--- title: "CCAT Math Questions: 8 Worked Examples | Cognitive Cat Prep" url: https://cognitivecatprep.com/ccat-math-questions updated: 2026-10-06 description: "Eight worked CCAT math questions, from percentages to number sequences, each with the fast route, the common trap and the time you have. Try them free." --- > Cognitive Cat Prep is an independent CCAT practice site. It is not affiliated with Criteria Corp or any employer. CCAT math · 8 worked questions · 18 seconds each # CCAT math questions, worked the fast way By [Avi Flombaum](https://avi.nyc) · Updated October 6, 2026 Math is the biggest slice of a CCAT-style test. Here are eight of our own practice questions, one per type, each with the worked answer, the faster route and the trap that catches people. This page is about the Criteria Cognitive Aptitude Test (CCAT), the hiring test, not the Canadian school test with the same initials. You get 50 questions in 15 minutes, and math is the largest share of them. Below are the math types you will see in our practice bank, one worked question for each, and the quickest honest route to each answer. For all four domains on one page, see [CCAT practice questions](https://cognitivecatprep.com/ccat-practice-questions). ## What CCAT math covers CCAT math is not hard math. Nothing here goes past what you learned by about ninth grade. What makes it hard is the clock: 15 minutes for 50 questions works out to 18 seconds each, and a math question that takes you 40 seconds costs you a question somewhere else. So the skill being tested is closer to number sense than to algebra. Can you see that 25% is a quarter? Can you turn an average into a total without writing anything down? Can you read the right row of a table on the first try? In our simulator's mix, math is 18 of the 50 questions. That is our mix, set from our own reading of the format, not a number published by Criteria. In our bank, math covers 12 types: Mental arithmetic, Percentages, Ratios & proportions, Averages, Speed & unit rates, Work rates, Algebra & word equations, Number sequences, Interleaved sequences, Fractions, Probability & counting, and Tables & charts. One thing other sites get wrong: number series are math. Each step is a difference or a ratio, so you solve them with arithmetic. Letter sequences are a different type, and we cover them on the [CCAT logic questions](https://cognitivecatprep.com/ccat-logic-questions) page. ## Your time budget for math At 18 seconds a question, 18 math questions is 5 minutes and 24 seconds on average. You will not spend it evenly. A clean arithmetic question should take you under 10 seconds. A table or a two-step fraction question can take 30. The point of a budget is to notice when one question is eating two questions' worth of time. A rule that works: if you cannot name the first step within about 10 seconds, pick the most likely answer and move on. Our practice score counts right answers only, so a guess never costs you points in our simulator. ## Eight worked CCAT math questions Each one is a question from our practice bank. Try it first, then open the answer for the worked solution and the fast route. ### Mental arithmetic Question 1 Mental arithmetic Harder A consultant bills $90 per hour. How much is charged for a meeting that lasts one hour and forty minutes? - A. $110 - B. $120 - C. $130 - D. $140 - E. $150 **Show the answer and the fast route** **Answer: E, $150** Forty minutes is two thirds of an hour, so the charge is $90 + $60 = $150. Reading 1 hour 40 minutes as 1.4 hours gives $126, a common decimal trap. The fast route $90 per hour is $1.50 per minute; 100 minutes × $1.50 = $150. **Fast route.** Turn the rate into a per-minute rate when the time is not a round number. $90 an hour is a dollar fifty a minute, and 100 minutes is $150. **Trap.** Reading “one hour and forty minutes” as 1.4 hours. Minutes are sixtieths, not tenths. That slip gives $126, which is not an option, so you burn time redoing the math. ### Percentages Question 2 Percentages Easier Sixty employees attended a training session, which was 40% of the staff. How many people are on the staff? - A. 24 - B. 100 - C. 150 - D. 240 - E. 84 **Show the answer and the fast route** **Answer: C, 150** 60 is 40% of the staff, so the staff is 60 / 0.4 = 150. The fast route If 40% is 60, then 10% is 15, and 100% is 150. **Fast route.** Scale from the percent you are given down to 10%, then up to 100%. If 40% is 60, 10% is 15, and 100% is 150. **Trap.** Taking 40% of 60. The question gives you the part and asks for the whole. Read which number is the part before you touch it. ### Ratios & proportions Question 3 Ratios & proportions Easier A bakery mixes flour and sugar in the ratio 5:2 by weight. One batch uses 35 pounds of flour. How many pounds of sugar does the batch need? - A. 10 - B. 12 - C. 14 - D. 16 - E. 49 **Show the answer and the fast route** **Answer: C, 14** One part is 35 ÷ 5 = 7 pounds. Sugar is 2 parts, so 2 × 7 = 14 pounds. 49 is the whole batch (flour plus sugar), not the sugar alone. The fast route Find one part, then multiply by the sugar's parts. **Fast route.** Find the size of one part, then multiply. 35 pounds of flour is 5 parts, so one part is 7 and sugar's 2 parts are 14. **Trap.** Answering with the whole batch. 49 is flour plus sugar. When a ratio question has an option that equals the total, check that the question asked for the total. ### Fractions Question 4 Fractions Medium Dana has $420. She spends 2/7 of it on a jacket and then 1/5 of what is left on shoes. How much money does she have left? - A. $204 - B. $216 - C. $228 - D. $240 - E. $252 **Show the answer and the fast route** **Answer: D, $240** After the jacket she keeps 5/7: 420 × 5/7 = 300. After the shoes she keeps 4/5 of that: 300 × 4/5 = 240. The trap $216 subtracts 2/7 and 1/5 of the original $420 instead of taking 1/5 of what was left. The fast route Multiply the kept fractions: 5/7 × 4/5 = 4/7, and 420 × 4/7 = 240. **Fast route.** Multiply what is kept, not what is spent. She keeps 5/7, then 4/5 of that: 5/7 × 4/5 = 4/7, and 4/7 of 420 is 240. **Trap.** Subtracting both fractions from the original amount. “Of what is left” means the second fraction applies to a smaller number. ### Probability & counting Question 5 Probability & counting Medium A team of 6 players must pick a captain and a different player as co-captain. How many ways can the two roles be filled? - A. 15 - B. 36 - C. 12 - D. 30 - E. 11 **Show the answer and the fast route** **Answer: D, 30** 6 choices for captain, then 5 for co-captain: 6 x 5 = 30. Order matters because the roles differ. The fast route Distinct roles: do not divide by 2. **Fast route.** Count choices step by step and multiply. Six people can be captain, then five are left for co-captain: 30. **Trap.** Dividing by 2 out of habit. You divide when order does not matter. Captain and co-captain are different jobs, so order matters. ### Tables & charts Question 6 Tables & charts Medium Combining both years in the agent table, what was Hale's average sale price per house? Agent sales, 2023 and 2024 | Agent | 2023 houses sold | 2023 sales ($) | 2024 houses sold | 2024 sales ($) | | --- | --- | --- | --- | --- | | Grant | 9 | 2880000 | 11 | 3520000 | | Hale | 12 | 3600000 | 14 | 4200000 | | Ibarra | 7 | 2450000 | 13 | 4030000 | | Jones | 10 | 3300000 | 10 | 3450000 | - A. $310,000 - B. $290,000 - C. $300,000 - D. $320,000 - E. $305,000 **Show the answer and the fast route** **Answer: C, $300,000** Total sales: 3,600,000 + 4,200,000 = 7,800,000. Total houses: 12 + 14 = 26. 7,800,000 / 26 = $300,000. The fast route Add sales and houses separately, then divide once. **Fast route.** Find Hale's row, add the sales across both years, add the houses, then divide once. 7.8 million over 26 houses is $300,000. **Trap.** Averaging the two yearly averages. Here both years happen to average $300,000, so you get lucky, but when the years differ and the house counts differ, that shortcut gives the wrong number. Totals over totals always works. ### Algebra & word equations Question 7 Algebra & word equations Easier If 5x + 18 = 78, what is x? - A. 14 - B. 12 - C. 11 - D. 17 - E. 13 **Show the answer and the fast route** **Answer: B, 12** Subtract 18, then divide by 5: (78 − 18) ÷ 5 = 12. The fast route Name the unknown once; translate the relationship before doing arithmetic. Solve it step by step 1. #### 1 Name the unknown Let x = the number we are solving for 2. #### 2 Translate the words into math - “5 times x, plus 18, equals 78” `5x + 18 = 78` 3. #### 3 Solve the equation, one move at a time Whatever you do to one side, do to the other to keep the two sides equal. 1. Start The equation 5x + 18 = 78 2. 1 Rule Subtract the same amount from both sides Subtract 18 from both sides 5x = 60 3. 2 Rule Divide both sides by the same nonzero number Divide both sides by 5 x = 12 4. #### 4 Answer x = 12. Check: 5 × 12 + 18 = 78. **Fast route.** Undo the operations in reverse order. Take away 18, then divide by 5. Or test the middle option: 5 × 12 + 18 = 78, done. **Trap.** Dividing before subtracting. 78 ÷ 5 first gives a decimal, which is your sign you went the wrong way. ### Number sequences Question 8 Number sequences Easier What comes next? 2, 6, 18, 54, 162, ? - A. 164 - B. 487 - C. 488 - D. 486 - E. 484 **Show the answer and the fast route** **Answer: D, 486** Multiply by 3 each time. The next number is 486. The fast route Check differences, then ratios. Make sure your rule fits every step. **Fast route.** Check the gaps first, then the ratios. The gaps here (4, 12, 36, 108) grow too fast to be adding, so try multiplying: each term is three times the last. **Trap.** Picking an answer that fits the last step but not every step. Check your rule against the first pair too. More of these, harder ones included, are on [CCAT number series questions](https://cognitivecatprep.com/ccat-number-series-questions). ## The math types not shown above Averages, Speed & unit rates, Work rates and Interleaved sequences are in the bank too. They share one habit: convert before you calculate. Turn an average into a total (average × count). Put a speed into the same units as the time. Add work rates, not completion times. Read an interleaved series as two series, every other term. These are the classic word problems, and they get their own page: [CCAT word problems](https://cognitivecatprep.com/ccat-word-problems). ## The traps that repeat across math - **The answer to a different question.** Many wrong options are the right number for a step you were not asked about: the total instead of the part, the change instead of the new value. Before you pick, reread the last line of the question. - **Decimals that look like minutes.** Time questions punish 1.4 hours read as 1 hour 40. - **Percent of what.** A percent change is always divided by the starting value. A drop from 250 to 200 is 20%, not 25%. - **Long division you did not need.** If you are dividing 7,800,000 by 26 the long way, stop and look for a round number. CCAT-style options are usually far enough apart to estimate. - **Spending 45 seconds to be sure.** A sure answer that costs you two other questions is a bad trade. ## How to practice CCAT math Work without a calculator. Our simulator does not give you one, and you should check your own invitation for the rules your employer set. Use scratch paper for the multi-step questions only. If you write down every arithmetic step, you are too slow. Drill the types that cost you the most time, not the ones you get wrong most. They are often different. A type you get right in 35 seconds is costing you more than a type you get wrong in 10. Then put it under the full clock. A [full CCAT practice test](https://cognitivecatprep.com/ccat-practice-test) mixes math with verbal, logic and spatial questions the way a CCAT-style test does, so you practice switching, not just solving. After the test, our AI coach shows which math types took you longest and why. If you have not tried one, the [free CCAT practice test](https://cognitivecatprep.com/free-ccat-practice-test) is one full test with a debrief, no card. ## The other three domains Math is one of four. See [CCAT verbal questions](https://cognitivecatprep.com/ccat-verbal-questions), [CCAT logic questions](https://cognitivecatprep.com/ccat-logic-questions) and [CCAT spatial reasoning questions](https://cognitivecatprep.com/ccat-spatial-reasoning-questions). ## Questions, answered **What kind of math is on the CCAT?** Arithmetic, percentages, ratios, fractions, averages, rates, simple equations, number series and reading tables. Nothing past early high school. The difficulty comes from doing it in about 18 seconds a question. **How many math questions are on the CCAT?** We cannot give you an official count, and Criteria does not publish one per domain. Our simulator uses 18 math questions out of 50, which is our own mix. **Can I use a calculator?** Our simulator has no calculator, and we recommend practicing without one. Check your test invitation for the rules your employer set. **Is number series math or logic?** We treat it as math, because each step is a difference or a ratio you work out with arithmetic. Letter sequences are logic. **What should I do if a math question is taking too long?** Pick the most likely answer and move on. Our practice score counts right answers only, so in our simulator a guess never costs you points. ## Keep going - [Question types: Verbal questions](https://cognitivecatprep.com/ccat-verbal-questions) - [Question types: Logic questions](https://cognitivecatprep.com/ccat-logic-questions) - [Question types: Spatial reasoning](https://cognitivecatprep.com/ccat-spatial-reasoning-questions) - [Question types: Number series](https://cognitivecatprep.com/ccat-number-series-questions)