[GMAT math practice question]

How many rectangles are found in the lattice below?

A. 90

B. 100

C. 120

D. 150

E. 180

## How many rectangles are found in the lattice below?

##### This topic has expert replies

- Max@Math Revolution
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## Your Answer

**A**

**B**

**C**

**D**

**E**

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- GMATGuruNY
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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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- Max@Math Revolution
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=>

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

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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