PRAXIS Math Core

Which of the following statements are true for all positive numbers r, s, and t ? Indicate ALL such statements.

r×(s+t)=(s+t)×r r+(s−t)=(r+s)−t

Bill takes a vitamin B pill every 3 days and a vitamin C pill every 4 days. If he takes both pills on day 1, for how many of the next 65 days will Bill take both pills on the same day?

five

A student used a calculator to divide a number by one third1313, when instead the student meant to multiply the number by 9. Which of the following single arithmetic operations can be performed to produce the intended result?

multiply by 3

At a fruit stand Jacob bought 12 apples for $0.45 each, 9 oranges for $0.55 each, 8 bananas for $0.32 each, and a watermelon for $3.00. What was the total cost for these purchases?

$15.91

If (x + 3/2) squared, equals the 49/4, which of the following could be the value of x ?

-5

The following table shows the frequency distribution for the number of children under 10 years old in 45 different families. What is the median number of children under 10 years old per family?

1

Results from a survey conducted in a certain grocery store showed that 3 out of 5 people preferred crispy-flakes cereal to crunchy-flakes cereal. Based on this survey, if a total of 2,500 customers bought one of these two cereals, how many most likely purchased crunchy-flakes cereal?

1,000

A hamburger franchise is owned by three people. One person owns seven twelfths of the franchise and the second person owns one sixth of the franchise. What fraction of the franchise does the third person own?

1/4

The following table shows the distribution of the employees in a certain company by age and marital status. Younger than 25 25 or Older Married 31 43Unmarried2620 If one of the employees is to be randomly selected, what is the probability that the employee selected will be unmarried and age 25 or older?

1/6

In a sequence of numbers, the first term is x and each term thereafter is twice the previous term. The fifth term is 160. What is the value of x ?

10

Which of the following numbers are equal to 1 0 comma 0 0 0 comma 0 0 010,000,00010,000,000 ? Indicate ALL such numbers.

10 million

In the preceding figure, 1ℓand ℓ2 are parallel. What is the value of y ?

116

Amy rents a table at a fair, for which she is charged a $10 daily rental fee. She purchases apples from a farmer for $0.60 each and sells them at her table for $1.00 each. If she expects to make a total profit of at least $50 for the day, what is the least number of apples she must sell?

150

The following circle graph shows the distribution of expenses for a recent conference. Conference Expenses The figure shows a circle graph titled "Conference Expenses." The circle is divided into the following four sections. Travel and Accommodations: 55%. Food: 25%. Printing: 15%. Miscellaneous: 5%. End figure description. If the printing expense is $2,400, what is the total expense for the conference?

16,000

Five students sold boxes of cookies to raise money for a charity. The number of boxes sold by each student is shown in the following bar graph. What is the mean number of boxes sold per student?

16.6

In a parking lot there are only white cars, green cars, and red cars. If one car is selected at random from the lot, the probability that the selected car would be a green car is one sixth and the probability that it would be a red car is one eighth. What is the probability that it would be a white car?

17/24

If a machine that works at a constant rate can fill 40 bottles of milk in 3 minutes, how many minutes will it take the machine to fill 240 bottles?

18

When 5,462.93 is multiplied by 10, which digit of the resulting number is in the tens place?

2

5 2/3÷2 1/2=

2 4/15

A local government spent 82 percent of the $12,500 budgeted for snow removal. How much of the budgeted money for snow removal was NOT spent?

2,250

Nineteen people ran 400 meters. Each point on the following scatterplot represents a person's time (in seconds) to complete the run and the weight (in pounds) of that person. The scatterplot also shows a line of best fit for the data. According to the graph, each increase of 8 pounds in a runner's weight tends to increase the runner's time by approximately how many seconds?

2.5

The price of a coat was reduced from $180 to $144. What is the percent decrease in the price of the coat?

20%

If n times kn×kn×k is divisible by 4, then n is divisible by 4 or k is divisible by 4. Which of the following is sufficient to show that the preceding statement is false?

2×6=12

If 9 x equals, 18 plus 3 y9x=18+3y9x=18+3y and y equals 3y=3y=3, what is the value of x ?

3

Which of the following expressions is equivalent to 13 x minus 2113x−2113x−21 for all numbers x ?

3(x−7)+10x

In the following scatterplot, each point represents the age, in years, and number of completed course credits for a group of 30 graduate students at a certain university. Of the students who have fewer than 40 completed course credits, what fraction are older than 24? Give your answer as a fraction.

3/4

In a game, a player is to select a coin at random from a collection of 8 red coins, 6 blue coins, 4 orange coins, and 2 white coins. What is the probability that the coin selected will be either red or orange?

3/5

In a group of 120 recruits at the police academy, 80 are college graduates and 25 are army veterans. If 15 of the recruits are both college graduates and army veterans, as shown in the preceding Venn diagram, how many are neither college graduates nor army veterans?

30

The preceding figure is composed of 5 equal-sized squares. If the perimeter of the figure is 96 inches, what is the area of the figure, in square inches?

320

The number of mold cells doubles every 12 minutes. At this moment, there are x mold cells present on a piece of bread. Which of the following represents the number of mold cells that will be present one hour from now?

32x

The preceding diagram represents a circular garden, where the straight path from point P to point Q goes through the center of the circle. The circumference of the circular garden is 120 yards. Approximately how long is the path from P to Q, in yards?

38

A map of Amy's city is drawn to scale. The actual distance from her home to her school is 9.5 miles, while on the map the same distance is 3.8 inches. If on the map the distance between the park and the train station is 1.6 inches, what is the actual distance between the park and the train station, in miles?

4.0

What is the greatest common divisor of 378 and 420 ?

42

In the preceding figure, triangle P Q R▵PQR▵PQR and triangle S T R▵STR▵STR are similar. What is the ratio of side S TSTST to side P QPQPQ ?

5/3

Heating oil is to be poured at the constant rate of 4.5 gallons per minute into a 400-gallon tank that already contains 115 gallons of heating oil. What fraction of the tank's total capacity will be full in 30 minutes?

5/8

What is the range of all integers greater than 40 and less than 99 that are multiples of 3 ?

54

On a hiking trip, the ratio of the number of children to the number of adults is 3 to 5. Which of the following could be the total number of children and adults on the hiking trip?

56

In a car lot, the ratio of the number of new cars to the number of preowned cars is 6 to 5. The total number of new and preowned cars on the lot is 66. If 4 new cars and 2 preowned cars are sold and are removed from the lot, what fraction of the remaining cars on the lot are preowned?

7/15

The following table shows Gerald's class schedule for a week. The first through the fifth time slots are 50 minutes each, and the sixth time slot is 75 minutes. On Thursday, what fraction of the time from 8:00 A.M. to 2:15 P.M. is Gerald scheduled to be in class?

7/15

Which of the following numbers is between 3 1/4 and 3 5/8?

7/2

In the preceding isosceles triangle, angle P is congruent to angle Q. If angle P has a measure of 53 degrees53°53°, what is the measure of angle R ?

74°

During a 5-day sale at a certain car dealership, 5 salespeople sold a total of 140 cars. The preceding pictograph represents the number of cars sold by each salesperson. How many cars does each full car symbol represent?

8

To find out how popular a particular television show is, a random sample of 500 viewers of the show's first episode was asked, "Are you likely to watch this show again?" Based on the responses shown in the preceding table, approximately how many viewers in the estimated television audience of 1.2 million who watched the first episode are likely to watch the show again?

816,000

Barry used a calculator to add the following five numbers. The figure shows the following addition problem: 51 plus 74, plus 93, plus 86, plus 61. End figure description. When Barry input the numbers in the calculator, he reversed the digits in one of the five numbers by mistake. The value of the sum produced by the calculator was off by 18 from the actual value of the sum. What is the number that was entered incorrectly in the calculator?

86

Doug is placing 175 books on shelves. If each shelf can hold at most 20 books, what is the least number of shelves needed to store the 175 books?

9

Calls to a certain local rescue squad are categorized as accident, fire, medical, and other. Of the 240 calls last month, one eighth of the calls were categorized as accident, one half of the calls were fire, one fourth of the calls were medical, and the remaining calls were other. The following five bar graphs are some attempts to represent last month's calls. Which of the preceding bar graphs best represents last month's calls?

Bar graph A

Information: Luke spent a total of 25 days visiting 3 people. First he visited his brother in Philadelphia, next he visited his cousin in New York City, and then he visited his friend in Boston. Problem: How many days did Luke spend visiting his brother? The preceding information is not sufficient to solve the problem. Which of the following additional pieces of information together with the preceding information is sufficient to solve the problem?

Luke spent an equal number of days visiting his friend and visiting his brother and spent half that number visiting his cousin.

The preceding figure shows rectangle P Q R SPQRSPQRS. Which of the following must be true?

PQ≅RS

Which of the preceding scatterplots shows a strong positive linear relationship between variables x and y ?

Scatterplot D

Step 1: Select a number x Step 2: Add 12 to the number Step 3: Multiply the result by 3 Step 4: Divide the result by 4 If the result of the preceding computation is 15, what is the value of x ?

x=8

Dawn deposited money into a savings account that earned no interest. After depositing the money, she made withdrawals of $25.50 from the account at regular time intervals. After 12 withdrawals, the balance of her account was $872. Which of the following equations models the balance, y, in dollars, of Dawn's savings account after x withdrawals?

y=1,178−25.50

The preceding scatterplot shows 20 data points as well as a line of best fit for the data. Which of the following is the equation of the line of best fit?

y=60−5x