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 →

Ramon wants to cut a rectangular board into identical square

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Fri Sep 11, 2015 12:33 pm
by duahsolo » Tue Jun 06, 2017 6:19 am
Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members
Location: Grand Central / New York
Thanked: 470 times

by Jay@ManhattanReview » Tue Jun 06, 2017 6:29 am
duahsolo wrote:Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
Since a square has equal sides and we do not wish to waste any of the board, we must have the maximum possible value of the side of the square such that the whole rectangular board is used up.

Given the dimensions of the board: 18x30, the Highest Common Factor of 18 and 30 would give us the maximum possible value of the side of the square.

HCF (GCD) of 18 and 30 = 6

Least number of squares = Area of the board / Area of the square = (18*30) / (6*6) = 15.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Geometry Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Beijing | Auckland | Milan | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Tue Jun 06, 2017 2:11 pm
Hi duahsolo,

We're asked to find the minimum number of identical SQUARES that be cut from an 18 in. x 30 in. board without 'wasting' any of the space. To accomplish this, we need to find a square whose dimensions will evenly divide into both 18 and 30; to find the LEAST number of squares, we'll need to find the largest number that evenly divides in. In this case, it's 6, so we'll be dealing with 6x6 squares.

18/6 = 3
30/6 = 5

Thus, we'll have (3)(5) = 15 squares at the minimum.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

by regor60 » Thu Jun 08, 2017 6:07 am
An algebraic approach:

N = number of squares to be minimized
X = side of the square

Total area of squares = N*X^2 = 18*30. To minimize N, need to maximize X

N= (3^2)(2^2)(3)(5)/(x^2).

By inspection, the maximum X that will divide into the numerator is 3*2,
leaving(3)(5) as the minimum number of squares
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Thu Jun 08, 2017 5:01 pm
I'd start by looking for a square that's a factor of the area of the rectangle:

18 * 30 = 2 * 3 * 3 * 2 * 3 * 5

So 2 * 2 * 3 * 3, or 36, is a factor of 540. That suggests that we might be able to form squares of area 36.

Looking at our rectangle dimensions (18 and 30), we notice that each divides by 6. 18 = 3 * 6 and 30 = 5 * 6, so we CAN cut the board into 3 lengths of 6 on the width and 5 lengths of 6 on the length.

That gives us 15 squares, each with area 36, so we're set!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8144
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: Ramon wants to cut a rectangular board into identical square

by Scott@TargetTestPrep » Mon Mar 02, 2020 5:49 am
duahsolo wrote: ↑
Tue Jun 06, 2017 6:19 am
 Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
To find the least number of square pieces Ramon can cut without wasting any of the board, we need to use the greatest common factor (GCF) of 18 and 30, which is 6. Thus, he can cut the board into 6-inch square pieces without wasting any of the board since 6 divides into both 18 and 30 and is the largest number that does so. Therefore, the least number of square pieces he can cut is:

(18 x 30) / (6 x 6) = (18/6) x (30/6) = 3 x 5 = 15

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Re: Ramon wants to cut a rectangular board into identical square

by Brent@GMATPrepNow » Mon Mar 02, 2020 7:05 am
duahsolo wrote: ↑
Tue Jun 06, 2017 6:19 am
 Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
If we aren't wasting any wood, the length and width must be divisible by one side of the square
So, this question is a clever way of asking us what the greatest common divisor (GCD) of 18 and 30
The GCD of 18 and 30 is 6, so if we cut squares that are 6 x 6, then we won't waste any wood.

We get something like this:
Image

So, we can cut 15 squares.
Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1