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805+ (Hard)|   Geometry|      
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tonebeeze
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A square board that has an area of 25 square inches is to be Updated on: 25 Mar 2014, 02:30
Originally posted by tonebeeze on 11 Mar 2011, 12:20.
Last edited by Bunuel on 25 Mar 2014, 02:30, edited 1 time in total.
Edited the OA.
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D
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95% (hard)

Question Stats:

43% (02:12) correct 57% (02:01) wrong based on 1023 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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D
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PareshGmat
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A square board that has an area of 25 square inches is to be 24 Mar 2014, 20:46
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Answer = D

Total = 8 squares

Bunuel, can you please change the OA to D?
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A square board that has an area of 25 square inches is to be 29 Sep 2017, 00:00
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Bunuel
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
Show more

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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A square board that has an area of 25 square inches is to be 29 Sep 2017, 00:22
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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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A square board that has an area of 25 square inches is to be 03 Oct 2017, 16:39
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Bunuel
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
Show more



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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A square board that has an area of 25 square inches is to be 22 Jul 2022, 07:51
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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
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A square board that has an area of 25 square inches is to be 15 Aug 2023, 13:24
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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.
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A square board that has an area of 25 square inches is to be 21 Jan 2024, 11:19
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PareshGmat
Answer = D

Total = 8 squares

Bunuel, can you please change the OA to D?
Show more

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

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!
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A square board that has an area of 25 square inches is to be 21 Jan 2024, 11:40
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Engineer1
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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


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

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!
Show more

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.
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A square board that has an area of 25 square inches is to be 21 Jan 2024, 13:42
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Bunuel
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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


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

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.
Show more

Thank you. Now I see why the diagram helped.
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