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605-655 (Medium)|   Geometry|      
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Bunuel
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Ramon wants to cut a rectangular board into identical square pieces. 13 Aug 2018, 04:52
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E
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45% (medium)

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62% (01:50) correct 38% (02:04) wrong based on 298 sessions

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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
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E
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Ramon wants to cut a rectangular board into identical square pieces. 13 Aug 2018, 07:23
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Bunuel
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
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HCF (18,30) = 15 ; Answer must be (E)
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Ramon wants to cut a rectangular board into identical square pieces. 13 Aug 2018, 07:37
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Bunuel
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
Show more

To get squares, both length and breadth should be the same. To get least number of squares, this side length should be maximum. So we are looking for the largest common factor of 18 and 30 which is 6.
The 18 inches side will be divided into 3 pieces and 30 inches side will be divided into 5 pieces.
Total number of pieces = 3 * 5 = 15

Answer (E)
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Ramon wants to cut a rectangular board into identical square pieces. 11 Oct 2020, 06:19
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Bunuel
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
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Solution:

Since the greatest common factor of 18 and 30 is 6, the largest square he can cut is 6 inches by 6 inches and thus the least number of square pieces he can cut is (18 x 30)/(6 x 6) = 3 x 5 = 15.

Answer: E
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Ramon wants to cut a rectangular board into identical square pieces. 16 Oct 2020, 03:07
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The area of the rectangular board is 18*30 = 540 sq. units.

Also, 540 = 5*2*2*3*3*3

Since the area of the area of a square is a perfect square number, from the factors of 540, the possiblilities are:

15 squares, each having area as 2*2*3*3 (side : 6 units)
60 squares, each having area as 3*3 (side : 3 units)
135 squares, each having area as 2*2 (side : 2 units)

15 is the least possible number of squares. Option E
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Ramon wants to cut a rectangular board into identical square pieces. 11 Jul 2022, 08:25
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