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
A box adds two numbers together. If the numbers are 7 and 4, what comes out of the box?
Show explanation
The box adds the two numbers: 7 + 4 = 11.
Skill tested: Solving simple quantitative rules
Question 2 of 12
Number Puzzles Practice Question
Quantitative
Triangle means multiply by 3. Circle means subtract 4. If you start with 7, then use Triangle and Circle, what is the result?
Show explanation
First multiply by 3: 7 x 3 = 21. Then subtract 4: 21 - 4 = 17.
Skill tested: Following ordered quantitative operations
Question 3 of 12
Number Puzzles Practice Question
Quantitative
Triangle means multiply by 3. Circle means subtract 2. If you start with 6, then use Triangle and Circle, what is the result?
Show explanation
First multiply by 3: 6 x 3 = 18. Then subtract 2: 18 - 2 = 16.
Skill tested: Following ordered quantitative operations
Question 4 of 12
Number Puzzles Practice Question
Quantitative
Use both equations. ◆ + ◆ = 8. ◆ + ● = 11. What number does ● represent?
Show explanation
From ◆ + ◆ = 8, each ◆ equals 4. Then 4 + ● = 11, so ● = 11 - 4 = 7.
Skill tested: Using one equation to substitute into a second equation
Question 5 of 12
Number Puzzles Practice Question
Quantitative
A machine doubles a number and then adds 2. If the input is 5, what is the output?
Show explanation
Double 5 to get 10, then add 2. The output is 12.
Skill tested: Using a one-variable input-output rule
Question 6 of 12
Number Puzzles Practice Question
Quantitative
A box adds two numbers together. If the numbers are 2 and 2, what comes out of the box?
Show explanation
The box adds the two numbers: 2 + 2 = 4.
Skill tested: Solving simple quantitative rules
Question 7 of 12
Number Puzzles Practice Question
Quantitative
Which number belongs in the box? 16 - □ = 7
Show explanation
The missing number is the difference between 16 and 7: 16 - 7 = 9.
Skill tested: Finding a missing element in a one-step equation
Question 8 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 9 of 12
Number Puzzles Practice Question
Quantitative
A box adds two numbers together. If the numbers are 9 and 3, what comes out of the box?
Show explanation
The box adds the two numbers: 9 + 3 = 12.
Skill tested: Solving simple quantitative rules
Question 10 of 12
Number Puzzles Practice Question
Quantitative
The same positive whole number fills every blank. Find the missing number: 2/3 * (___ + 9) = 30.
Show explanation
Multiply 30 by 3/2 to obtain 45, then subtract 9: 36.
Skill tested: fraction applied to sum
Question 11 of 12
Number Puzzles Practice Question
Quantitative
The same positive whole number fills every blank. Find the missing number: 3/4 * ___ = 45.
Show explanation
One quarter is 45 / 3 = 15, so four quarters equal 60.
Skill tested: fraction of unknown
Question 12 of 12
Number Puzzles Practice Question
Quantitative
A machine doubles a number and then adds 5. If the input is 7, what is the output?
Show explanation
Double 7 to get 14, then add 5. The output is 19.
Skill tested: Using a one-variable input-output rule
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.