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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Ramon wants to cut a rectangular board into identical square
This topic has expert replies
GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
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.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
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.
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
-
regor60
- Master | Next Rank: 500 Posts
- Posts: 415
- Joined: Thu Oct 15, 2009 11:52 am
- Thanked: 27 times
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
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
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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!
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!
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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:
So, we can cut 15 squares.
Answer: E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
