Missing Number Reasoning Tricks: Matrix, Triangle and Circle Questions with Answers for SSC

Missing number questions give numbers in a matrix, a triangle, a circle or a set of figures, and one number is missing. The numbers follow one rule, and you must find it. These missing number reasoning tricks for SSC show where to look first, the rules that are used again and again, and solved questions for every figure.

Where to Look for the Rule

Common Rules

Method

1. Take the complete row, column or figure and write the numbers.
2. Try sum, difference, product and division of the numbers.
3. Try the square, the cube and mixed rules (multiply and add).
4. Check the same rule on the second complete row or figure.
5. Put the rule on the row or figure with the missing number.

Solved Examples

Example 1 (row). 4, 5, 20; 3, 6, 18; 7, 2, ?
The third number is the product of the first two (4 × 5 = 20, 3 × 6 = 18). So 7 × 2 = 14.

Example 2 (column). The columns are (3, 4, 7), (5, 6, 11) and (7, 8, ?).
In each column the third number is the sum of the first two. So 7 + 8 = 15.

Example 3 (triangle). In the triangles, the top number is the sum of the two bottom numbers. The first triangle has bottom 5 and 3 and top 8. The second has bottom 6 and 4 and top 10. The third has bottom 7 and ? and top 12.
The missing number is 12 − 7 = 5.

Example 4 (sum of squares). 2, 3, 13; 4, 5, 41; 6, 7, ?
2² + 3² = 13 and 4² + 5² = 41. So 6² + 7² = 36 + 49 = 85.

Example 5 (circle). A circle has the outer numbers 2, 3, 4, 5 and the centre 14. Another has 1, 2, 3, 4 and the centre 10. The third has 3, 4, 5, 6 and the centre ?
The centre is the sum of the outer numbers, so 3 + 4 + 5 + 6 = 18.

Example 6 (difference). 15, 9, 6; 20, 12, 8; 30, 18, ?
The third number is the difference of the first two: 30 − 18 = 12.

Common Mistakes

• Checking only one row, and not testing the rule on the second row.
• Using the wrong order in a difference (always larger minus smaller).
• Not trying the columns when the rows have no rule.
• Forgetting squares, cubes and the mixed rules.

Quick Tips

• Always test the rule on two rows or two figures.
• Try the rows first and the columns second.
• Know the squares up to 20 and the cubes up to 10.
• For circles, try the sum of all outer numbers first.

Quick Revision Points

• Try sum, difference, product, division, square and cube in this order.
• The same rule works in every row and every figure.
• In a circle the centre is often the sum of the outer numbers.
• In a triangle the top is often the sum of the bottom numbers.
• Check the rule on a second figure before answering.

Practice Questions With Answers

1. 5, 4, 20; 6, 3, 18; 8, 2, ?
   Answer: 16
2. 7, 3, 10; 8, 4, 12; 9, 5, ?
   Answer: 14
3. Triangles: top = sum of the bottom numbers. 9 = 4 + 5 and 12 = 7 + 5. If the bottom numbers are 6 and 8, what is the top?
   Answer: 14
4. A circle has the outer numbers 5, 6, 7, 8. The rule is the sum. Find the centre.
   Answer: 26
5. 2 → 6, 3 → 12, 4 → ?
   Answer: 20
6. 20, 8, 12; 30, 14, 16; 40, 22, ?
   Answer: 18
7. 2, 3, 6; 3, 4, 12; 4, 5, ?
   Answer: 20
8. The columns are (2, 4, 6), (3, 5, 8) and (5, 7, ?). The third is the sum of the first two. Find the missing number.
   Answer: 12
9. 1 → 2, 2 → 9, 3 → 28, 4 → ?
   Answer: 65 (cube plus 1)
10. What should you do first in a missing number question?
    Answer: Find the rule on a complete row or figure

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Reasoning notes page, read the previous topic Number Series Reasoning and the next topic Data Sufficiency Reasoning. Also read Inserting the Missing Character.

Frequently Asked Questions

What is a missing number question?

It is a question in which numbers are arranged in a figure and one number is missing, which you find by the rule of the other numbers.

How do I find the rule?

Try sum, difference, product, division, square and cube on a complete row or figure.

Should I check the rows or the columns first?

Check the rows first. If there is no rule, check the columns.

What is the rule in a triangle?

Usually the top or the centre number is the sum or the product of the other numbers.

What is the rule in a circle?

Usually the centre is the sum of the outer numbers, but check the second circle to confirm.

How many figures should I check?

Check at least two complete figures to be sure that the rule is correct.

What if no rule works?

Try a mixed rule such as multiply and add, or square and subtract.

Which squares and cubes should I learn?

Learn the squares up to 20 and the cubes up to 10.

Is this topic asked in SSC exams?

Yes. Missing number questions are asked in SSC reasoning papers.

How much time should I take?

About 40 seconds for one question.

What are common mistakes?

Testing one row only and getting the order of a subtraction wrong.

How can I improve my speed?

Practise 10 questions daily and learn the common rules table.