CCAT Math Questions: Free Practice, Examples & Prep Tips

## What Math Questions to Expect on the CCAT?

There are 18 numerical reasoning questions on the CCAT test (out of 50 overall), divided into several different types. These include basic math and calculations, word problems, number series, and tables and graphs questions.

Since you have only 15 minutes to complete the CCAT, you'll need to solve some of these numerical questions in as little as 18 seconds per question. Adding this to the fact that many candidates struggle with math makes solving these questions even more difficult.

To help you get a feel for CCAT's math questions, we'll go over each type and provide sample questions with full explanations and tips (taken from our CCAT prep course).

## Basic Math and Calculations

There are 2-3 basic arithmetic questions on the CCAT, and they usually come in two forms:

1. "Which of the following is the largest/smallest value" questions
2. Direct calculations of percentages, averages, ratios, and more

### Practice Questions

Question #1

Which of the following is the smallest value?

A. 0.0015

B. 0.0105

C. 0.1005

D. 0.0051

E. 0.00151

The correct answer is (A) – 0.0015

The Decimal System enables writing numbers as large or as small as one wishes, using the decimal point.

Digits can be placed to the left or right of a decimal point, presenting values greater than one or less than one. To the left of the decimal point is a whole number (e.g. 45 in 45.589).

Moving to the left of the decimal point, every number gets 10 times bigger: ...Hundreds <- Tens <- Ones. To the right of the decimal point, the first digit means tenths (1/10). Moving to the right of the decimal point, every number gets 10 times smaller (one-tenth as big): Tenths -> Hundredths -> Thousandths…

As can be seen, all answer-options have 0 ones. Therefore, move to the right of the decimal point and compare their tenth values.

You can immediately dismiss answer-option (C) since it has 1 tenth while all other answer-options have 0 tenths. You are left with answer-options (A), (B), (D) and (E).

Comparing their hundredths values, you can immediately dismiss answer-option (B) since it has 1 hundredth while all other answer-options have 0 hundredths. You are left with answer-options (A), (D) and (E).

Therefore, move to the thousandths place and compare them:
Answer-option (A) – 0.0015 – 1 thousandths
Answer-option (D) – 0.0051 – 5 thousandths
Answer-option (E) – 0.00151 – 1 thousandths

As can be seen, you can dismiss answer-option (D) since it has the 5 thousandths, while (A) and (E) has smaller thousandths value of 1.

You are left with answer-options (A) and (E). Both have the same ten thousandths value of 5. However, while answer-option (A) ends there, answer-option (E) also have a hundred thousandths value of 1, making it larger than (A):
Answer-option (A) – 0.0015 – 0 hundred thousandths
Answer-option (E) – 0.00151 – 1 hundred thousandths

Therefore, answer-option (A) presents the smallest value.

Notice! Moving further to the right, the absence of digits is equivalent to writing 0. For example:
Answer-option (A) - 0.0015 can also be written as 0.00150, making it easier to compare with answer-option (E):

Notice! In case all or some of the answer-options have the same tenths/hundredths/thousandths values etc. move on to the next place to the right of the decimal point and compare the values, until you find a difference.

Question #2

53 is 25% of what number?

A. 13.25

B. 92.75

C. 159

D. 141.5

E. 212

The correct answer is (E) - 212.

100% = 100*53/25 = 4*53 = 4*50 + 4*3 = 200 + 12 = 212

You can also find the answer by using a basic multiplication table method. If 53 is 25%, that means that the whole number is 4 times 53. If we split the 53*4 to 50*4 + 3*4, we know that the number we are looking for has to end with 2 (3*4=12). The only option that ends with 2 is 212.

## Word Problems

There are 13-14 math word problems on the CCAT, which are divided into the following types:

• Direct calculation problems using the four operations
• Percentages problems
• Averages problems
• Ratios problems
• Distance, rate, and time problems

### Practice Questions

Question #1

Research conducted on a sample of 2500 flu patients has found that 28% felt better after up to 2 days following the initial medication, 22% felt better after up to 4 days, and the rest did not feel any improvement. How many did not benefit from the treatment?

A. 50

B. 72

C. 1250

D. 500

E. 1200

The correct answer is (C) - 1250.

It is evident when reading the question carefully that 50% of flu patients felt an improvement when taking the medication (28 + 22 = 50). This means that half of the patients did not feel any improvement. Note that the question refers to the number of patients that did not feel any improvement rather than the percentage - 50% of 2500 = 1250.

Question #2

The Formula One race car broke the world record, driving 200 miles in 10 minutes. How fast did it drive at mph?

A. 200

B. 210

C. 1200

D. 1920

E. 2000

The correct answer is (C) - 1200.

If the car traveled 200 miles in 10 minutes, in one hour it will drive 6 times that distance (10 minutes is 1/6 of an hour).

Therefore, the distance traveled in one hour will be:

6*200=1200 miles

This value will therefore be the speed of the car: 1,200 mph.

Question #3

Three photo albums have an average of 23 photos per album: 12 in one, 24 in the second, and 33 in the third. How many photos will each album have on average if we add another 6 to the second album?

A. 25

B. 21

C. 22

D. 23

E. 24

The correct answer is (A) - 25.

There are two ways to solve this problem:

1. Elimination
Take a look at the answer options. Answers (B), (C), and (D) are either lower than or identical to the old average. Since the number of photos in the second album increased (24+6=30), the average will increase as well. Answer (A) is the only one which is higher than 23, and is, therefore, the correct answer.

2. Average calculation
Calculate the sum of the new set of numbers, and then divide by the number of items. In this particular case, however, you can use a much shorter calculation: the difference between the new number of photos and old number of photos is 6.

Divide this by the number of items to learn how much the average will increase:
(Difference between sums of items) / (number of items) = 6/3 = 2
The average will increase by 2. Thus, the new average will be: 23+2 = 25.

## Number Series

There are 1-2 number series questions on the CCAT, one of them would be with letters and the other with numbers.

### Practice Questions

Question #1

13 | 21 | 34 | 55 | 89 | ?

A. 105

B. 107

C. 149

D. 144

E. 123

The correct answer is (D) - 144.

The series in this question follows the Fibonacci sequence principle- each number equals the sum of the previous two numbers.
Thus: 55+89 = 144

Question #2

What would be the next group of letters in the following series?

ghg ... hhh ... ihi ... jhj ?

A. lhl

B. khk

C. llh

D. kkh

E. hkk

The correct answer is (B) - KHK.

The first and last letters of each group are identical;
The second letter of each group is always an H.

Based on this, eliminate answers C, D, and E.
When examining the pattern that the outer letters follow, you can quickly notice a consecutive sequence:
G H I J K

The outer letters of the missing group must therefore be K.

## Tables and Graphs

There are usually two tables & graphs questions on the CCAT, appearing towards the end of the test in most cases (from questions 30 to 50).

### Practice Question

If the number of people eligible for work in 2012 was 5 million, what is the difference in the number of unemployed people holding a Bachelor's degree and unemployed people with a Master's degree?

A. 50

B. 500

C. 5,000

D. 50,000

E. 500,000

The correct answer is (D) - 50,000.

There are 2 ways to solve this question:

(1) Calculate the number of unemployed people with a Bachelor's degree and then subtract the number of unemployed people with a Master's degree to arrive at the correct answer:
5,000,000*0.05-5,000,000*0.04=50,000.

(2) Calculate the difference in the unemployment rate between people with a Bachelor's degree and people with a Master's degree and then multiply by the total number of the eligible workforce: (0.05-0.04)*5,000,000= 50,000.

* Note that option 2 is a viable option only under the assumption that the data was extracted from the same population.

## What Math Formulas Should You Know for the CCAT?

To answer each of the CCAT numerical questions correctly, you should have a good grasp of specific math formulas and math foundational skills.

If you haven't touched math for a while, it's highly recommended to go over the following formulas and foundations, as all the math questions on the test are built around them.

• Basic math skills: Four operations (addition, subtraction, multiplication, division), decimals, fractions, percentages, ratios, averages
• Math rate formulas - work, speed, distance, and time
• Tables, charts, and graphs analysis

## Can You Use a Calculator on the CCAT?

You're not allowed to use a calculator (also not on your phone) while taking the CCAT. However, you're allowed to use scratch paper for calculations and notes.

Unless you're taking a proctored version of the CCAT, which is administered in some companies such as Vista Equity, no one will know if you're using a calculator or not. Your browser is not recorded during the exam, and you don't need to turn on a webcam.

That said, if you cheat using a calculator and then be asked to take the proctored version (also called the "CCAT Verification test"), you'll probably score much lower than on your first sitting.

Note: While scratch papers are permitted, it will often be quicker to use mental math and shortcut techniques (such as estimation and elimination) for your calculations.

## CCAT Math Tips to Increase Your Chances of Scoring High

• You won't be able to return to previous questions on the CCAT, so it's important not to skip too many questions or get stuck on any question for too long. The general rule of thumb is: if after 10 seconds you are not progressing towards answering the question within another 20 seconds, eliminate as many wrong answers as you can, guess, and move on.
• There's no penalty for wrong answers. So, if you have only several seconds left, try to solve as many questions as possible. Remember that even a random answer still has 20% of being correct.
• Use estimations to avoid unnecessary calculations:
1. Round up the numbers to figures which are more comfortable to work with.
3. Rule out the unlikely answers, hopefully remaining with only one option left

## Continue Practicing for the CCAT Test

Keep practicing for the CCAT so that you take the test while being as prepared as possible and score high.

Try our free CCAT sample test and access the complete CCAT test prep course with 6 full-length simulations and dozens of extra practice drills (including math).