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Ramon wants to cut a rectangular board into identical square

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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
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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
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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

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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
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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!
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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

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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
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