# PRAXIS Mathematics Practice Test

#### Jane is creating a unique paint color that calls for one part coloring to every four parts white paint. For a total of 12 gallons of colored paint, how much coloring will Jane require?

Explanation:

The ratio of coloring to white is 1:4.

A total of 12 gallons of colored paint are needed.

Let c represent the amount of coloring in the 12 gallons.

The amount of white is then 12 – c.

Set up the proportion c/12−c= 1?4.

Use cross-multiplication to solve the equation for c.

12–c=4c

12=5c

5c=12

c=12/5=2 2/5

Because of the 1:4 ratio, 3 gallons may seem like a correct answer (divide 12 by 4). It is not correct because the total
amount of paint is 12 gallons. If the problem stated that 12 gallons of white paint were used, then 3 gallons would
have been correct. But, if you use 3 gallons of colored paint plus the 12 gallons of white paint, you would use 15 gallons
of paint and that is not what the problem specifies. These problems can be tricky. Be sure to read them carefully.

#### Students were required to provide an equal approach to express the ratio 8:6 on a test. In the document attached,
four of the responses are listed. Which one is the most accurate?

Student A: 8/6

Student B: 3/2

Student C: 6:8

Student D: 4/3

Explanation:

Ratios can also be written as fractions with the first item in the ratio as the numerator and the second item as the denominator,
as student D has done.

Student A has given a fraction equivalent to the original ratio and is also correct.

The answer given by student B is not an equivalent fraction to the original ratio.

The order of the ratio must be preserved, so student C is incorrect.

#### When adding fractions with dissimilar denominators, the common denominator should be the least common multiple of the denominators. When adding the fractions 5/6 and 7/9, what common denominator should you use

Explanation:

54 and 36 are common multiples of 6 and 9, but they are not the least common multiple.

To find the least common multiple, examine the prime factors of 6 and 9:

6 = 2 x 3 and 9 = 3 x 3

6 and 9 share one instance of the prime factor 3, so the least common multiple will contain one 3 coming from the
overlap and the other 3 coming from the prime factorization of 9.

Multiply the prime factors together to compute the LCM:

2 x 3 x 3 = 18

#### The following is a breakdown of a year-end test that includes math, science, and language arts questions: The language arts portion accounts for 30% of the overall score, while the math and science sections each account for 35% of the overall score. What is Marys' overall score if he received an 89 on the math exam, an 85 on the science section, and a 76 on the language arts section? Your answer should be rounded to the nearest whole number.

Explanation:

This is a weighted average question. Multiply each score by the percentage of the total that it accounts for:

weighted math score: 89⋅0.35=31.15

weighted science score: 85⋅0.35=29.75

weighted language arts score: 76⋅0.3=22.8

The overall score is the sum of the weighted scores:

31.15+29.75+22.8=83.7, rounded to the nearest whole number, is 84.

#### Choose the response that is the polar opposite of the statement: Prime numbers are usually odd three-digit numbers.

Explanation:

129=3×43, so it is not prime.

#### A clothing retailer is offering a deal on boots with a 10% discount and gloves with a 15% discount. A pair of boots typically
costs b, and a pair of gloves typically costs g.

Which of the following expressions best describes the total cost of one pair of boots and two pairs of gloves during this sale?

Explanation:

The discounted price of the boots is b – 0.1b=0.9b.

Similarly, the discounted price of a pair of gloves is g–0.15g=0.85g.

The total cost of 1 pair of boots and 2 pairs of gloves during the sale is

0.9b+2(0.85g)=0.9b+1.7g.

#### James is about to go on an 840-mile long-distance bicycle adventure. He calculates that he can go 160 miles each day on
average. On the day ____ of the trip, he will arrive.

Which option indicates the proper fill-in-the-blank number?

Explanation:

To find the total number of days traveled given the total mileage and the miles per day traveled, divide the total mileage
by the number of days.

This can be seen by looking at the measurable units.

miles÷miles/day = miles⋅days./mile = days
The given unit of the answer is days, so that is what we require. This shows that division was the correct operation to do.

The result is 5.25 days.

He will arrive during the 6th day, because, after 5 days, he still has 0.25 (1/4) of a day of travel remaining. He will arrive after
1/4 of the 6th day has elapsed.

#### 5 less than 3 times a number equals half of it. What number is it?

Explanation:

Start with 12x=3x−5

x/2 = 3x−5 Multiply both sides by 2.

x=6x−10 Subtract 6x from both sides.

−5x=−10 Divide both sides by −5

x=2

#### Which one(s) demonstrates a correct statement?

A) xy(5t⋅2)=5xyt⋅2xy

B) ab(2x−3)=2abx−3ab

C) 6rt(m+2n)=12mnrt

D) 4d(9c÷8c)=36cd÷32dp

Explanation:

The distributive property does not work over multiplication or division, so that rules out choices a and d. The distributive
property does work over addition, but choice c should be 6rt(m+2n)=6mrt+12nrt, not 12mnrt. That leaves choice b which
is done correctly.

#### Sally has a yard sale going on. She earned sales of $15, $21, $12, and $9 in the first four hours. She had hoped for an hourly wage of $15, but with $14.25, she is a little short of her objective. How much sales must she make in the fifth hour to raise her hourly average to $15?

Explanation:

An average is calculated by dividing a total by the number of items.

In this case, the total sales divided by the number of hours, to give an average of sales per hour. In this case, we know the
number of hours will be 5.

She wants an average of $15 per hour, so that means that totalsales/5 = 15, or totalsales=5⋅15, or $75.

She has $57 in sales after 4 hours, so she must get $18 more in sales to reach $75 by the end of 5 hours.

#### Tim's socks are strewn around in a drawer. There are four pairs of blue socks, eight pairs of black socks, and four pairs of brown socks. He pulls a blue sock from the drawer at random. What are the chances that the second sock he picks up will be blue as well?

Explanation:

The probability of a random event is the number of successful possibilities divided by the total number of possibilities.

After Jack has taken the first sock, there are 15 remaining as the total number of possible socks.

Of these, there are 3 remaining blue socks, which represent successful events.

The probability is then:

3/15

which simplifies to:

1/5

#### Jerry invests in a 24-foot fence to keep his garden safe. He intends to create a rectangle garden. With this amount of fencing, what is the size of the largest rectangular garden Jim can create?

Explanation:

The 24 feet of fencing is the perimeter of his garden. For a rectangle with width w and length l, the perimeter P is P=2w+2l.

In this case 2w+2l=24, or w+l=12. He must use a length and width of the rectangle that adds up to 12 feet.

The possible combinations are 1 x 11, 2 x 10, 3 x 9, 4 x 8, 5 x 7, and 6 x 6.

The combination with the highest product, which is the area, is 6 x 6.

A square is a special form of rectangle. The area is 6 x 6 = 36 square feet.

#### A farmer wants to know how much insect damage his corn crop has, so he picks 75 plants at random from different parts of the cornfield and inspects each one for damage. Nine of the 75 plants had been infested with corn borers. He understands that each acre has around 31,000 plants, and he has a 50-acre field to work with. In a 50-acre field, how many afflicted plants would you expect to find?

Explanation:

Start by calculating the total number of plants.

31,000×50=1,550,000

Set up a proportion to calculate the number of infested plants.

9/75 = x/1,550,000

x=186,000

#### Which of the following data sets has a median that is higher than the mean?

a) {20,23,24,24,29,34,35}

b){12,17,22,28,28,33,34}

c) {24,26,29,29,29,34,35}

d) {19,21,27,27,30,34,35}

Explanation:

The median is the value in the middle. The mean is the average; the sum of all values divided by the number of values.
The results for each set are:

a) {20,23,24,24,29,34,35} The median is 24 and the mean is 27(.)

b) {12,17,22,28,28,33,34} The median is 28 and the mean is 24.9(.)

c) {24,26,29,29,29,34,35} The median is 29 and the mean is 29.4(.)

d) {19,21,27,27,30,34,35} The median is 27 and the mean is 27.6(.)

#### △ABC≅△DEF Is given

DE=15

EF=12

DF=9

What is △ABC perimeter ?

Explanation:

The two triangles are congruent, so corresponding sides of △ABC are congruent to those of △DEF.

This means both triangles will have the same perimeter: 15+12+9=36

#### What is the perfect square of these numbers?

Explanation: A perfect square is a number formed when a whole number is multiplied by itself. The number 169 is formed by 13 multiplied by 13.

#### Jayson, a student, gets 37 out of 55 on the first test, 47 out of 72 on the second, and 41 out of 64 on the third. Jayson's highest percent score is

Explanation:

Test 1: 37÷55≈67%

Test 2: 47÷72≈65%

Test 3: 41÷64≈64%

#### Which of the following would be considered an improper fraction?

Explanation:

An improper fraction has a numerator that is larger than the denominator.

#### Which of the following is the same as the 4:12 ratio?

Explanation:

Ratios can also be expressed as fractions, with the first term as the numerator and the second term as the denominator.
The 4 should become the numerator and the 12 should become the denominator.

The result is 4/12.

You can simplify the fraction by dividing the 4 and the 12 by 4.

4÷4=1

12÷4=3

The fraction becomes 1/3

#### What percentage of 150 is 32 percent?

Explanation:

To find a percentage of a number you convert the percent to a decimal and then multiply that by the given number.
To convert the percent to a decimal, you multiply 32×0.01=0.32. Then, you need to take that answer and multiply it
by your original amount of 150.

0.32×150=48

#### Mary reads a book every 45 minutes and finishes three chapters. How long does one chapter take her to read?

Explanation:

To find the unit rate, you set up a proportion and simplify to find how long it takes to get 1 chapter. You can look at it like this:

3/45 = 1/x

You cross multiply to get

3x=45

Divide both sides by 3 to isolate x.

3x÷3=45÷3

x=15

#### Which of the following is not a 42 factor?

Explanation:

A factor of a number can evenly divide that number.

#### To determine the weight of a bowling ball, which unit should be used?

Explanation:

In the metric system, weight (technically, mass) is measured in kilograms. Meters and centimeters measure
length. Volume is measured in milliliters.

#### Mike awoke to a temperature of 17 degrees below zero on a Fahrenheit thermometer. Throughout the day, the temperature soared by 12 degrees. What is the current Fahrenheit temperature?

Explanation:

You start at 32 because 32 is the freezing point of water in Fahrenheit.

First, you subtract 17 from 32:

32−17=15

Next, you add 12 to that result:

15+12=27

#### 10 3/5 is equal to which of the following?

Explanation:

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the
numerator. Place this number over the given denominator.

10 3/5

10×5 = 50

50 + 3 = 53

53/5