CCAT Math Questions: Mental Math Shortcuts and Worked Examples

CCAT math questions use school-level arithmetic, but you get about 18 seconds each and no calculator. You do not need to be a math expert. What helps most is knowing a few shortcuts and not getting stuck on long calculations.

This guide covers the math types we practice, the mental math tricks that save the most time, and a worked example for each.

What CCAT math questions look like

On the real CCAT, math is scored together with logic in one area that Criteria calls math and logic. Criteria describes it as measuring problem solving, arithmetic, logic, and numerical reasoning. Its candidate prep page mentions basic algebra, proportions, and word problems, and says calculators are not allowed. One of Criteria's own sample questions is an averages problem.

In our practice tests, the math family covers word problems, percentages, ratios, averages, rates, and reading small tables. Keep scratch paper handy if your test instructions allow it, but aim to do most steps in your head.

Percentages

Percent questions reward a few simple habits:

• 10% is a decimal shift. 10% of 240 is 24. Half of that, 12, is 5%. Add them and 15% is 36.
• Swap when it is easier. x% of y equals y% of x. So 8% of 50 is the same as 50% of 8, which is 4.
• Percent change uses the starting number. Change divided by the original value. A rise from $40 to $50 is 10 out of 40, or 25%. A drop from $50 back to $40 is 10 out of 50, or 20%.

Worked example

A store's monthly visitors rose from 1,200 to 1,500. By what percent did visitors increase?

1. 20%
2. 25%
3. 30%
4. 33%
5. 300%

Answer: B. 25%. The increase is 300. Divide by the starting value: 300 out of 1,200 is one quarter, or 25%. Answer A is the trap you get by dividing by the new value, 1,500.

Ratios

Use the parts method. Add the numbers in the ratio to get the total number of parts. Divide the total amount by the parts to get the size of one part, then multiply.

Worked example

A mix uses flour and sugar in a ratio of 3 to 2. The mix weighs 40 ounces. How much flour does it contain?

1. 16 ounces
2. 20 ounces
3. 24 ounces
4. 26 ounces
5. 30 ounces

Answer: C. 24 ounces. 3 + 2 = 5 parts. 40 divided by 5 is 8 ounces per part. Flour is 3 parts, so 3 × 8 = 24.

Averages

For missing-value questions, always work with totals: average × count = total. For straight averages, pick a round number near the middle and average the differences instead of adding big numbers.

Worked example

Four test scores are 82, 90, 75, and 85. What is the average?

1. 81
2. 82
3. 83
4. 84
5. 85

Answer: C. 83. Compare each score with 80: +2, +10, −5, +5. The differences add up to +12. Divide by 4 to get +3, so the average is 80 + 3 = 83.

The totals method handles the other common version. If 5 numbers average 14, they add up to 70. If four of them are 10, 12, 15, and 18, which add up to 55, the fifth must be 15.

Rates and work

Two formulas cover most rate questions. Distance equals speed times time. For people or machines working together, add their rates, not their times.

Worked example

One printer finishes a job in 3 hours. A second printer finishes the same job in 6 hours. How long does the job take if both print at the same time?

1. 1.5 hours
2. 2 hours
3. 2.5 hours
4. 4.5 hours
5. 9 hours

Answer: B. 2 hours. The first printer does 1/3 of the job per hour and the second does 1/6. Together that is 2/6 + 1/6 = 3/6, or half the job per hour, so the whole job takes 2 hours. Answer D is the average of the two times, a common trap. Working together must be faster than the faster printer alone.

Reading small tables

Table questions give you a few numbers and ask for a difference, a total, or a percent change. Read the question first, then go to the table for only the numbers you need.

Worked example

By what percent did units sold grow from Q1 to Q4?

1. 33%
2. 45%
3. 50%
4. 60%
5. 150%

Answer: C. 50%. Q4 minus Q1 is 60. Divided by the starting value, 120, that is one half, or 50%. Answer A divides by the wrong number, and E is the ratio of Q4 to Q1, not the growth.

Fractions worth knowing by heart

Many CCAT math questions are faster if you can switch between fractions and percents without thinking:

• 1/2 = 50%, 1/4 = 25%, 3/4 = 75%
• 1/3 ≈ 33.3%, 2/3 ≈ 66.7%
• 1/5 = 20%, 1/6 ≈ 16.7%
• 1/8 = 12.5%, 3/8 = 37.5%

Speed tips for CCAT math

• Look at the options first. If they are far apart, a rough estimate is enough to pick the right one.
• Write only what you need. A couple of numbers on scratch paper beats copying out the whole problem.
• Watch the units. Minutes versus hours and percent versus percentage points are classic traps.
• Know when to leave. Criteria's advice is to make an educated guess if you spend more than a minute on a problem. On a 15-minute test, a long calculation can cost you three or four easier questions later.

For a mixed set of practice items, try our CCAT sample questions.

Build speed with timed math practice

Shortcuts only help if you use them without thinking, and that comes from repetition. Get unlimited full-length CCAT-style tests and short math drills, with a short explanation for every question and a section breakdown after each test.

Not affiliated with Criteria Corp: Aptitude Practice is an independent practice site, and CCAT is a trademark of Criteria Corp used here only to describe the test we help you prepare for.