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

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

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

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

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.

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!

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.

Thank you. Now I see why the diagram helped.