Ramon wants to cut a rectangular board into identical square pieces...

[BTGmoderatorLU]

Source: Manhattan Prep

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

The OA is E

[Jay@ManhattanReview]

Source: Manhattan Prep

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

The OA is E

Since we want the least no. of identical squares, the side of each square must be equal to HCF of 18 and 30.

HCF of 18 and 30 = 6.

Least no. of identical squares = 18/6 * 30/6 = 3*5 = 15

The correct answer: E

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

Source: Manhattan Prep

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

The OA is E

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