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A square board that has an area of 25 square inches is to be cut into

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A square board that has an area of 25 square inches is to be cut into [#permalink]

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New post 28 Sep 2017, 22:54
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D
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Question Stats:

54% (01:18) correct 46% (01:07) wrong based on 47 sessions

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A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2 or 3 inches What is the least number of such square pieces into which the board can be cut?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
[Reveal] Spoiler: OA

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Re: A square board that has an area of 25 square inches is to be cut into [#permalink]

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New post 28 Sep 2017, 23:00
Bunuel wrote:
A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2 or 3 inches What is the least number of such square pieces into which the board can be cut?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9


Area of Square with side 5 = 25
Area of Square with side 3 = 9
Area of Square with side 2 = 4
Area of Square with side 1 = 1

only one square with side 3 can come (area covered = 9, area left 16)
3 squares with side 2 can come = (area covered = 12 + 9, area left 4)
4 squares with side 1 will come

D
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Re: A square board that has an area of 25 square inches is to be cut into [#permalink]

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New post 28 Sep 2017, 23:22
area of the square = 25 = 5*5
area of 3 inch square = 3*3 = 9
since 5(side of square) - 3( Side of 3 inch square) < 3 so no more 3 inch is possible

area of 2 inch square = 2*2 = 4
area remaining 25 -9= 16

The reaming portion is not a square
hence 2 inch square only 3 is possible

So remaining area = 16-4*3 = 4
so 1 inch square need = 4

So total number = 1+3+4 = 8

Answer should be D

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Re: A square board that has an area of 25 square inches is to be cut into [#permalink]

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New post 03 Oct 2017, 15:39
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Bunuel wrote:
A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2 or 3 inches What is the least number of such square pieces into which the board can be cut?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9


Image

A partition of the square board of 25 square inches is shown above. We see that we need one 3-inch square (red square), three 2-inch squares (blue square) and four 1-inch squares (white square), thus we need a total of 1 + 3 + 4 = 8 square pieces.

Answer: D
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Kudos [?]: 984 [1], given: 5

Re: A square board that has an area of 25 square inches is to be cut into   [#permalink] 03 Oct 2017, 15:39
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