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How many rectangles are found in the lattice below?

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How many rectangles are found in the lattice below?  [#permalink]

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New post 09 Apr 2019, 00:11
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Question Stats:

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[GMAT math practice question]

How many rectangles are found in the lattice below?

Attachment:
4.9.png
4.9.png [ 1.72 KiB | Viewed 665 times ]


A. 90
B. 100
C. 120
D. 150
E. 180

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Re: How many rectangles are found in the lattice below?  [#permalink]

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New post 09 Apr 2019, 08:23
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2
MathRevolution wrote:
[GMAT math practice question]

How many rectangles are found in the lattice below?

Attachment:
4.9.png


A. 90
B. 100
C. 120
D. 150
E. 180



The question basically asks to choose two lines from 5 rows and 2 lines from 6 columns, so 5C2*6C2=\(\frac{5*4}{2}*\frac{6*5}{2}=5*2*3*5=150\)

D
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Re: How many rectangles are found in the lattice below?  [#permalink]

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New post 09 Apr 2019, 21:17
2
The length has 6 lines
and width has 5 lines
to make a rectangle take any 2 lines from width and other 2 lines from length
hence 6c2 and 5c2
thus 6c2*5C2
=150
thus D
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Re: How many rectangles are found in the lattice below?  [#permalink]

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New post 11 Apr 2019, 01:47
=>

Each rectangle is uniquely determined by the intersections between two vertical lines and two horizontal lines.
Since we have 6 vertical lines and 5 horizontal lines, the number of rectangles is 6C2*5C2 = 15*10 = 150.

Therefore, D is the answer.
Answer: D
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Re: How many rectangles are found in the lattice below?  [#permalink]

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New post 11 Apr 2019, 02:01
Are we also taking square into accounts?
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Re: How many rectangles are found in the lattice below?  [#permalink]

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New post 12 Apr 2019, 11:24
heisenberg11 wrote:
Are we also taking square into accounts?


A squares are a rectangle, actually.
However, it doesn't matter for this question.

Happy Studying !!!
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Re: How many rectangles are found in the lattice below?  [#permalink]

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New post 13 Apr 2019, 04:17
heisenberg11 wrote:
Are we also taking square into accounts?


Yes, we are taking squares too into account since squares are also rectangles..
I can say..
Squares are rectangles. Rectangles are parallelogram and parallelogram are quadrilateral.
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Re: How many rectangles are found in the lattice below?   [#permalink] 13 Apr 2019, 04:17
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