CBEST Math Practice Test

Use our free CBEST Math practice test to review the most important skills and concepts that you must know for this certification exam. Our CBEST math test includes 50 multiple choice practice questions with detailed explanations. You are not allowed to use a calculator.

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Question 1

Which of the following is the BEST estimate of 3995 × 102?

A
450,000
B
400,000
C
350,000
D
300,000
E
250,000
Question 1 Explanation: 
The correct answer is (B). The number 3995 is close to 4000, and the number 102 is close to 100. The estimated product can then be written as (4000)(100) = 400,000. (Note that the actual product is 407,490.)
Question 2

Gina buys nine pens at \$1.10 per pen. Which of the following represents the change she would receive if she purchased the pens using a \$20 bill?

A
\$20 – (9)(\$1.10)
B
(\$20 – 9)(\$1.10)
C
\$20 + (9)(\$1.10)
D
(\$20 – \$1.10)(9)
E
\$20 – 9 – \$1.10
Question 2 Explanation: 
The correct answer is (A). The cost of the nine pens is (9)(\$1.10). Since Gina paid with a \$20 bill, her change will be the difference between \$20 and the cost of the nine pens. Thus, her change is \$20 – (9)(\$1.10).
Question 3

Each day, Marquis takes two pills of type A medicine, three pills of type B medicine, and one pill of type C medicine. How many pills will he take in 14 days if he forgets to take the type B pills on each of two days?

A
84
B
81
C
78
D
75
E
72
Question 3 Explanation: 
The correct answer is (C). Each day, Marquis is supposed to take a total of six pills. If he takes all of his medication for 14 days, he will take:

(14)(6) = 84 pills

If he forgets to take the three pills of type B on two occasions, this total will reduce by (3)(2) = 6 pills. If he forgets to take his type B pills, he will take:

84 – 6 = 78 pills in 14 days
Question 4

Which of these decimals is the greatest?

A
0.028
B
0.0082
C
0.82
D
0.28
E
0.8088
Question 4 Explanation: 
The correct answer is (C). To determine which of these four numbers is greatest, look for the largest digit in the tenths place (the first place to the right of the decimal). Choices (C) and (E) have an “8” in that position, while the other option have either a “2” or a “0.” From this we know that (C) and (E) are greater than the others.

Since they both have an “8” in the tenths place, we need to see which has the greatest number in the hundredths place. Choice (C) has a “2” in the hundredths place while choice (E) has a “0.” Therefore choice (C) is greater.
Question 5

Three boxes of crayons, identified as Box A, Box B, and Box C, contain the same four colors, as shown in the following chart.


 

What percent of all the crayons that are green or brown are contained in Box B?

A
48%
B
43%
C
40%
D
30%
E
26%
Question 5 Explanation: 
The correct answer is (D). The total number of crayons that are green or brown is 12 + 9 + 2 + 8 + 3 + 6 = 40. In Box B, the number of crayons that are green or brown is 9 + 3 = 12. Thus, percent of green or brown crayons in Box B is:

$\dfrac{12}{40} * 100\% = 30\%$
Question 6

Solve for x:

3(x + 1) = 5(x − 2) + 7

A
−2
B
2
C
½
D
−3
E
3
Question 6 Explanation: 
The correct answer is (E). Begin by distributing the 3 and the 5 through their respective parentheses, then combine like terms on each side of the equal sign:
3(x + 1) = 5(x − 2) + 7
3x + 3 = 5x − 10 + 7
3x + 3 = 5x − 3

Add 3 to both sides to maintain the equality:
3x + 6 = 5x

Subtract 3x from both sides and then divide the resulting equation by 2 to solve for x as follows:
6 = 2x
3 = x

Remember that any time a variable is solved for in an equation, the calculated value can be verified by substituting it into the original equation and determining whether it yields a true statement.
Question 7

Susan, Gus, Harold, and Jeff were left an inheritance by their grandfather. If Susan receives one-eighth of the inheritance, Gus receives one quarter of the inheritance, Harold receives three-eighths of the inheritance, and Jeff receives the remainder, what fraction of the inheritance does Jeff receive?

A
$\dfrac{1}{4}$
B
$\dfrac{5}{16}$
C
$\dfrac{3}{8}$
D
$\dfrac{3}{4}$
E
$\dfrac{1}{3}$
Question 7 Explanation: 
The correct answer is (A). We can add up the fractions received by Susan, Gus, and Harold as follows:

$\dfrac{1}{8} + \dfrac{1}{4} + \dfrac{3}{8}$

$= \dfrac{1}{8} + \dfrac{2}{8} + \dfrac{3}{8}$

$= \dfrac{6}{8} = \dfrac{3}{4}$

We can find the fraction Jeff receives by subtracting the sum of the other three fractions from one, since all the fractions must add up to one. Jeff will receive:

$1 - \dfrac{3}{4} = \dfrac{1}{4}$
Question 8

A flight began 6,135,000 feet west of Denver and ended 2,851,000 feet east of Denver. Which of the following is the best estimate of the distance traveled by the flight?

A
9,000,000 feet
B
3,200,000 feet
C
8,900,000 feet
D
9,100,000 feet
E
9,000 feet
Question 8 Explanation: 
The correct answer is (A). Based on the answer choices, it makes good sense to round to the nearest 100,000 feet:

6,135,000 = 6,100,000

2,851,000 = 2,900,000

Adding our estimates together we get:

6,100,000 + 2,900,000 = 9,000,000 feet
Question 9

Use the information below to answer the question that follows.


 

A business recorded the number of customers who visited the store throughout the week. How many days had a number of visitors greater than the average number of visitors for the entire week?

A
6 days
B
4 days
C
5 days
D
2 days
E
3 days
Question 9 Explanation: 
The correct answer is (E). To answer the question we need to determine the average number of visitors for the week:

$\frac{13 + 12 + 16 + 19 + 25 + 33 + 22}{7}$ $= \frac{140}{7} = 20$

How many days had more than 20 visitors?

Fri = 25
Sat = 33
Sun = 22

3 days exceeded the 20-visitor average.
Question 10

On a map, the length of the road from Town X to Town Y is measured to be 18 inches. On this map, ¼ inch represents an actual distance of 10 miles. What is the actual distance, in miles, from Town X to Town Y along this road?

A
580
B
720
C
960
D
1140
E
1296
Question 10 Explanation: 
The correct answer is (B). Here we are given a ratio: ¼ inch on the map = 10 miles, so 1 inch on the map = 40 miles. If the map-distance between the towns is 18 inches, then the actual distance must be: 18 × 40 = 720 miles
Question 11

Izzy randomly picks out and keeps a marble from a bag that contains 4 red marbles, 7 blue marbles, 9 yellow marbles, and 6 green marbles. Then Abi picks a marble at random from the same bag. If Izzy’s marble is green, what is the probability that Abi’s marble will also be green?

A
$\dfrac{3}{65}$
B
$\dfrac{5}{26}$
C
$\dfrac{3}{13}$
D
$\dfrac{1}{5}$
E
$\dfrac{6}{26}$
Question 11 Explanation: 
The correct answer is (D). Since Izzy keeps her marble, the number of green marbles and the total number of marbles both reduce by 1. So there will be 5 green marbles and 25 total marbles:

Probability = $\dfrac{5}{25} = \dfrac{1}{5}$
Question 12

If Gabriela needed to buy 9 bottles of soda for a party in which 12 people attended, how many bottles of soda will she need to buy for a party in which 8 people are attending?

A
6
B
7
C
8
D
10
E
12
Question 12 Explanation: 
The correct answer is (A). We can set up a proportion to solve:

$\dfrac{9 \text{ bottles}}{12 \text{ people}} = \dfrac{x \text{ bottles}}{\text 8 \text{ people}}$

Cross-multiply to solve a proportion:

(9)(8) = (12)(x)
72 = 12x
6 = x
Question 13

Use the information below to answer the question that follows.

 
  • Four employees each put a business card in a bowl.

  • After mixing, each employee removes one card from the bowl at random.

  • The first employee to remove a card from the bowl does not get his own card.

 

Based on the information above, which of the following conclusions can be made with certainty:

A
It is possible that two employees drew their own cards.
B
No one drew his own card.
C
Exactly one must have drawn his own card.
D
It is possible that three employees drew their own cards.
E
If the first employee drew the third employee's card, then the third employee must have drawn the first employee's card.
Question 13 Explanation: 
The correct answer is (A). Begin by labeling the employees A, B, C, D. Let A be the employee who draws the first card and let B be the employee whose card is drawn by A:



Answer A is certainly possible (employees C and D could draw their own cards).

Answer B could occur, but it is not guaranteed.

Answer C could occur, but it is not guaranteed.

Answer D is impossible.

Answer E could occur, but it is not guaranteed.
Question 14

Use the information below to answer the question that follows.

 
  • Heidi owns only three pairs of footwear: (1) a pair of black boots, (2) a pair of brown boots, and (3) a pair of running shoes.

  • If snow is forecast on a day Heidi works, she always wears boots.

  • Heidi never wears her brown boots if she will be working in the paint department that day.

 

If Heidi is not wearing her black boots, but is working in the paint department today, which of the following conclusions can be made?

A
She is wearing her brown boots.
B
Snow is not forecast for today.
C
She will wear her brown boots tomorrow.
D
Snow is forecast for tomorrow.
E
She no longer owns black boots.
Question 14 Explanation: 
The correct answer is (B).

Since Heidi is working in the paint department today, she definitely will not be wearing her brown boots.

But, we are told that she is not wearing her black boots.

Since she only owns one pair of brown boots and one pair of black boots, she must not be wearing boots.

If she is not wearing boots, then snow must not have been forecast for today, since she always wears boots when snow is forecast.
Question 15

Use the information that is given below to answer the question that follows.

  • Eric is older than Ross

  • Erin is older than Rosanna

  • Rosanna is younger than Eric

 

Based on the information above, which of the following is a possible arrangement listed from oldest to youngest?

A
Erin, Rosanna, Eric, Ross
B
Erin, Ross, Rosanna, Eric
C
Ross, Erin, Eric, Rosanna
D
Eric, Ross, Erin, Rosanna
E
Eric, Rosanna, Erin, Ross
Question 15 Explanation: 
The correct answer is (D).

We are given 3 facts:
(i) Eric is older than Ross
(ii) Erin is older than Rosanna
(iii) Rosanna is younger than Eric

Use the process of elimination to determine the correct answer.

A. Erin, Rosanna, Eric, Ross: WRONG, violates (iii)
B. Erin, Ross, Rosanna, Eric: WRONG, violates (iii)
C. Ross, Erin, Eric, Rosanna: WRONG, violates (i)
D. Eric, Ross, Erin, Rosanna: CORRECT
E. Eric, Rosanna, Erin, Ross: WRONG, violates (ii)
Question 16

Logan correctly answered 70% of the spelling bee questions. If there were 220 questions total, how many did he answer incorrectly?

A
66
B
154
C
82
D
129
E
60
Question 16 Explanation: 
The correct answer is (A). If he got 70% correct, then he must have gotten 30% incorrect. We can translate 30% of of 220 to:

$\dfrac{30}{100} \ast 220 = 66$
Question 17

The measurements of Sara’s bedroom window are 2 yards 6 inches wide by 1.5 yards high. What are the dimensions of her bedroom window in inches?

A
18 × 30
B
36 × 18
C
52 × 78
D
78 × 54
E
82 × 54
Question 17 Explanation: 
The correct answer is (D). To convert yards to inches, multiply the number of yards by 36 (there are 36 inches in a yard). So 2 yards 6 inches equals:

(2)(36) + 6 = 78

For the second dimension:

(1.5)(36) = 54
Question 18

The sum of 7 numbers is greater than 140 and less than 210. Which of the following could be the average (arithmetic mean) of the numbers?

A
20
B
30
C
34
D
160
E
26
Question 18 Explanation: 
The correct answer is (E). The formula for the average of a set of numbers is the sum of the numbers divided by the number of terms:

Avg = 140 ÷ 7
Avg = 20

Avg = 210 ÷ 7
Avg = 30

Therefore, the sum must be between 20 and 30.
Question 19
A teacher creates a final exam with 75 questions and expects it to take 90 minutes to complete. The exam consists of 19 short-answer questions with the remainder of the questions being multiple choice. How much time does the teacher expect his students to spend on each of the multiple choice questions?
 

Which single piece of information is necessary to solve the problem above?

A
the number of multiple choice questions
B
the time the teacher expects each short-answer question to take
C
the percentage of questions that are multiple choice
D
the number of students taking the exam
E
the average time the teacher expects each question on the exam to take
Question 19 Explanation: 
The correct answer is (B). Since there are 75 questions on the exam and 19 of the questions are short-answer, we can determine that there are 56 multiple choice questions.

Let a = average time required for each multiple choice question.
Let b = average time required for each short-answer question.

Since the exam is expected to take a total of 90 minutes:

a(56) + b(19) = 90

If we are given b, the time required for each short-answer question, we can use the above equation to solve for a, the time required for each multiple choice question.
Question 20
A truck driver leaves the depot at 10:30am and arrives at the destination after averaging 60 miles per hour for the 125 mile trip. He waits at the destination while the truck is unloaded, then drives directly back to the depot following the same route. If the truck averages 50 miles per hour for the return trip, how long did the driver wait at the destination while his truck was being unloaded?
 

Which single piece of additional information is required to solve this problem?

A
The distance from the depot to the destination
B
The time it took to drive from depot to destination
C
The maximum speed the truck travelled on its return trip
D
The time when the truck returned to the depot
E
The time required for the truck to travel from destination to depot
Question 20 Explanation: 
The correct answer is (D). The truck travels 60 mph for 125 miles on the outbound trip:

$\dfrac{60 \text{ miles}}{1 \text{ hour}} = \dfrac{125 \text{ miles}}{x \text{ hours}}$

$\rightarrow x = 2\frac{1}{12} \text{ hours}$ $(2 \text{ hours } 5 \text{ minutes})$

The truck travels 50 mph for 125 miles on the return trip:

$\dfrac{50 \text{ miles}}{1 \text{ hour}} = \dfrac{125 \text{ miles}}{y \text{ hours}}$

$\rightarrow y = 2\frac{1}{2} \text{ hours}$ $(2 \text{ hours } 30 \text{ minutes})$

Total driving time = 2 hours 30 minutes + 2 hours 5 minutes = 4 hours 35 minutes

If we were told when the driver returned to the depot, we could use this information along with the time that he left the depot (10:30 am) to determine the total amount of time he was gone.

For example, let's assume we were told he returned to the depot at 3:30 pm. That would mean he was gone a total of 5 hours.

Of those 5 hours, 4 hours and 35 minutes were spent driving.

That means it must have taken 25 minutes (5 hours − 4 hours 35 minutes) to unload the truck.
Question 21
A carnival game offers 4 different stuffed animal prizes. There are two different animals, an ape and a tiger, and each is offered in a small and large size. There are 48 total prizes in the cabinet. 16 are large and 18 of the small prizes are apes.
 

Which of the following can be determined?

A
The total number of tigers
B
the total number of apes
C
the number of small tigers
D
the number of large tigers
E
the number of large apes
Question 21 Explanation: 
The correct answer is (C). To help us visualize the data, let's construct a table:



If there are 48 total prizes and 16 are large, then 32 (48 − 16) must be small.

If there are 32 small prizes and 18 of the small prizes are apes, then 14 of the small prizes must be tigers.
Question 22

Liam earns \$8.00 per hour and worked 40 hours. Charlie earns \$20.00 per hour. How many hours would Charlie need to work to equal Liam’s earnings over 40 hours?

A
12
B
16
C
18
D
20
E
100
Question 22 Explanation: 
The correct answer is (B). Begin by calculating Liam’s total earnings after 40 hours:

40 hours × \$8 per hour = \$320

Next, divide this total by Charlie's hourly rate to find the number of hours Charlie would need to work:

\$320 ÷ \$20 per hour = 16 hours
Question 23

Elsa brought home $1\frac{2}{3}$ pizzas that were left over from her office party. The next day her husband ate five-twelfths of a pizza and her kids ate one-half of a pizza. How much pizza was left?

A
$\dfrac{11}{12}$
B
$\dfrac{5}{6}$
C
$\dfrac{3}{4}$
D
$\dfrac{2}{3}$
E
$\dfrac{7}{12}$
Question 23 Explanation: 
The correct answer is (C). First convert the mixed fraction to an improper fraction. To do this, multiply the whole number with the denominator, add this to the numerator, and place the resulting value above the original denominator.

$1\dfrac{2}{3} = \dfrac{5}{3}$

Next subtract the amount of pizza that is eaten from this number:

$\dfrac{5}{3} - \dfrac{5}{12} - \dfrac{1}{2}$

To do this subtraction you need to find a common denominator. The lowest common denominator for 3, 12, and 2 is 12, since each of the numbers can be divided evenly into 12. Rewrite the fractions with 12 as the denominator. Then subtract and simplify:

$= \dfrac{20}{12} - \dfrac{5}{12} - \dfrac{6}{12}$

$= \dfrac{9}{12} = \dfrac{3}{4}$
Question 24

Which of the following would be the best unit of measurement to specify the width of a fingernail?

A
Centimeter
B
Foot
C
Kilogram
D
Inch
E
Millimeter
Question 24 Explanation: 
The correct answer is (E). When determining the best unit of measurement there is no set rule to follow, you are just looking for something that will result in a 'reasonable' number. Something in the range of 5 to 100 units would normally be a good target. You don't want it to measure less than 1 unit and you don't want it to measure in the thousands of units either. The width of a fingernail is definitely less than an inch and maybe about 1 centimeter, so these are not good options. A millimeter is about the thickness of a credit card, and would therefore be the best option.
Question 25

The shoes Jake wants to buy normally sell for $70. There is a 25% off sale on these shoes. To figure out the sale price of the shoes Jake uses the following expression:

$70 − (0.25 × 70)$

Which of the following methods could Jake also use to determine the sale price?

A
$\frac{25}{200}$ × 70
B
70 ÷ 0.25
C
(1 − 0.25) × 70
D
70 − 25
E
70 ÷ (1 + 0.25)
Question 25 Explanation: 
The correct answer is (C). Let's start by looking the expression that is given in the question:

70 − (0.25 × 70)

Here we are taking the original amount and subtracting away 25% of the original amount.

If we take away 25% of the original amount, we will be left with 75% of the original amount.

0.75 × 70 would give the same result.

We can rewrite this as:

(1 − 0.25) × 70
Question 26

Jon likes to tip 20% at restaurants. To figure out the tip he should leave for a \$35 meal, he uses the following expression:

$0.20 × 35$

Which of the following expressions could Jon have also used?

A
$\dfrac{35}{10} × 2$
B
$35 ÷ (1 − 0.20) − 35$
C
$\dfrac{35 × 100}{20}$
D
$\dfrac{35 − 20}{2}$
E
$35 ÷ 4$
Question 26 Explanation: 
The correct answer is (A). Dividing any number by 10 will give you the value of 10% of the original number.

So, $\frac{35}{10}$ gives us 3.50 which is 10% of 35.

To find 20% of 35, we simply double the value we found for 10%.

Thus, $\frac{35}{10}$ × 2 = 7.00 provides the correct result.
Question 27

If a bus travels 360 kilometers in 5 hours, how many kilometers will it travel in 9 hours when driving at the same speed?

A
72
B
288
C
620
D
648
E
660
Question 27 Explanation: 
The correct answer is (D). First calculate the distance the bus travels in 1 hour:

360 km ÷ 5 hours = 72 km per hour

Then multiply this number by the total number of hours traveled:

9 hours × 72 km per hour = 648 km

Notice that the final calculation yields the correct units; this helps to confirm that the calculation is correct.
Question 28

A vase contains 60 marbles, all of which are red or orange. If the ratio of red marbles to orange ones is 1:5, what is the total number of red marbles in the vase?

A
8
B
10
C
12
D
15
E
50
Question 28 Explanation: 
The correct answer is (B). We know that the ratio is 1:5. This means that for every six marbles one of them is red and five are orange. So $\frac{1}{6}$ of the marbles are red:

$\frac{1}{6}$ × 60 = 10
Question 29

Cameron purchased a new hat that was on sale for \$5.40. The original price was \$9.00. What percentage discount was the sale price?

A
5.4%
B
54.0%
C
40.0%
D
60.0%
E
45.0%
Question 29 Explanation: 
The correct answer is (C). The percentage discount is the reduction in price divided by the original price. The difference between original price and sale price is:

$\$9.00 − \$5.40 = \$3.60$

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

$\$3.60 ÷ \$9.00 = \dfrac{3.60}{9.00}$

$= \dfrac{360}{900}$ $= \dfrac{40}{100}$ $= 40 \%$
Question 30

Use the menu below to answer the question that follows.



Neil ordered the following for his family: two cheeseburgers, one hamburger, two large fries, one small fries, and three small sodas. If the total calories for the order is 3370, what is the missing calorie information on the menu?

A
1000
B
400
C
450
D
480
E
900
Question 30 Explanation: 
The correct answer is (C). Let's begin by totaling the calories for the items we are able to:

Two cheeseburgers = 2 × 530 = 1,060 calories

One hamburger = 430 calories

One small fries = 230 calories

Three small sodas = 3 × 250 = 750 calories

If we subtract each of the known calories from the total calories for the order we will know how many calories came from two large fries:

3,370 − 1,060 − 430 − 230 − 750 = 900

900 calories came from two orders of large fries. Each order of fries must be 450 calories.
Question 31

Use the table below to answer the question that follows.



If a truck travels from Boston to Albany to Cincinnati to Destin, how many miles will the truck travel in total?

A
1620 miles
B
2440 miles
C
1390 miles
D
2230 miles
E
1780 miles
Question 31 Explanation: 
The correct answer is (A). Let's determine the distance traveled for each of the three legs of the trip using the provided table:

Boston to Albany = 170 miles

Albany to Cincinnati = 720 miles

Cincinnati to Destin = 730 miles

The total distance = 170 + 720 + 730 = 1620 miles
Question 32

Use the table below to answer the question that follows.



What percentage of the seven vehicles shown in the table were pickups?

A
46%
B
5%
C
60%
D
16%
E
54%
Question 32 Explanation: 
The correct answer is (E). To find the percentage of vehicles that were pickups, we need to first divide the total number of pickups sold by the total number of all seven vehicles sold:

$\frac{(750,000 + 500,000 + 450,000)}{3,160,000}$ $= \frac{1,700,000}{3,160,000} =$ 0.538

To convert to a percentage, we need to multiply by 100.

0.538 × 100 = 53.8%

54% is the closest answer.
Question 33

A restaurant cooked $3\frac{2}{5}$ pounds of rice before opening, and another $1\frac{4}{7}$ pounds later in the afternoon. What was the total amount that they cooked?

A
$\dfrac{145}{34} \text { pounds}$
B
$\dfrac{174}{35} \text { pounds}$
C
$\dfrac{168}{35} \text { pounds}$
D
$\dfrac{159}{34} \text { pounds}$
E
$\dfrac{119}{35} \text { pounds}$
Question 33 Explanation: 
The correct answer is (B). To add mixed number fractions, first convert them to improper fractions, then find a common denominator and add the numerators, placing them over the common denominator. Reduce the final fraction if necessary.

To convert a mixed fraction to an improper fraction, multiply the whole number with the denominator, add this to the numerator, and place the resulting value above the original denominator.

$3\dfrac{2}{5} = \dfrac{17}{5}$

$1\dfrac{4}{7} = \dfrac{11}{7}$

Now find the lowest common denominator between 5 and 7. Since they are both prime numbers, their lowest common denominator is their product, 35. We can rewrite both fractions:

$\dfrac{17}{5} = \dfrac{119}{35}$

$\dfrac{11}{7} = \dfrac{55}{35}$

Now that the denominators are the same, we can add the numerators:

$\dfrac{119}{35} + \dfrac{55}{35} = \dfrac{119 + 55}{35}$ $= \dfrac{174}{35}$
Question 34

The weight, in pounds, of a truck with its load is given by the equation below where $w$ represents the total weight of the truck and its load, and $q$ represents the quantity of castings it is hauling. In the equation, what does the number 35,000 represent?

$w = 500q + 35{,}000$

A
The combined weight of the truck and a full load of castings
B
The weight of the truck with no load
C
The weight of each casting
D
The maximum weight of castings that the truck can haul
E
The total weight of the castings
Question 34 Explanation: 
The correct answer is (B). We are told that $w$ represents the total weight of the truck and its load, and $q$ represents the quantity of castings it is hauling.

If a truck is hauling no castings, $q = 0$.

When $q = 0$, $w = 500(0) + 35,000$ $ = 35,000$.

In other words, the weight of the truck by itself (i.e. hauling no castings) is 35,000 lbs.
Question 35

Kara buys groceries once a week. In the past four visits she has spent \$116.25, \$130.07, \$128.82, and \$109.53. If the individual amounts spent are rounded to the nearest \$10, what is the estimate of Kara's total spending for all four visits?

A
$480
B
$484.70
C
$490
D
$484.67
E
$460
Question 35 Explanation: 
The correct answer is (C). Begin by rounding each of the four amounts to the nearest \$10:

\$116.25 → Closer to \$110 or \$120? → \$120
\$130.07 → Closer to \$130 or \$140? → \$130
\$128.82 → Closer to \$120 or \$130? → \$130
\$109.53 → Closer to \$100 or \$110? → \$110

To find total spending, we sum up our four estimates:

\$120 + \$130 + \$130 + \$110 = \$490
Question 36

Aaron determines that 23 gallons of gas are used by his lawn care business in a typical week. If the gas usage is rounded to the nearest 5 gallons, how many gallons would he expect to use in 12 weeks?

A
300 gallons
B
320 gallons
C
276 gallons
D
240 gallons
E
287 gallons
Question 36 Explanation: 
The correct answer is (A). First, we need to round 23 gallons to the nearest 5 gallons:

23 → Closer to 20 or 25? → 25

Next, we need to multiply 25 by 12:

$\require{cancel} \dfrac{25 \text{ gallons}}{\cancel{\text{week}}} × 12 \require{cancel} \cancel{\text{weeks}}$ $= 300 \text{ gallons}$
Question 37

Use the information below to answer the question that follows.


 

What is the average number of hurricanes affecting the US per decade?

A
11
B
13
C
14
D
15
E
18
Question 37 Explanation: 
The correct answer is (D). To find the average, add up all the numbers, then divide by how many numbers there are:

$\text{Avg} =$ $\frac{20 + 14 + 11 + 18 + 14 + 19 + 9}{7}$

$\text{Avg} = \frac{105}{7} = 15$
Question 38

Use the information below to answer the question that follows.


 

This pie chart shows Al’s monthly expenses. If Al spent a total of $1,550 in one month, how much did he spend on clothes in that month?

A
$77.50
B
$232.50
C
$775
D
$7.75
E
$1,627.50
Question 38 Explanation: 
The correct answer is (A). From the pie chart it can be seen that clothing represents 5% of his monthly expenses. Recall that 5% is equivalent to $\frac{5}{100}$ or 0.05:

0.05 × \$1,550 = \$77.50
Question 39

Tina has six 5-gallon jugs of iced tea that she needs to distribute into 2-gallon jugs. Tina uses the following expression to determine how many 2-gallon jugs will be required.

(6 × 5) ÷ 2

Which of the following expressions could Tina have also used?

A
5 ÷ 2
B
(6 × 2) ÷ 5
C
$\frac{2}{5}$ × 6
D
(6 ÷ 5) × 2
E
$\frac{5}{2}$ × 6
Question 39 Explanation: 
The correct answer is (E). Consider Tina's first expression, (6 × 5) ÷ 2. First, she determines the total amount of iced tea:

$6 \require{cancel} \cancel{\text{jugs}}$ × $\require{cancel} \dfrac{5 \text{ jugs}}{\cancel{\text{jug}}}$ $= 30 \text{ jugs}$

Next, she determines how many 2-gallon jugs would be required to hold the same amount:

$30 \require{cancel} \cancel{\text{gallons}} × \require{cancel} \dfrac{1 \text{ jug}}{ 2\cancel{\text{gallons}}}$ $= 15 \text{ jugs}$

An alternate approach would use the expression,

$\dfrac{5}{2} × 6$

First, she determines how many 2-gallon jugs are contained within each 5-gallon jug:

5 $\require{cancel} \cancel{\text{gallons}}$ × $\require{cancel} \dfrac{1 \text{ jug}}{ 2\cancel{\text{gallons}}}$ $ = \dfrac{5}{2} \text{ jugs}$

$= 2\dfrac{1}{2} \text{ jugs}$

So each 5-gallon jug will fill $2\frac{1}{2}$ 2-gallon jugs. Next, she determines how many 2-gallon jugs are required to hold 6 5-gallon jugs:

$\require{cancel} \dfrac{\frac{5}{2} \text{ 2-g jugs}}{\cancel{\text{5-g jugs}}}$ × $6~ \require{cancel} \cancel{\text{5-g jugs}}$

$= 15 \text{ 2-gallon jugs}$
Question 40

Use the diagram below to answer the question that follows.


 

What is the distance traveled when completing one lap around the track?

A
2900 meters
B
4700 meters
C
2200 meters
D
2000 meters
E
3400 meters
Question 40 Explanation: 
The correct answer is (E). Each grid space travelled is 100m. The distance travelled in one lap is simply the sum of the grid spaces required to make one lap of the circuit.


As you count around the race track you should end up at 34. Giving a total distance of 34 × 100m = 3400m.
Question 41

Use the information below to answer the question that follows.


 

This chart shows the net points scored in five different games. What is the difference between the highest net points scored and the average (mean) net points scored for the 5 games?

A
−3
B
4
C
−1
D
2
E
1
Question 41 Explanation: 
The correct answer is (B). The highest net points scored occured in Game 4 and was +3 points.

To find the average (mean) points scored for the 5 games we need to find the sum of the points scored and divide by 5 (the number of values being summed):

$\frac{(−4) + (0) +(−2) + (3) + (−2)}{5} $ $ =\frac{−5}{5} = −1$

The difference between the highest score and the average score =

(3) − (−1) = 3 + 1 = 4
Question 42

What is the ones digit in the divisor of the problem below?



A
7
B
3
C
6
D
9
E
5
Question 42 Explanation: 
The correct answer is (A).

Dividend = Divisor ∗ Quotient + Remainder

150 = $x$ ∗ 8 + 14

We can either guess and check using each answer or use algebra to solve for $x$:
150 = $x$ ∗ 8 + 14
150 − 14 = $x$ ∗ 8
136 = $x$ ∗ 8
$\frac{136}{8} = x$
$\, x$ = 17

The missing ones digit in the divisor = 7
Question 43

Alexis has two boards. The first board is $8\frac{11}{16}$ feet long and the second is $11\frac{1}{4}$ feet long. How much longer is the second board than the first?

A
$2 \frac{11}{16}$ feet
B
$3 \frac{7}{8}$ feet
C
$3 \frac{5}{16}$ feet
D
$2 \frac{9}{16}$ feet
E
$2 \frac{3}{4}$ feet
Question 43 Explanation: 
The correct answer is (D). To find the difference in length between the two boards, we need to subtract the shorter length ($8\frac{11}{16}$) from the longer length ($11\frac{1}{4}$).

When dealing with subtracting fractions you must first find a common denominator (the least common multiple of the two denominators). In this case we have denominators of 16 and 4, and the least common multiple is 16.

Since $8\frac{11}{16}$ already has a denominator of 16, no change is required. On the other hand, we need to change $11\frac{1}{4}$ to $11\frac{4}{16}$.

At this point we need to solve: $11\frac{4}{16} − 8\frac{11}{16}$.

The easiest way will be to “count up” from the lower number. To get from $8\frac{11}{16}$ to 9, we need to add $\frac{5}{16}$; to get from 9 to 11 we need to add 2; and to get from 11 to $11\frac{4}{16}$ we need to add $\frac{4}{16}$.



$\frac{5}{16} + 2 + \frac{4}{16} = 2\frac{9}{16}$

The difference in length between the two boards is $2 \frac{9}{16}$ feet.
Question 44

Use the chart below to answer the question that follows.


 

The chart above shows X and Y values from a linear function. Based on the information provided, what is the missing X value?

A
−10.0
B
−9.5
C
−11.5
D
−10.5
E
−11.0
Question 44 Explanation: 
The correct answer is (D). In a linear function the change in X and Y values will remain constant. We can see that the Y values change by +1.5 (increase by 1.5) each time the X values change by −2.5 (decrease by 2.5).

To determine the missing X value, we need to take −8.0 and subtract (decrease by) 2.5:

−8.0 − 2.5 = −10.5

The missing X value is −10.5.
Question 45

Which of the following lists the mixed numbers correctly, creating a true statement?

A
$5\frac{1}{5} \gt 4\frac{4}{5} \gt 4\frac{2}{5}$
B
$3\frac{5}{7} \lt 3\frac{2}{7} \lt 4\frac{3}{7}$
C
$1\frac{2}{3} \gt 2\frac{1}{3} \gt 1\frac{1}{3}$
D
$9\frac{1}{9} \lt 8\frac{8}{9} \lt 8\frac{5}{9}$
E
$2\frac{4}{7} \lt 3\frac{1}{7} \lt 2\frac{6}{7}$
Question 45 Explanation: 
The correct answer is (A). First it is important to remember the proper orientation of the > (greater than) and < (less than) signs. As silly as it sounds, it might be easiest to picture the symbol as an alligator’s mouth which is always going to “eat” the larger number. In other words, 3 > 2 and 3 < 5. Notice that in both cases the open end of the “mouth” is faced towards the number of greater value.

Next, we need to understand that mixed numbers consist of the number of “wholes” plus a fractional portion. $3\frac{5}{8}$ means “3 wholes plus five-eighths.” You could picture it as 3 whole pizzas plus 5 out of 8 slices of a 4th pizza.

$5\frac{1}{8} \gt 4\frac{7}{8}$. “5 wholes plus 1 slice out of 8” is always going to be more than “4 wholes plus any fraction (in this case 7 slices out of 8).”

Putting all of this together, the only true statement is (A). “5 wholes plus 1 slice out of 5” is greater than “4 wholes plus 4 slices out of 5” which is greater than “4 wholes plus 2 slices out of 5.”
Question 46

Which of the following correctly lists three fractions that are each greater than $\frac{1}{2}$?

A
$\dfrac{4}{9}, \dfrac{6}{8}, \dfrac{7}{11}$
B
$\dfrac{6}{13}, \dfrac{7}{12}, \dfrac{7}{13}$
C
$\dfrac{2}{3}, \dfrac{3}{8}, \dfrac{3}{6}$
D
$\dfrac{5}{8}, \dfrac{4}{6}, \dfrac{6}{11}$
E
$\dfrac{5}{6}, \dfrac{6}{9}, \dfrac{3}{7}$
Question 46 Explanation: 
The correct answer is (D). To determine whether a given fraction is greater than $\frac{1}{2}$, find half the denominator (bottom number); or take the denominator and divide by 2.

If the numerator (top number) is greater than half the denominator then the fraction itself is greater than $\frac{1}{2}$.

In this case: $\frac{5}{8}$ is greater than $\frac{1}{2}$ because 5 is greater than 4 (half of the denominator, 8).

$\frac{4}{6}$is greater than $\frac{1}{2}$ because 4 is greater than 3 (half of the denominator, 6).

$\frac{6}{11}$is greater than $\frac{1}{2}$ because 6 is greater than 5.5 (half of the denominator, 11).
Question 47

Yosemite Mule Tours offers three tours of equal length each day. The “45 Minute Break” between tours is used to unload the previous group and prepare the next group of mules. Based on this information and the schedule below, at what time does “Tour Two” end?



A
1:40 PM
B
1:55 PM
C
3:00 PM
D
1:05 PM
E
2:10 PM
Question 47 Explanation: 
The correct answer is (B). Perhaps the simplest way to approach this question is to recognize that “Tour Two” ends 45 minutes before the beginning of “Tour Three”.

“Tour Three” begins at 2:40 PM. “Tour Two” ends 45 minutes earlier, or 1:55 PM.
Question 48

In what year was the difference in the share of steel production between China and North American approximately 25%?



A
2006
B
1998
C
2010
D
2014
E
2002
Question 48 Explanation: 
The correct answer is (A). In 2008 we see that the Chinese share was approximately 37% (somewhere between 35% and 40%) and the North American share was just below 10%. It is at this point that the difference between China and North America is closest to 25%.
Question 49

According to the chart below, in which four-year period listed in the answer choices did United States health care spending as a % of GDP increase the most?



A
1972–1976
B
2002–2006
C
1986–1990
D
1982–1986
E
1996–2000
Question 49 Explanation: 
The correct answer is (C). From 1986 to 1990 U.S. health care spending as a % of GDP changed from 10.5% to 12.5%, a 2% change. In each of the other four-year periods listed, it changed 1% or less.
Question 50

The chart below shows the distance between four different cities. Use this chart to help you answer the question below.



Wes is driving from Cincinnati to Destin. If he has averaged 80 miles per hour so far and has been driving for 2.5 hours, approximately how far is he from Destin?

A
640 miles
B
580 miles
C
610 miles
D
530 miles
E
490 miles
Question 50 Explanation: 
The correct answer is (D). Begin by using the chart to determine the total distance from Cincinnati to Destin. It does not matter whether we look in the third column and forth row or the fourth column and third row; in both cases the distance is 730 miles between the cities.

Next, determine the distance traveled in 2.5 hours at an average of 80 mph. If we are traveling 80 miles in one hour, in 2.5 hours we will travel 80 ∗ 2.5 or 80 + 80 + 40 (“all of 80 plus all of 80 plus half of 80”) which gives us 200 miles.

Wes has traveled 200 miles of the 730 miles. This means he has 530 miles (730 − 200) remaining in his trip to Destin.
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