GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #361 : Problem Solving Questions

The width of a rectangle is twice the length. Find an equation representing the perimeter.

$\textup{I. }l \cdot2l$

$\textup{II. }4l + 2l$

$\textup{III. }6l^2$

Possible Answers:

$\textup{II only}$

$\textup{I and II}$

$\textup{I only}$

$\textup{III only}$

$\textup{II and III}$

Correct answer:

$\textup{II only}$

Explanation:

The perimeter of a rectangle can be found by adding up all the sides:

l + l + w + w = 2l + 2 w

We are told the width of the rectangle is twice its length so w=2l , inserting this into our equation for the perimeter leaves us with:

2l + 2w=2l + 2(2l)=2l + 4l , which is II

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Example Question #361 : Problem Solving Questions

Find the perimeter of a rectangle whose width is and length is .

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a rectangle:

$P=2(w+l)=2(7+6)=2\cdot13=26$

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Example Question #8 : Calculating The Perimeter Of A Rectangle

Rectangle 1

Note: figure NOT drawn to scale

Give the perimeter of the above rectangle.

Possible Answers:

$3^{x^{2}+x}$

$3^{2x+1}$

$8 \cdot 3 ^{x}$

$2 \cdot 3^{x+1}$

$3^{x+2}$

Correct answer:

$8 \cdot 3 ^{x}$

Explanation:

The perimeter of a rectangle is the sum of the lengths of its sides. Since a rectangle has two pairs of sides of the same lengths, this will be

$P = 3^{x}+ 3^{x}+ 3^{x+1}+ 3^{x+1}$

$=1 \cdot 3^{x}+ 1 \cdot 3^{x}+3 \cdot 3^{x}+3 \cdot 3^{x}$

$=(1 + 1 +3 +3) \cdot 3^{x}$

$=8 \cdot 3^{x}$

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Example Question #362 : Problem Solving Questions

The area of a rectangle is 85; its length is x - 17 . What is its width?

Possible Answers:

$51 - \frac{1}{2}x$

$\frac{85}{x-17 }$

$\frac{5}{x }$

102-x

$\frac{68}{x }$

Correct answer:

$\frac{85}{x-17 }$

Explanation:

The product of the length and the width of a rectangle is its area, so divide area by length to get width. This is simply $\frac{85}{x-17 }$ .

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Example Question #2 : Calculating The Length Of The Side Of A Rectangle

The perimeter of a rectangle is ; its width is 4t -26 . Which of the following expressions is equal to the length of the rectangle?

Possible Answers:

$\frac{45}{2t-13}$

116-4t

71+4t

71-4t

$\frac{45}{2t+13}$

Correct answer:

71-4t

Explanation:

Substitute P = 90, W = 4t-26 and solve for :

2 L + 2W = P

2 L + 2 (4t-26) = 90

2 L + 8t-52 = 90

2 L + 8t-52 + 52 - 8t= 90 + 52 - 8t

2 L =142 - 8t

$2 L \div 2=\left (142 - 8t \right ) \div 2$

L =71-4t

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Example Question #124 : Geometry

Rectangle A and Rectangle B have the same area. Rectangle A has length 80% that of Rectangle B, and its width is 120 centimeters. What is the width of Rectangle B?

Possible Answers:

$140 \textrm{ cm}$

Not enough information is given to answer the question.

$96 \textrm{ cm}$

$1 \textrm{ m}$

$144 \textrm{ cm}$

Correct answer:

$96 \textrm{ cm}$

Explanation:

Let and be the length and width of Rectangle B.

Then the width of Rectangle A is 80% of , or 0.8W . Its length is 120.

The area shared by the two can be expressed as both and $0.8W \cdot 120 = 96W$ . We can set the two equal to each other and calculate :

LW =96W , or L = 96 .

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Example Question #121 : Geometry

Craig is building a fence around his rectangular back yard. He knows that the yard is feet longer than twice the width. What is the width of the yard if Craig needs 160 feet of fencing to completely enclose the yard?

Possible Answers:

55ft

35ft

15ft

25ft

45ft

Correct answer:

25ft

Explanation:

The length is 5 more twice the width. Let y be the length of the yard and w the width.

y=2w+5

The perimeter of the yard is 160, so we can write:

2(y+w)=160

2(2w+5+w)=160

10+6w=160

w=25

The yard is 25 feet wide and 55 feet long.

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Example Question #126 : Geometry

A rectangle has an area of . If the width of the rectangle is , what is its length?

Possible Answers:

Correct answer:

Explanation:

Using the formula for the area of a rectangle, we can solve for the unknown length. We are given the area and the width, so we can solve for the length as follows:

A=LW

36=L(4)

$L=\frac{36}{4}=9$

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Example Question #2 : Calculating The Length Of The Side Of A Rectangle

The length of a rectangle is twice its width. If the rectangle's area is $288 \ in^2$ , what is its length?

Possible Answers:

$14 \ in$

$12 \ in$

$24 \ in$

$6 \ in$

Correct answer:

$24 \ in$

Explanation:

We're told the length is twice the width so l=2w

$A=l \times w=(2w)(w)$

288=2w^2

144=w^2

12=w

Remember, we're being asked for the length, not the width so:

$l=2w=2(12)=24 \ in$

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Example Question #3 : Calculating The Length Of The Side Of A Rectangle

A rectangle with a perimeter of has a width times that of its length. Find its length.

Possible Answers:

21.6

5.4

10.8

Correct answer:

5.4

Explanation:

The perimeter of a rectangle is found by 2l + 2w . Since we are told w=4l , we can substitute this into our equation and solve for the length.

54 = 2l + 2(4l)

54 = 10l

l = 5.4

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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #361 : Problem Solving Questions

Example Question #361 : Problem Solving Questions

Example Question #8 : Calculating The Perimeter Of A Rectangle

Example Question #362 : Problem Solving Questions

Example Question #2 : Calculating The Length Of The Side Of A Rectangle

Example Question #124 : Geometry

Example Question #121 : Geometry

Example Question #126 : Geometry

Example Question #2 : Calculating The Length Of The Side Of A Rectangle

Example Question #3 : Calculating The Length Of The Side Of A Rectangle

All GMAT Math Resources

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