Ramon wants to cut a rectangular board into identical square

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Ramon wants to cut a rectangular board into identical square

by swerve » Wed Dec 04, 2019 1:13 pm

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

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Source: Beat The GMAT — Problem Solving | Wed Dec 04, 2019 1:13 pm

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[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

by [email protected] » Wed Dec 04, 2019 4:46 pm

Hi swerve,

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, the largest side that divides into both 18 and 30 is 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

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Dec 08, 2019 7:09 pm

swerve wrote: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

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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