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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## How many rectangles are found in the lattice below? ##### This topic has expert replies Elite Legendary Member Posts: 3110 Joined: 24 Jul 2015 Location: Las Vegas, USA Thanked: 19 times Followed by:36 members ### How many rectangles are found in the lattice below? by Max@Math Revolution » Mon Apr 08, 2019 11:07 pm ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] How many rectangles are found in the lattice below? A. 90 B. 100 C. 120 D. 150 E. 180 Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World's First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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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?

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

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:
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

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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.