Ramon wants to cut a rectangular board into identical square

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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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

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

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:


So, we can cut 15 squares.
Answer: E

Cheers,
Brent