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

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

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Updated on: 25 Mar 2014, 02:30
6
00:00

Difficulty:

95% (hard)

Question Stats:

38% (01:20) correct 62% (01:24) wrong based on 213 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

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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Re: Cutting a square board  [#permalink]

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11 Mar 2011, 12:42
1
tonebeeze 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

This is best done by drawing a figure. You can do this in 8 squares - one $$3*3$$, 3 squares of $$2*2$$ each and 4 squares of $$1*1$$ each.
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Re: Cutting a square board  [#permalink]

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11 Mar 2011, 14:55
I agree that the answer should be 8. What kind of question is this? Is there any mathamatical way to solve this?
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Re: Cutting a square board  [#permalink]

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11 Mar 2011, 17:45

6

two (3x3) , one (2x2) , three (1x1)'s
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Re: Cutting a square board  [#permalink]

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11 Mar 2011, 22:41
I got the answer 8 as well, by drawing the square in grid divided shape.
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Re: Cutting a square board  [#permalink]

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11 Mar 2011, 22:42
2
Spidy001 wrote:

6

two (3x3) , one (2x2) , three (1x1)'s

Spody001 - You cannot cut 2 3x3 squares from one 5x5 square. two 3x3 would need the square to be at least 6x6. Please draw a figure and you will be able to see it better.
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Re: Cutting a square board  [#permalink]

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12 Mar 2011, 07:15

one 3*3 ,two 2*2 and 4 1*1
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20 Mar 2014, 23:33
A square board that has an area of 25 sq.inches is to be cut into pieces, each of which is a square with sides of length 1,2,3 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
Math Expert
Joined: 02 Sep 2009
Posts: 47157

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21 Mar 2014, 02:53
2
SomIyer wrote:
A square board that has an area of 25 sq.inches is to be cut into pieces, each of which is a square with sides of length 1,2,3 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

Merging similar topics. Please refer to the discussion above.

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

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24 Mar 2014, 20:46
3
1

Total = 8 squares

Bunuel, can you please change the OA to D?
Attachments

sq.jpg [ 28.84 KiB | Viewed 3793 times ]

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

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25 Mar 2014, 02:30
PareshGmat wrote:

Total = 8 squares

Bunuel, can you please change the OA to D?

Edited the OA. Thank you.
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Re: A square board that has an area of 25 square inches is to be  [#permalink]

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17 Apr 2016, 03:37
I don't think it's a that much hard problem
draw a figure of 5 * 5 square with 1 *1 small squares
it can be easily deduced that only one 3 * 3 square fits into the larger square
similarly only three 2* 2 square fits into the larger square
and lastly the remaining slots can be filled by four 1 * 1 square
Total = 8
Attachments

File comment: use the given diagram to solve the given problem

square with 1 by 1 small squares shown.jpg [ 17.68 KiB | Viewed 2562 times ]

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

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02 Aug 2017, 00:21
PareshGmat wrote:

Total = 8 squares

Bunuel, can you please change the OA to D?

I solved in similar manner...but it took over 3 minutes to get the answer... Is there any smarter way? Or we need to visualize and then check the options.
The clue was we can take only one 3*3 square and then fit the rest with as max dimension as possible i.e. 2*2 on priority and then 1*1.
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Re: A square board that has an area of 25 square inches is to be &nbs [#permalink] 02 Aug 2017, 00:21
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