# PERT (Math) Practice Test

#### What is 18% of 222 when it's rounded up to the nearest whole number?

Explanation:

Recall that 18% is equivalent to both 0.18 and 18100.

Consequently, 18% of 222 is the same as 0.18⋅222 or 18100⋅222.

Find the product and round to the nearest whole number to solve:

18100⋅222=18⋅2.22=39.96 rounded to the nearest whole number is 40.

#### Jack wants to build a 7-foot-wide, 10-foot-long platform. How many boards will he need to do the work if the boards are 6 inches wide by 2 feet long?

Explanation:

To find the area Joey needs to cover, 7 x 10 = 70 square feet.

Convert inches to feet: 6 inches = .5 feet.

Each board measures .5 x 2 feet, which equals coverage of 1 square foot.

He will need 70 of these to cover 70 square feet.

#### What percentage discount did Jenny obtain on her purchase if the item's original price was $30.00 and she only paid $24.00 for it?

Explanation:

Joan’s discount was $6.00 since $30.00 - $24.00 = $6.00.

This amount (6) / the original price (30) = .2

.2 equals .20, which is equal to 20%.

#### Solve for y as follows:

3.98−0.8y=−2.86

Explanation:

Isolate the variable to solve.

Begin by subtracting 3.98 from both sides of the equation:

−0.8y = −2.86−3.98

−0.8y = −6.84

Divide both sides by -0.8 to solve for y:

y = −6.84−0.8

y = 8.55

#### The summer fair had a total of 28 tickets sold. The cost of a child's ticket is $2.50, while an adult's ticket is $3.75. How many child tickets were sold if the total cost of the tickets sold was $82.50?

Explanation:

Use the information given to generate two equations.

The sum of the child tickets, C, and the adult tickets, A, is 28.

Stated algebraically:

C+A = 28

The cost per child’s ticket is $2.50 and the cost per adult’s ticket is $3.75, and the total cost was $82.50.

Stated algebraically:

2.5C+3.75A = 82.5

Multiply the first equation by −3.75 and use the method of elimination to directly solve for C:

−3.75C−3.75A=−105, which can be added to the second equation in order to eliminate the C variable:

2.5C+(−3.75C)+3.75A+(−3.75A)=82.5+(−105), which becomes:

−1.25C=−22.5, so C = 18

#### What is the graph's slope of 5x+2y=18?

Explanation:

5x+2y = 18

2y = −5x+18

y = −2.5x+9

This is now in the form y = mx+b, so m must be −2.5

#### In a basketball game, a player makes 17 of her 25 shots. What percentage of her shots were successful?

Explanation:

A percentage is a number represented as a fraction of 100.

In this case, the basketball player has made 17 of the 25 total shots taken.

This can be first represented as a fraction then converted to a percentage.

Expressed as a fraction:

(made)/ (total) = 17/25

To represent this as a percentage, we would usually divide 17 into 25 and then multiply the resulting decimal by
100 to convert it. But if we recognize that 25 is a factor of 100, we can express this fraction as a percentage in
one step by multiplying the numerator and denominator by 4:
17/25⋅4/4 = 68/100 = 68

#### What is the connection between the graphs of 2y=4x+5 and 12x+y=6?

Explanation:

Remember y = mx+b.

The equation 2y = 4x+5 can be rewritten as y = 2x+2.5, showing that its graph would have a slope of 2.

The equation 12x+y = 6 can be rewritten as y = −12x+6, showing that its graph would have a slope of −12.

The slopes are negative reciprocals of each other, indicating that the lines are perpendicular.

#### Which of the following isn't a prime factor of 300?

Explanation:

All four numbers are factors of 300, but 4 is not a prime number.

#### How much salt is required to make 500 g of a 0.9 percent salt solution?

Explanation:

0.9% expressed as a decimal is 0.009.

0.009×500 g = 4.5 g

#### The length of a rectangle is 8 times its width, and its perimeter is 60. What is the size of the area?

Explanation:

If we let the width be w, the length will be w+8.

We can write an equation for the perimeter.

P=2l+2w

P=2(w+8)+2w

2w+16+2w=60

4w+16=60

4w=44

w=11

l=11+8=19

A=lw=11×19=209

#### According to a poll, 57 individuals out of 380 believed that space aliens have visited Earth. How many people in a city of 40,000 people are likely to believe that space aliens have visited Earth, based on that result?

Explanation:

The percent of people believing this is 57/380

Multiply this percentage by 40,000 to find the number of people believing this in the city.

40,000×57/380

6,000

#### How many times greater than the original volume will the new volume be if you double the length of a cube's edge?

Explanation:

Take any size cube you want, say a 1 by 1 by 1 cube, which would have a volume of 1×1×1=1. If you double the
edge length, it will now have a volume of 2×2×2=8. The new volume is 8 times the original volume. This works
the same for any size cube you start with.

#### Which fraction is the same as 60/96?

Explanation:

Reduce 60/96

5⋅12/8⋅12

5/8

Reduce 45/72

5⋅9/8⋅9

5/8

#### When a = 1 and b = 2 and y = 3ab + 2b3, what is y?

Explanation:

Substitute the given values for a and b into the equation and then evaluate to find y:

y = 3ab + 2b3

y = 3(1)(2) + 2(23)

y = 6 + 16

y = 22

#### What is the answer to 181.5 percent of 18?

Explanation:

Recall that the % symbol means ‘per hundred.’ So, 181.5% is equivalent to 181.5100 or 1.815.

Converting a percentage to a decimal always entails moving the decimal point two places to the left.

Multiply this decimal value with 18 to answer the question:

1.815 × 18 = 32.67

#### 3x(2 + 5y) is equivalent to which of the following expressions?

Explanation:

Begin by assessing the form in which the answer choices are written. As no answer choice contains a parenthetical
expression, start by distributing the 3x through the parentheses. Multiply 3x by each of the terms inside of the parentheses
and combine any like terms to simplify:

3x(2 + 5y)

= 3x(2) + 3x(5y)

= 6x + 15xy

#### What is the value of the following expression? 26 − 7(3 + 5) ÷ 4 + 2

Explanation:

We can use PEMDAS to evaluate the expression. (PEMDAS is a technique for remembering the order of operations.
It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) According to the
rules, we must evaluate the expression in the parentheses first:

26 − 7(3 + 5) ÷ 4 + 2

= 26 − 7(8) ÷ 4 + 2

Then we perform multiplication and division in order from left to right as follows:

26 − 7(8) ÷ 4 + 2

= 26 − 56 ÷ 4 + 2

= 26 − 14 + 2

Finally, we perform addition and subtraction in order from left to right as follows:

26 − 14 + 2

= 12 + 2

= 14

#### How many prime numbers are there between the digits 10 and 25?

Explanation:

A prime number is a number with no factors other than 1 and itself. Therefore, we can solve this problem by listing the
numbers from 10 to 25 and eliminating those which are clearly divisible by some other number.

It is only necessary to list the odd numbers in this range, since the even numbers are all divisible by 2:

11, 13, 15, 17, 19, 21, 23, 25

Eliminate numbers divisible by 3: 15, 21

Eliminate numbers divisible by 5: 25

A quick check will tell us that none of the remaining numbers are divisible by anything other than themselves and 1.

That leaves: 11, 13, 17, 19, and 23, for a total of 5 numbers.

#### What was Jenny's tip percentage on a breakfast that cost $86.89 if she left a $10.16 tip?

Explanation:

If you want to know what percent A is of B, you divide A by B, then take that number and move the decimal place
two spaces to the right:

10.16 ÷ 86.89 = 0.1169

Move the decimal two spaces to the right to find the percentage:

= 11.69%

This is approximately equal to 12%.

#### Triangle ABC has the coordinates (2,7), (3,6), and (4,5) in a coordinate plane. What are the coordinates of the new image if triangle ABC is reflected across the y-axis?

Explanation:

One way to solve this problem is to draw the figure and then count how many units each point is from the y-axis,
and to then count the same number of units in the opposite direction to find each point’s reflection. A more efficient
method is to recognize that reflecting over the y-axis causes the x-value to switch sign and does not influence the
y-value of the point.

Reflecting (−2,7), (−3,6), (4,5) across the y-axis produces the points (2,7), (3,6), (−4,5).

#### What is the equation of the line passing through (4, –1) and having a –5 slope?

Explanation:

The general slope-intercept form of the equation of a line is y = mx + b, where m is the slope and
b is the y-intercept.

By substitution of the given point and given slope, we have:

–1 = (–5)(4) + b

So, b = –1 + 20 = 19, and the required equation is y = –5x + 19.

#### Jack bought a new hat for $5.06 that was on sale. The initial cost was $9.20. What was the sale price's % discount?

Explanation:

The percentage discount is the reduction in price divided by the original price. The difference between
original price and sale price is:

$9.20 − $5.06 = $4.14

The percentage discount is this difference divided by the original price:

$4.14 ÷ $9.20 = 0.45

Convert the decimal to a percentage by multiplying by 100%:

0.45 × 100% = 45%

#### ABC is a triangle having coordinates of (3, 1), (6, 1), and (7, 1), respectively (1, 3). A′(3, 3), B′(0, 3), and C′(5, 5) are the translated points. Find the translation rule.

Explanation:

The rule of translation is the rule, which when applied to the first set of points, yields the second set of points.
The difference between the x values of the non-translated and translated points is:

(x2 − x1) = (−3 − 3) = (0 − 6) = (−5 − 1) = −6

This corresponds to a shift of 6 units to the left.

Likewise, for the y values:

(y2 − y1) = (3 − 1) = (3 − 1) = (5 − 3) = 2

This corresponds to a vertical shift of 2 units.

#### In the grid below, what percentage of the squares are shaded?

Explanation:

The percentage of squares that are shaded can be expressed as the ratio of the number of shaded squares to the
total number of squares all multiplied by 100%, stated algebraically:

%=shaded squarestotal squares∗100%

And, substituting the values:

%=83100∗100%=83%