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

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Math Expert
Joined: 02 Sep 2009
Posts: 47157
A square board that has an area of 25 square inches is to be cut into  [#permalink]

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28 Sep 2017, 23:54
00:00

Difficulty:

45% (medium)

Question Stats:

54% (01:19) correct 46% (01:08) wrong based on 49 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

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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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29 Sep 2017, 00:00
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

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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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29 Sep 2017, 00:22
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

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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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03 Oct 2017, 16:39
1
1
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

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.

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Re: A square board that has an area of 25 square inches is to be cut into &nbs [#permalink] 03 Oct 2017, 16:39
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