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How many rectangles are found in the lattice below?

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[GMAT math practice question]

How many rectangles are found in the lattice below?

Image

A. 90
B. 100
C. 120
D. 150
E. 180
Image
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by GMATGuruNY » Tue Apr 09, 2019 3:47 am
Max@Math Revolution wrote:[GMAT math practice question]

How many rectangles are found in the lattice below?

Image

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

To form a rectangle, we must combine as HORIZONTAL LENGTH with a VERTICAL LENGTH:

Horizontal length:
Number of ways to choose a horizontal length of 1:
AB, BC, CD, DE, EF = 5
Number of ways to choose a horizontal length of 2:
AC, BD, CE, DF = 4
Number of ways to choose a horizontal length of 3:
AC, BE, CF = 3
Number of ways to choose a horizontal length of 4:
AD, BF = 2
Number of ways to choose a horizontal length of 5:
AF = 1
Total ways = 5+4+3+2+1 = 15

Vertical length:
Number of ways to choose a vertical length of 1:
AG, GH, HI, IJ = 4
Number of ways to choose a vertical length of 2:
AH, GI, HJ = 3
Number of ways to choose a vertical length of 3:
AI, GJ = 2
Number of ways to choose a vertical length of 4:
AJ = 1
Total ways = 4+3+2+1 = 10

To combine our horizontal options with our vertical options, we multiply:
15*10 = 150

The correct answer is D.
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by Max@Math Revolution » Wed Apr 10, 2019 11:59 pm
=>

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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