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m14 #20

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m14 #20 [#permalink] New post 05 Aug 2009, 19:38
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

OA is B..

but lets say you were to assume there were last black tiles. we're minimizing Black to maximize difference between White and Black.
if you were to put black tiles on the diagonal, white tiles can fill the rest of the space on the 10x10 grid - you'd get 10 black tiles and 90 white tiles.

is my logic wrong?
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Re: m14 #20 [#permalink] New post 05 Aug 2009, 20:07
Your logic isn't wrong, you're just not done answering the question yet. The question asks for the "maximum difference" meaning, what is the difference between the # of black tiles and the # of white tiles. 90 - 10 = 80....Answer B

viperm5 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

OA is B..

but lets say you were to assume there were last black tiles. we're minimizing Black to maximize difference between White and Black.
if you were to put black tiles on the diagonal, white tiles can fill the rest of the space on the 10x10 grid - you'd get 10 black tiles and 90 white tiles.

is my logic wrong?

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Intern
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Joined: 09 Feb 2009
Posts: 17
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Re: m14 #20 [#permalink] New post 05 Aug 2009, 20:23
jallenmorris wrote:
Your logic isn't wrong, you're just not done answering the question yet. The question asks for the "maximum difference" meaning, what is the difference between the # of black tiles and the # of white tiles. 90 - 10 = 80....Answer B

viperm5 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

OA is B..

but lets say you were to assume there were last black tiles. we're minimizing Black to maximize difference between White and Black.
if you were to put black tiles on the diagonal, white tiles can fill the rest of the space on the 10x10 grid - you'd get 10 black tiles and 90 white tiles.

is my logic wrong?


wow that i guess im really tired. should call it a night then.
thanks!
cant believe i missed that. :|
Re: m14 #20   [#permalink] 05 Aug 2009, 20:23
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