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

Question

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. 5
B. 6
C. 7
D. 8
E. 9

PareshGmat · Accepted Answer

Answer = D

Total = 8 squares

Bunuel, can you please change the OA to D?

Luckisnoexcuse · Answer

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

nagu · Answer

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

JeffTargetTestPrep · Answer

https://i.imgur.com/dhvRF3V.png

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

stoned · Answer

hi 
Can any please clear my doubt 
in this question why are not we considering the case where one square is with an area of and 4 squares are with an area of 4 each giving a total of 5 squares.

Thanks

vedha0 · Answer

keep placing biggest possible squares until u can place no more.
u can place 1 3*3 square. in the left out area, at max u can 3 2*2 squares. what is left is 4 1*1 squares' area. so answer is 1+3+4 i.e., 8 squares.

Engineer1 · Answer

Okay, I was making it overly simple and realized it is a "Very Hard" question.

But the Total area of the original square = 25. Therefore, the sum of area of the smaller squares should be 25. This is my basis. Is this correct? To begin with, 1 sq. w/ side 1: Area 1 Similarly, 1 sq. w/ side 2: Area 4 1 sq. w/ side 3: Area 9 Remaining area = 25- (4+9+1) = 11 11 sq. meters area can be summed up by: 1 sq. w/ side 3: Area 9 2 sq. w/ side 1: Area 2. Therefore, total small squares = 3+ 3 = 6. This question is asking for least number of squares, so I tried making it as least as possible. How can the OA be 8? KarishmaB chetan2u MartyMurray Please help me understand. Also, do we really need a diagram to solve this? Thank you!

Bunuel · Answer

The key here is that cutting two intact 3x3 squares from a 5x5 square is not possible. The 5x5 square doesn't have enough area to accommodate two full 3x3 squares without overlapping.

Engineer1 · Answer

Thank you. Now I see why the diagram helped.

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

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

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