Missing Number Questions for SSC: The Short Answer
SSC reasoning papers often show sets of three numbers, a grid, or a figure in which every group follows the same rule, and ask for the number that replaces the question mark. The method is to find one rule that works for every complete group, then apply it to the incomplete one. Test the rules in a fixed order: products and sums first, then squares and cubes, then mixed rules such as a × b − b.
Key takeaway for SSC: Always confirm the rule on two complete groups before using it. Many rules fit one group by chance; very few fit two. Every rule on this page was checked with a program against both complete groups.
These questions appear in the reasoning sections of SSC CGL, SSC CHSL, SSC MTS, SSC GD and SSC CPO, usually worded as "select the number that can replace the question mark (?) in the following sets". For missing terms in a row of numbers, see number series questions for SSC CGL.
Rule-Testing Order for Number Sets
| Step | Try | Example rule |
|---|---|---|
| 1 | Product or sum of the first two | a × b, a + b |
| 2 | Product with an adjustment | a × b + a + b, a × b − b, a × b − 1 |
| 3 | Squares | a² + b², a² − b, (a − b)² |
| 4 | Sum or difference, then multiply | (a + b) × 2, (a + b) × 3 |
| 5 | Cubes | a³ + b, a³ − b |
Missing Number in Sets: Solved Examples
Example 1
(4, 6, 34); (7, 3, 31); (5, 9, ?)
Check a × b + a + b: 4 × 6 + 4 + 6 = 34 and 7 × 3 + 7 + 3 = 31, both correct. Then 5 × 9 + 5 + 9 = 59.
Example 2
(9, 14, 67); (6, 11, 25); (8, 15, ?)
Products are far too big, so try squares: 9² − 14 = 67 and 6² − 11 = 25, both correct. Then 8² − 15 = 49.
Example 3
(13, 4, 48); (9, 7, 56); (12, 5, ?)
13 × 4 − 4 = 48 and 9 × 7 − 7 = 56, so the rule is a × b − b. Then 12 × 5 − 5 = 55.
Missing Number in a Grid
| Column 1 | Column 2 | Column 3 | |
|---|---|---|---|
| Row 1 | 6 | 5 | 26 |
| Row 2 | 7 | 4 | 24 |
| Row 3 | 9 | 3 | ? |
In each row, third number = first × second − 4: 6 × 5 − 4 = 26 and 7 × 4 − 4 = 24. So ? = 9 × 3 − 4 = 23.
In grid questions, check rows first, then columns. If neither works, compare the sum of each row or column.
Missing Number in a Figure
Three triangles have the numbers 3, 4, 5 at the corners with 60 in the middle, 2, 6, 7 with 84, and 4, 5, 6 with ?.
The middle number is the product of the corners: 3 × 4 × 5 = 60 and 2 × 6 × 7 = 84. So ? = 4 × 5 × 6 = 120.
How to Solve Missing Number Questions Fast
- Compare the size of the third number with the first two. Much bigger means a product or a square.
- Test the simplest rule first and check it on both complete groups.
- If the product is close but not exact, look for a small adjustment (+ a, − b, − 1).
- For grids, try rows, then columns, then row or column totals.
- Apply the rule to the incomplete group and check that the answer is among the options.
Common Mistakes in Missing Number Questions
- Accepting a rule after checking only one group.
- Reading a set in the wrong order: (a, b, c) usually means c comes from a and b.
- Ignoring negative results: (a − b)² gives the same value for a − b and b − a.
- Mixing row and column rules in one grid.
Missing Number Practice Questions with Answers
- (8, 5, 39); (6, 7, 41); (9, 4, ?) Answer: 35. Rule: a × b − 1.
- (12, 3, 45); (10, 4, 42); (7, 6, ?) Answer: 39. Rule: (a + b) × 3.
- (5, 2, 21); (7, 3, 43); (6, 4, ?) Answer: 28. Rule: a² − 2b.
- (14, 6, 64); (11, 3, 64); (15, 9, ?) Answer: 36. Rule: (a − b)².
For timed practice, take the SSC MTS Number Series Mock Test 04 and the SSC GD Number Series Mock Test 03, which include missing-number sets.
Missing Number FAQs
How do I find the rule in a missing number question?
Start with the product and sum of the first two numbers and compare them with the third. Adjust with a small addition or subtraction, then try squares. Confirm the rule on every complete group.
Why should a rule be checked on two groups?
Several different rules can give the same result for one group. Checking a second group removes the rules that only fit by chance.
Are missing number questions asked in SSC GD and SSC MTS?
Yes. Number sets and simple grids appear in the reasoning sections of SSC GD, SSC MTS, SSC CHSL, SSC CGL and SSC CPO.
Practice Next
- Topic tests: SSC MTS Number Series Mock Test 04, SSC GD Number Series Mock Test 03, SSC CHSL Series Mock Test 02 and SSC MTS Reasoning Sectional Mock Test 08.
- Related notes: number series questions for SSC CGL, mathematical operations questions for SSC CGL and analogy questions for SSC CGL.
- Browse all study notes.