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100 white and black tiles will be used to form a 10x10 squar

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100 white and black tiles will be used to form a 10x10 squar [#permalink] New post 26 Dec 2010, 23:01
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100 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?

A. 75
B. 80
C. 85
D. 90
E. 95

M14-20
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Jul 2014, 03:50, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: 100 white and black tiles will be used to form a 10x10 squar [#permalink] New post 26 Dec 2010, 23:14
ohfred wrote:
100 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?

75
80
85
90
95


80?

90 white or black subtracted from 10 white or black.

At first I got 90, but realized the double counting I was doing.
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Re: 100 white and black tiles will be used to form a 10x10 squar [#permalink] New post 26 Dec 2010, 23:53
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You required 100 tiles in total
As per question we have to find maximum difference possible between white and black tiles.
So, we have to find, as per condition, maximum white tiles(black) can be used and minimum blac tiles(white) tiles that must be used.

In any case, maxium black and white tiles that can be used to form the square is 90.( 9 tiles of same color in any row or column:: 9 * 10).
and minimum blac or white tiles that can be used to form the squaare is 10( 1 tiles every row or column = 1 * 10 )

90 - 10 = 80
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Re: 100 white and black tiles will be used to form a 10x10 squar [#permalink] New post 23 Jul 2014, 17:45
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Re: 100 white and black tiles will be used to form a 10x10 squar [#permalink] New post 23 Jul 2014, 17:55
ohfred wrote:
100 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?

75
80
85
90
95


The attached illustration should help you understand how we arrived at the answer.

90-10 = 80

Answer is B
Attachments

Untitled.png
Untitled.png [ 2.2 KiB | Viewed 104 times ]

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Re: 100 white and black tiles will be used to form a 10x10 squar [#permalink] New post 23 Jul 2014, 18:01
Answer = B

Please refer diagram below

90 - 10 = 80

Bunuel: Kindly change the "Topic Name" from "Re: Can someone explain this tile question?" to the question...

Thanks :)
Attachments

box.png
box.png [ 8.34 KiB | Viewed 102 times ]


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Re: 100 white and black tiles will be used to form a 10x10 squar   [#permalink] 23 Jul 2014, 18:01
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