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Mathematical operations and missing numbers for SSC CGL

"If + means × and − means ÷…" Symbol-substitution, sign-swapping and missing-number questions blend reasoning with arithmetic. They are quick marks if you substitute first, apply BODMAS correctly and test every rule on every row. Seven question types, eight worked examples and a practice set with answers.

31 Oct 2026 8 min read

In this guide
  1. How they appear in SSC CGL
  2. First, BODMAS done properly
  3. Worked examples
  4. Missing numbers in grids and figures
  5. Common mistakes
  6. Practice
  7. What to do next

Mathematical operations questions look like arithmetic, but they are really a test of discipline. The numbers are small. The marks are lost when you substitute a symbol wrongly, apply BODMAS in the wrong order, or accept a missing-number rule after checking only one row.

How they appear in SSC CGL

These questions sit in the General Intelligence and Reasoning section of Tier 1 and in the Reasoning module of Tier 2. The number per shift varies, but the formats repeat:

FormatWhat you are asked
Symbol substitution"If + means ×, − means ÷…", find the value
Letter-coded operations"If P means +, Q means −…", find the value
Interchange two signsWhich swap makes the equation true?
Interchange two numbersWhich two numbers must swap places?
Choose the sign sequenceFill the blanks with the right order of signs
Defined operation"a # b = 2a + 3b", evaluate an expression
Missing number in a figureGrid, triangle or circle with one number hidden

First, BODMAS done properly

Most errors here are order-of-operations errors. The rule is:

  1. Brackets first.
  2. Of (and powers, if any).
  3. Division and Multiplication have equal rank. Do them from left to right.
  4. Addition and Subtraction have equal rank. Do them from left to right.

The word BODMAS tempts people to divide before multiplying. Take 18 ÷ 3 × 4: left to right gives 6 × 4 = 24, not 18 ÷ 12 = 1.5.

Worked examples

1. Symbol substitution. If + means ×, − means ÷, × means − and ÷ means +, find 12 + 4 − 2 × 6 ÷ 3.

  • Substitute: 12 × 4 ÷ 2 − 6 + 3.
  • Multiply and divide left to right: 12 × 4 = 48, 48 ÷ 2 = 24.
  • Add and subtract left to right: 24 − 6 + 3 = 21.

2. Letter-coded operations. If P means +, Q means −, R means × and S means ÷, find 18 S 3 R 4 P 6 Q 2.

  • Substitute: 18 ÷ 3 × 4 + 6 − 2.
  • Left to right: 18 ÷ 3 = 6, 6 × 4 = 24.
  • Then 24 + 6 − 2 = 28.

3. Interchange two signs. Which two signs must be interchanged to make the equation correct? 12 + 6 × 3 − 4 ÷ 2 = 6

Write each trial in one line:

SwapNew expressionValue
+ and −12 − 6 × 3 + 4 ÷ 2−4
+ and ×12 × 6 + 3 − 4 ÷ 273
− and ÷12 + 6 × 3 ÷ 4 − 214.5
× and ÷12 + 6 ÷ 3 − 4 × 26

The answer is × and ÷. In the exam, test the options given, not all six possible swaps, and stop when one balances.

4. Interchange two numbers. Which two numbers should be interchanged to make the equation correct? 6 + 8 × 3 − 12 ÷ 4 = 40

Options: (a) 6 and 8 (b) 8 and 12 (c) 3 and 4 (d) 12 and 4

  • (a) 8 + 6 × 3 − 12 ÷ 4 = 8 + 18 − 3 = 23. No.
  • (b) 6 + 12 × 3 − 8 ÷ 4 = 6 + 36 − 2 = 40. Yes.
  • (c) 6 + 8 × 4 − 12 ÷ 3 = 6 + 32 − 4 = 34. No.
  • (d) 6 + 8 × 3 − 4 ÷ 12 gives a fraction, so it cannot be 40.

Answer: (b). Shortcut: the left side is 27 before any swap, so you need a bigger product term. Moving 12 next to × 3 does that.

5. Choose the sign sequence. Select the correct combination of signs to replace the blanks: 18 _ 3 _ 4 _ 5 _ 7 = 22

Options: (a) ÷, ×, +, − (b) ×, ÷, +, − (c) ÷, +, ×, − (d) +, ×, ÷, −

  • (a) 18 ÷ 3 × 4 + 5 − 7 = 24 + 5 − 7 = 22. Yes.
  • (b) 18 × 3 ÷ 4 + 5 − 7 = 13.5 − 2 = 11.5. No.
  • (c) 18 ÷ 3 + 4 × 5 − 7 = 6 + 20 − 7 = 19. No.
  • (d) 18 + 3 × 4 ÷ 5 − 7 = 18 + 2.4 − 7 = 13.4. No.

Answer: (a). Options that produce decimals can often be struck out at a glance.

6. Defined operation. If a # b = a² − b², find (5 # 3) # 2.

  • Inner bracket first: 5 # 3 = 25 − 9 = 16.
  • Then 16 # 2 = 256 − 4 = 252.

Write the formula beside the question so you don't mix up a and b.

Missing numbers in grids and figures

Here the question hides one number in a grid, a triangle or a circle cut into sectors. The rule usually works along rows, down columns, or from the outer numbers to the centre.

FigureRules to try, in order
Grid (3 × 3)Row sum or product; third = first ○ second (+, ×, squares); then columns
Triangle with a centre numberSum of corners, product of corners, sum × or − a constant
Circle in sectorsOpposite sectors add or multiply to the same value; clockwise series

7. Grid. The rows read:

Col 1Col 2Col 3
3425
512169
68?

Try the simplest rules first. Sum (3 + 4 = 7) and product (12) fail on row 1. Sum of squares works: 3² + 4² = 9 + 16 = 25, and 5² + 12² = 25 + 144 = 169. So ? = 6² + 8² = 36 + 64 = 100.

8. Triangles. Three triangles each have three corner numbers and a centre number: corners 2, 3, 4 with 24 in the centre; corners 1, 5, 6 with 30; corners 3, 3, 2 with ?.

The sum of the first corners is 9, not 24, so sum fails. The product works on both complete triangles: 2 × 3 × 4 = 24 and 1 × 5 × 6 = 30. So ? = 3 × 3 × 2 = 18.

Common mistakes

MistakeFix
Calculating before substitutingRewrite the full expression first
Doing ÷ before × regardless of position÷ and × are equal rank; go left to right
Stopping after one row fitsTest the rule on every complete row
Mixing up a and b in a defined operationWrite the formula beside the question
Testing all six sign swapsTest only the options given

Practice

  1. If + means ÷, − means ×, × means − and ÷ means +, find 36 + 4 − 3 × 5 ÷ 2.
  2. If P means ×, Q means ÷, R means + and S means −, find 40 Q 8 P 6 R 9 S 4.
  3. Which two signs should be interchanged to make this correct? 16 ÷ 4 + 3 × 5 − 2 = 15
    • (a) + and × (b) ÷ and − (c) + and − (d) × and ÷
  4. Which two numbers should be interchanged to make this correct? 9 + 5 × 2 − 8 ÷ 4 = 25
    • (a) 9 and 5 (b) 5 and 2 (c) 2 and 4 (d) 8 and 4
  5. If a # b = 2a + 3b, find (4 # 1) # 2.
  6. If a $ b = a² + b² − ab, find 5 $ 3.
  7. In a grid, the rows read (2, 3, 13), (4, 1, 17) and (3, 5, ?). Find ?.
  8. Triangles have corners (2, 4, 5) with centre 11 and (3, 6, 1) with centre 10. Find the centre for corners (4, 7, 3).

Answers

  1. 24. 36 ÷ 4 × 3 − 5 + 2 = 27 − 5 + 2 = 24.
  2. 35. 40 ÷ 8 × 6 + 9 − 4 = 30 + 5 = 35.
  3. (a). 16 ÷ 4 × 3 + 5 − 2 = 12 + 5 − 2 = 15. As given, the left side is 4 + 15 − 2 = 17.
  4. (c). 9 + 5 × 4 − 8 ÷ 2 = 9 + 20 − 4 = 25. Swapping 5 and 2 gives 9 + 10 − 2 = 17, a common trap.
  5. 28. 4 # 1 = 8 + 3 = 11; then 11 # 2 = 22 + 6 = 28.
  6. 19. 25 + 9 − 15 = 19.
  7. 34. Sum of squares: 4 + 9 = 13, 16 + 1 = 17, so 9 + 25 = 34.
  8. 14. Sum of corners: 2 + 4 + 5 = 11 and 3 + 6 + 1 = 10. Product fails (40, 18). So 4 + 7 + 3 = 14.

What to do next

  1. Do 15 substitution and swap questions with a strict "rewrite first" rule. If a grid resists for 40 seconds, mark it and move on.
  2. Keep a list of missing-number rules you meet in mocks (sum of squares, product, product plus one).
  3. Pair this topic with number and letter series, which trains the same "test on every term" habit, and with coding and decoding for substitution practice.

A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .

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