BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

How many rectangles are found in the lattice below?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 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

[GMAT math practice question]

How many rectangles are found in the lattice below?

Image

A. 90
B. 100
C. 120
D. 150
E. 180
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

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
Top
Post new topic Post Reply
• Page 1 of 1