CogAT Number Puzzles Practice Questions
Number Puzzles questions ask students to reason through missing values, number relationships, and structured quantitative patterns.
Practice original CogAT-style number puzzle questions with answer explanations.
How to use this practice page
- Read each question carefully before selecting an answer.
- Choose A, B, C, or D, then check the answer explanation.
- Look for the reasoning rule instead of guessing from the first thing you notice.
- Use the explanations to talk through the thinking process with your child or student.
Skills practiced: missing number reasoning, quantitative logic, pattern balancing, and flexible problem solving.
Number Puzzles Practice
Select an answer for each question, then check your work to see the explanation.
Question 1 of 12
Number Puzzles Practice Question
Quantitative
Use both equations. ◆ + ◆ = 42. ◆ + ● = 41. What number does ● represent?
Show explanation
From ◆ + ◆ = 42, each ◆ equals 21. Then 21 + ● = 41, so ● = 41 - 21 = 20.
Skill tested: Using one equation to substitute into a second equation
Question 2 of 12
Number Puzzles Practice Question
Quantitative
The same positive whole number fills every blank. Find the missing number: ___ / 5 + 8 = 3 * 7.
Show explanation
Three times 7 is 21; subtract 8 to obtain 13, then multiply by 5: 65.
Skill tested: inverse divide then add
Question 3 of 12
Number Puzzles Practice Question
Quantitative
A box adds two numbers together. If the numbers are 8 and 2, what comes out of the box?
Show explanation
The box adds the two numbers: 8 + 2 = 10.
Skill tested: Solving simple quantitative rules
Question 4 of 12
Number Puzzles Practice Question
Quantitative
Use both equations. ◆ + ● = 47. ◆ + ◆ + ● = 72. What number does ● represent?
Show explanation
The second equation has one extra ◆, so ◆ = 72 - 47 = 25. Substitute into the first equation: 25 + ● = 47. Therefore ● = 47 - 25 = 22.
Skill tested: Eliminating and substituting across two quantitative equations
Question 5 of 12
Number Puzzles Practice Question
Quantitative
The same positive whole number fills every blank. Find the missing number: 5 * ___ - 17 = 48.
Show explanation
Add 17 to get 65, then divide by 5: 13.
Skill tested: inverse multiply then subtract
Question 6 of 12
Number Puzzles Practice Question
Quantitative
A box adds two numbers together. If the numbers are 3 and 5, what comes out of the box?
Show explanation
The box adds the two numbers: 3 + 5 = 8.
Skill tested: Solving simple quantitative rules
Question 7 of 12
Number Puzzles Practice Question
Quantitative
Which number belongs in the box? 9 - □ = 4
Show explanation
The missing number is the difference between 9 and 4: 9 - 4 = 5.
Skill tested: Finding a missing element in a one-step equation
Question 8 of 12
Number Puzzles Practice Question
Quantitative
The same positive whole number fills every blank. Find the missing number: (___ - 5) / 4 = (___ + 7) / 6.
Show explanation
Cross multiplying gives 6x - 30 = 4x + 28. Therefore 2x = 58 and x = 29.
Skill tested: equal ratios with offsets
Question 9 of 12
Number Puzzles Practice Question
Quantitative
Triangle means multiply by 3. Circle means subtract 6. If you start with 3, then use Triangle and Circle, what is the result?
Show explanation
First multiply by 3: 3 x 3 = 9. Then subtract 6: 9 - 6 = 3.
Skill tested: Following ordered quantitative operations
Question 10 of 12
Number Puzzles Practice Question
Quantitative
Use both equations. ◆ + ◆ = 10. ◆ + ● = 26. What number does ● represent?
Show explanation
From ◆ + ◆ = 10, each ◆ equals 5. Then 5 + ● = 26, so ● = 26 - 5 = 21.
Skill tested: Using one equation to substitute into a second equation
Question 11 of 12
Number Puzzles Practice Question
Quantitative
Triangle means multiply by 3. Circle means subtract 2. If you start with 5, then use Triangle and Circle, what is the result?
Show explanation
First multiply by 3: 5 x 3 = 15. Then subtract 2: 15 - 2 = 13.
Skill tested: Following ordered quantitative operations
Question 12 of 12
Number Puzzles Practice Question
Quantitative
Use both equations. ◆ + ● = 39. ◆ + ◆ + ● = 65. What number does ● represent?
Show explanation
The second equation has one extra ◆, so ◆ = 65 - 39 = 26. Substitute into the first equation: 26 + ● = 39. Therefore ● = 39 - 26 = 13.
Skill tested: Eliminating and substituting across two quantitative equations
Next practice steps
Next, try Number Analogies, Number Series, or return to Quantitative Practice.
For grade-based mixed practice, choose a grade from the Practice menu.