4:00 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemand 5 seats left Start anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

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