AAPL wrote: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

OA E.

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

Hi All,

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