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PSAT Math : PSAT Mathematics

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10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Rectangles

A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the area of the rectangle?

Possible Answers:

5x + 10

10(x + 1)

6x² + 5

6x² + 10x

5x + 5

Correct answer:

6x² + 10x

Explanation:

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.

A = lw = (3x + 5)(2x) = 6x² + 10x

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Example Question #41 : Quadrilaterals

Para-rec1

Rectangle ABCD is shown in the figure above. Points A and B lie on the graph of y = 64 – x² , and points C and D lie on the graph of y = x² – 36. Segments AD and BC are both parallel to the y-axis. The x-coordinates of points A and B are equal to –k and k, respectively. If the value of k changes from 2 to 4, by how much will the area of rectangle ABCD increase?

Possible Answers:

352

176

272

544

Correct answer:

176

Explanation:

Para-rec2

Para-rec3

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Example Question #641 : Geometry

George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 $ft^{2}$ and costs $40. One quart of paint covers 100 $ft^{2}$ and costs $15. How much money will he spend on the blue paint?

Possible Answers:

$\$80$

$\$70$

$\$30$

$\$40$

$\$55$

Correct answer:

$\$70$

Explanation:

The area of the walls is given by $A = 2wh + 2lh = 2(12)(10) + 2(15)(10) = 540 ft^{2}$

One gallon of paint covers 400 $ft^{2}$ and the remaining 140 $ft^{2}$ would be covered by two quarts.

So one gallon and two quarts of paint would cost $\$40 + \$15 + \$15 = \$70$

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Example Question #2 : How To Find The Area Of A Rectangle

Daisy gets new carpet for her rectangluar room. Her floor is $21\ ft \times 24\ ft$ . The carpet sells for $5 per square yard. How much did she spend on her carpet?

Possible Answers:

$\$225$

$\$280$

$\$310$

$\$120$

$\$350$

Correct answer:

$\$280$

Explanation:

Since $3\ ft=1\ yd$ the room measurements are 7 yards by 8 yards. The area of the floor is thus 56 square yards. It would cost $5\cdot 56=\$280$ .

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Example Question #642 : Geometry

The length of a rectangular rug is five more than twice its width. The perimeter of the rug is 40 ft. What is the area of the rug?

Possible Answers:

$125\ ft^{2}$

$75\ ft^{2}$

$50\ ft^{2}$

$100\ ft^{2}$

$150\ ft^{2}$

Correct answer:

$75\ ft^{2}$

Explanation:

For a rectangle, $P=2w+2l$ and $A=lw$ where $w$ is the width and $l$ is the length.

Let $x=width$ and $2x+5=length$ .

So the equation to solve becomes $40=2x+2(2x+5)$ or $40=6x+10$ .

Thus $x=5\ ft$ and $2x+5=15\ ft$ , so the area is $75\ ft^{2}$ .

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Example Question #181 : Sat Mathematics

The front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?

Possible Answers:

192 ft²

768 ft²

1536 ft²

2464 ft²

1536 ft²

Correct answer:

1536 ft²

Explanation:

Glass Area per Window = 8 ft x 6 ft = 48 ft²

Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows

Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft²

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Example Question #23 : Rectangles

Rectangle

Note: Figure NOT drawn to scale

AB = 13, BC = 7, AD = 9, DF = 3

What percent of Rectangle ACGF is pink?

Possible Answers:

$48\frac{3}{4} \%$

$46\frac{2}{3} \%$

$55 \frac{5}{9} \%$

$50 \%$

$44 \frac{4}{9} \%$

Correct answer:

$48\frac{3}{4} \%$

Explanation:

The pink region is Rectangle ABED . Its length and width are

L = AB = 13

W = AD = 9

so its area is the product of these, or

$A = 13 \times 9 = 117$ .

The length and width of Rectangle ACGF are

L = AC = AB + BC = 13+7 = 20

W =AF = AD + DF=9+3 = 12

so its area is the product of these, or

$20 \times 12 = 240$ .

We want to know what percent 117 is of 240, which can be answered as follows:

$\frac{117}{240} \times 100 \% = 48\frac{3}{4} \%$

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Example Question #24 : Rectangles

Rectangle

Note: Figure NOT drawn to scale

Refer to the above diagram.

40% of Rectangle ACGF is pink. AB = 20, AD = 15, BC = 10 .

Evaluate .

Possible Answers:

DF = 12

DF = 5

DF = 15

DF = 8

DF = 10

Correct answer:

DF = 10

Explanation:

Rectangle ABED has length L = AB = 20 and width W = AD = 15 , so it has area

$LW = 20 \times 15 = 300$ .

300 is 40% of, or 0.40 times, the area of Rectangle ACGF , which we will call . We can determine as follows:

0.40 A = 300

$A = 300 \div 0.4 = 750$ .

The length of Rectangle ACGF is

L = AC = AB + BC = 20 + 10 = 30 ,

so its width is

$W = AF = 750 \div 30 = 25$ .

Since

W = AF= AD + DF ,

25 = 15 + DF

DF = 10

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Example Question #323 : Plane Geometry

Rectangle

Note: Figure NOT drawn to scale

AB = 24, BC = 6, AD = 12, DF = 3

What percent of Rectangle ACGF is white?

Possible Answers:

$40 \%$

$25 \%$

$36 \%$

$33 \frac{1}{3} \%$

$44 \frac{4}{9} \%$

Correct answer:

$36 \%$

Explanation:

The pink region is Rectangle ABED . Its length and width are

L = AB = 24

W = AD = 12

so its area is the product of these, or

$24 \times 12 = 288$ .

The length and width of Rectangle ACGF are

L = AC = AB + BC = 24 + 6 =30

W =AF = AD + DF= 12 + 3 = 15

so its area is the product of these, or

$30 \times 15 = 450$ .

The white region is Rectangle ABED cut from Rectangle ACGF , so its area is the difference of the two:

450 - 288 = 162 .

So we want to know what percent 162 is of 450, which can be answered as follows:

$\frac{162}{450} \times 100 \% = 36 \%$

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Example Question #13 : How To Find The Area Of A Rectangle

Rectangle

Note: Figure NOT drawn to scale

AB = 20, BC = 8, AD = 10, DF = 4

Give the ratio of the perimeter of Rectangle ACGF to that of Rectangle ABED .

Possible Answers:

5:3

2:1

5:2

4:3

7:5

Correct answer:

7:5

Explanation:

The perimeter of Rectangle ABED is

P = AB +BE + ED + AD

Opposite sides of a rectangle are congruent, so

AB= ED = 20, AD = BE = 10

and

P = 20 + 10 + 20 + 10 = 60

The perimeter of Rectangle ACGF is

P = AC + CG + GF + AF

Opposite sides of a rectangle are congruent, so

GF = AC = AB + BC = 20 + 8 = 28 ,

CG = AF = AD + DF = 10 + 4 = 14 ,

and

P = 28 + 14+ 28 + 14= 84

The ratio of the perimeters is

$\frac{84}{60} = \frac{84 \div 12}{60 \div 12} = \frac{7}{5}$ - that is, 7 to 5.

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Rectangles

Example Question #41 : Quadrilaterals

Example Question #641 : Geometry

Example Question #2 : How To Find The Area Of A Rectangle

Example Question #642 : Geometry

Example Question #181 : Sat Mathematics

Example Question #23 : Rectangles

Example Question #24 : Rectangles

Example Question #323 : Plane Geometry

Example Question #13 : How To Find The Area Of A Rectangle

All PSAT Math Resources

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