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

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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...

by swerve » Mon Feb 05, 2018 6:08 am

Ramon wnats 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.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer.

The total area of the rectangular board is 18 * 30 = 540 but what can I do with it? I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Mon Feb 05, 2018 6:08 am

GMAT/MBA Expert

[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] » Mon Feb 05, 2018 10:15 am

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 number 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 » Tue Feb 06, 2018 5:09 pm

swerve 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

To find the least number of square pieces Ramon can cut without wasting any of the board, we need 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 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]