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Number of rectangles in the grid shown which are not squares is
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Bunuel
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Number of rectangles in the grid shown which are not squares is [#permalink] New post  15 Feb 2021, 07:00
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Number of rectangles in the grid shown which are not squares is

(A) 160
(B) 162
(C) 170
(D) 185
(E) 190



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nick1816
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Re: Number of rectangles in the grid shown which are not squares is [#permalink] New post  15 Feb 2021, 13:06
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Number of rectangles = 7C2 * 5C2 = 210

Number of squares = 6*4 + 5*3 + 4*2 + 3*1 = 50

Number of rectangles in the grid shown which are not squares = 210- 50=160


Bunuel wrote:
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Number of rectangles in the grid shown which are not squares is

(A) 160
(B) 162
(C) 170
(D) 185
(E) 190



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Gmatpractitioner
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Number of rectangles in the grid shown which are not squares is [#permalink] New post  15 Feb 2021, 15:19
nick1816 Why did you do the step you did to calculate rectangles? I followed a similar methodology for calculating rectangles as you did for squares and got 84 rectangles :(. Trying to see where I am going wrong
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Brian123
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Re: Number of rectangles in the grid shown which are not squares is [#permalink] New post  15 Feb 2021, 18:38
Gmatpractitioner wrote:
nick1816 Why did you do the step you did to calculate rectangles? I followed a similar methodology for calculating rectangles as you did for squares and got 84 rectangles :(. Trying to see where I am going wrong


I tried the same approach and got 156. Can anybody help with the counting approach?
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nick1816
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Re: Number of rectangles in the grid shown which are not squares is [#permalink] New post  15 Feb 2021, 18:57
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There are 5 horizontal lines and 7 vertical lines in the grid. To make a rectangle, we need 2 horizontal lines and 2 vertical lines.

Total number of ways to select 2 horizontal lines = 5C2 = 10

Total number of ways to select 2 vertical lines = 7C2 = 21

Total number of rectangles in the grid = 10*21=210



Gmatpractitioner wrote:
nick1816 Why did you do the step you did to calculate rectangles? I followed a similar methodology for calculating rectangles as you did for squares and got 84 rectangles :(. Trying to see where I am going wrong
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