CCAT Practice Test Numerical Reasoning — Questions and Answers

Question 1: 1. Allan runs 30 kilometers in three hours. Clark, on the other hand, takes 2 hours and 20 minutes to travel the same distance. How long will it take Allan and Clark to cross the finish line if they are both running a 15-kilometer race?

30 minutes
45 minutes
20 minutes (Correct answer)
15 minutes

Correct answer: 20 minutes

First, calculate each person's speed. Allan's speed is 30 km / 3 hours = 10 km/hr. Clark's time for 30 km is 2 hours and 20 minutes, which is 140 minutes or 7/3 hours, so his speed is 30 km / (7/3 hr) = 90/7 km/hr. For a 15 km race, Allan takes 15 km / 10 km/hr = 1.5 hours (90 minutes), and Clark takes 15 km / (90/7 km/hr) = 7/6 hours (70 minutes). The question asks how long it will take 'Allan and Clark to cross the finish line', which implies the difference in their finish times: 90 minutes - 70 minutes = 20 minutes.

Question 2: 2. Kath's wardrobe contains 5 shirts, 3 ties, 6 trousers, and 2 coats. How many different sets can she create each time she wears a garment from a different category?

220
140
180 (Correct answer)
250

Correct answer: 180

To find the total number of different sets Kath can create, you multiply the number of options for each independent category. She has 5 shirts, 3 ties, 6 trousers, and 2 coats. Therefore, the total number of combinations is 5 * 3 * 6 * 2. This calculation results in 180 different sets.

Question 3: 3. One cookbook cost $9.50. Derek intends to purchase three cookbooks. How much does he have to pay when he goes to the store's checkout?

$28.50 (Correct answer)
$27
$28
$26.50

Correct answer: $28.50

To find the total cost, you simply multiply the price of one cookbook by the number of cookbooks Derek intends to buy. One cookbook costs $9.50, and he wants to buy three. So, the total cost is $9.50 * 3. This calculation equals $28.50.

Question 4: 4. What number is 80% of 48?

65
60 (Correct answer)
55
75

Correct answer: 60

The question 'What number is 80% of 48?' is phrased to imply '48 is 80% of what number?'. To solve this, let the unknown number be X. The equation becomes 0.80 * X = 48. Dividing 48 by 0.80 gives X = 60. Therefore, 48 is 80% of 60.

Question 5: 5. Brian has 65 pink and green balls in a box. When he counts them, he notices that there is a 3 pink ball to 10 green ball ratio. What is the total number of green balls he has?

35
18
50 (Correct answer)
48

Correct answer: 50

The ratio of pink to green balls is 3:10, meaning for every 3 pink balls, there are 10 green balls. The total number of ratio parts is 3 + 10 = 13. Since there are 65 balls in total, each ratio part represents 65 / 13 = 5 balls. To find the number of green balls, multiply the green ratio part (10) by the value of each part: 10 * 5 = 50 green balls.

Question 6: 6. What would the next number in the following series be? 1 … 3 … 7 … 15 … 31 … ?

82
90
76
63 (Correct answer)

Correct answer: 63

This is a number series where each subsequent number is generated by multiplying the previous number by 2 and adding 1. Starting with 1: (1 * 2) + 1 = 3; (3 * 2) + 1 = 7; (7 * 2) + 1 = 15; (15 * 2) + 1 = 31. Following this pattern, the next number is (31 * 2) + 1 = 62 + 1 = 63.

Question 7: 7. Which of the following is the smallest value?

1.12
0.04 (Correct answer)
0.05
0.09

Correct answer: 0.04

To find the smallest value among decimals, first compare the whole number parts. All options have a whole number part of 0 or 1. Options B, C, and D start with 0. Comparing their tenths digits, 0.04, 0.05, and 0.09, the smallest is 0.04. Options A (1.12) is larger because its whole number part is 1.

Question 8: 8. Mike wishes to purchase strawberry ice cream. The cost of an ice ball is $1.50, but there is a promotion in which the fourth ball is free if three are purchased. How much should he pay if he buys four scoops of ice cream for himself and four for his girlfriend?

$9.50
$11
$9 (Correct answer)
$12.50

Correct answer: $9

Mike needs 8 scoops in total (4 for himself + 4 for his girlfriend). The promotion states that the fourth ball is free if three are purchased, meaning a set of 4 scoops costs the price of 3. Since he needs 8 scoops, this is equivalent to two sets of 4 scoops. Each set costs 3 * $1.50 = $4.50. Therefore, the total cost for two sets is 2 * $4.50 = $9.00.

Question 9: 9. What would the next number in the following series be? 1 … 10 … 2 … 9 … 3 … ?

8 (Correct answer)
12
4
10

Correct answer: 8

This series alternates between two distinct patterns. The numbers in the odd positions (1st, 3rd, 5th) are 1, 2, 3, which are increasing by 1. The numbers in the even positions (2nd, 4th) are 10, 9, which are decreasing by 1. The next number in the series is in the 6th position, following the decreasing pattern of the even positions. Therefore, the next number after 9 is 8.

Question 10: 10. On Thursday, 50 children purchased roller coaster tickets. How many tickets were sold during those two days if 30% more children bought a ticket to this ride on the following Friday?

115 (Correct answer)
80
120
100

Correct answer: 115

First, calculate the number of tickets sold on Friday. 30% more than Thursday's 50 tickets means 50 + (0.30 * 50) = 50 + 15 = 65 tickets. To find the total tickets sold over the two days, add Thursday's sales to Friday's sales. So, 50 (Thursday) + 65 (Friday) = 115 tickets.

Question 11: 11. Per kilo of Italian rice, the price is 5 cents. The seller offers a 20% discount for 4 kilos purchased. How much did Jocelyn pay in total if she purchased 12 kilos of rice?

$50
$58
$65
$48 (Correct answer)

Correct answer: $48

Assuming '5 cents' is a typo and should be '$5' to align with the dollar options, the price per kilo is $5. A 20% discount for 4 kilos means the price for 4 kilos is (4 * $5) * (1 - 0.20) = $20 * 0.80 = $16. Jocelyn purchased 12 kilos, which is 3 sets of 4 kilos. Therefore, the total cost is 3 * $16 = $48.

Question 12: 12. Which of the following is the greatest value?

1.010
1.8 (Correct answer)
1.2
1.003

Correct answer: 1.8

To find the greatest value among decimals, compare the whole number parts first. All options have a whole number part of 1. Next, compare the tenths digits. Option B has 1.8, option C has 1.2, and options A and D have 1.0. Since 8 is the largest tenths digit, 1.8 is the greatest value.

Question 13: 13. 20 is 20% of number _______.

100 (Correct answer)
250
50
300

Correct answer: 100

To find the number of which 20 is 20%, you can set up an equation: 20 = 0.20 * X, where X is the unknown number. To solve for X, divide 20 by 0.20. This calculation yields X = 100. So, 20 is 20% of 100.

Question 14: 14. Daniel seasoned a soup with 1/4 cup of salt. Later, he decided it needed more salt, so he added another 1/8 cup. Daniel added how many cups of salt to the soup in total?

4
3/8 (Correct answer)
2/4
3

Correct answer: 3/8

To find the total amount of salt, you need to add the two fractions: 1/4 cup + 1/8 cup. First, find a common denominator, which is 8. Convert 1/4 to 2/8. Now, add the fractions: 2/8 + 1/8 = 3/8. Daniel added a total of 3/8 cups of salt.

Question 15: 15. During a 5-hour drive, a car travels at 65 miles per hour for the first 2 hours, then drops to 40 miles per hour for the final three hours. How far did the car travel on the trip?

200
180
250 (Correct answer)
300

Correct answer: 250

To find the total distance, calculate the distance for each part of the trip and add them together. For the first 2 hours, the car traveled 65 miles/hour * 2 hours = 130 miles. For the final 3 hours, it traveled 40 miles/hour * 3 hours = 120 miles. The total distance traveled is 130 miles + 120 miles = 250 miles.

Question 16: 16. Thomas has averaged 41 home runs per season over the last 8 seasons. How many home runs did he hit in those 8 seasons?

338
280
328 (Correct answer)
200

Correct answer: 328

To find the total number of home runs, multiply the average number of home runs per season by the number of seasons. Thomas averaged 41 home runs per season for 8 seasons. So, the total home runs are 41 * 8. This calculation results in 328 home runs.

Question 17: 17. What is the following number in the series? 128 64 32 16 ?

24
36
4
8 (Correct answer)

Correct answer: 8

The series follows a simple division pattern where each subsequent number is half of the preceding number. To find the next number, divide 16 by 2, which results in 8. This consistent halving operation defines the sequence.

Question 18: 18. 3/4 cup sugar is required for a recipe that yields 18 cookies. How much sugar would it take to make two dozen cookies from the same recipe?

1 1/3 cups
1 cup (Correct answer)
2 cups
1 1/2 cups

Correct answer: 1 cup

First, determine the amount of sugar needed per cookie by dividing 3/4 cup by 18 cookies, which is 1/24 cup per cookie. Since two dozen cookies equal 24 cookies, multiply 1/24 cup by 24 to find the total sugar required. This calculation yields 1 cup of sugar for two dozen cookies.

Question 19: 19. What is the following number in the series? 13, 9, 14, 8, 15, ?

9
7 (Correct answer)
6
10

Correct answer: 7

This is an alternating series with two distinct patterns. The numbers in the odd positions (1st, 3rd, 5th) increase by 1 (13, 14, 15). The numbers in the even positions (2nd, 4th) decrease by 1 (9, 8). Following this pattern, the next number in the even sequence is 8 - 1, which is 7.

Question 20: 20. What is the following number in the series? 12, 12, 24, 8, 2, 10, ?

60 (Correct answer)
40
8
20

Correct answer: 60

The series follows a pattern of alternating operations and increasing numbers. The sequence of operations is: divide by 1, multiply by 2, divide by 3, divide by 4, and multiply by 5. Following this established pattern, the next operation is to multiply the last number (10) by 6, which yields 60.

Question 21: 21. Ezra is 15 years old, and his sister is exactly twice his age. When Ezra turns 19, how old will his sister be?

32
34 (Correct answer)
30
36

Correct answer: 34

First, calculate the sister's current age by doubling Ezra's current age: 15 years * 2 = 30 years. Then, determine the number of years that will pass until Ezra turns 19, which is 19 - 15 = 4 years. Add these 4 years to the sister's current age to find her age when Ezra is 19: 30 + 4 = 34 years old.

Question 22: 22. What is the following number in the series? 45, 15, 30, 30,10, 20, ?

40
10
20 (Correct answer)
5

Correct answer: 20

The series can be broken into repeating sets of three numbers, where the first number of each set is divided by 3 to get the second number, and the second number is then multiplied by 2 to get the third number. For example, (45 / 3 = 15, 15 * 2 = 30) and (30 / 3 = 10, 10 * 2 = 20). The next number in the series will be the start of the next triplet, which is the last number of the previous triplet, 20.

Question 23: 23. A plumber acquires 6,000 toilet sinks. Over the next four days, he plans to install 20% of all sinks. How many toilet sinks will he install on each of the four days if he divides his work evenly?

500
300 (Correct answer)
400
450

Correct answer: 300

First, calculate 20% of the total 6,000 toilet sinks to determine how many sinks will be installed: 0.20 * 6,000 = 1,200 sinks. Since this work is to be divided evenly over four days, divide the total number of sinks to be installed by 4. This results in 1,200 / 4 = 300 sinks installed per day.

Question 24: 24. A box of candy costs $0.10. For $2.50, how many boxes can you get?

18
20
14
25 (Correct answer)

Correct answer: 25

To find out how many boxes of candy can be purchased, divide the total amount of money available by the cost of a single box. In this case, divide $2.50 by $0.10. The calculation $2.50 / $0.10 equals 25, meaning 25 boxes of candy can be bought.

Question 25: 25. What would the next number in the series be? 7 | 14 | 28 | 32 | 64 | 128 | ? | ?

132 | 264 (Correct answer)
205 | 520
260 | 1120
352 | 680

Correct answer: 132 | 264

The series follows a repeating pattern of operations. It consists of two multiplications by 2, followed by an addition of 4. Specifically, the pattern is (x2, x2, +4), then (x2, x2, +4) again. Following 128, the next operation is +4, yielding 132, and then the subsequent operation is x2, resulting in 264.

CCAT Practice Test Numerical Reasoning

1.
Allan runs 30 kilometers in three hours.
Clark, on the other hand, takes 2 hours and 20 minutes to travel the same distance.
How long will it take Allan and Clark to cross the finish line if they are both running a 15-kilometer race?