Mathematical Operations Questions for SSC CGL: The Short Answer
Mathematical operations (also called sign interchange or symbol substitution) questions give a rule such as "'+' means '×' and '−' means '÷'" and ask for the value of an expression, the pair of signs to swap, or the equation that becomes correct. The method never changes: first rewrite the whole expression with the real signs, then solve it strictly by BODMAS (division and multiplication from left to right, then addition and subtraction from left to right).
Key takeaway for SSC: Most wrong answers come from solving before substituting, or from doing addition before division. Rewrite the line once, cleanly, and the question becomes plain arithmetic. Every worked answer on this page was computed with a program, not by hand.
This topic sits in the General Intelligence and Reasoning section of SSC CGL, SSC CHSL, SSC MTS, SSC GD and SSC CPO. For other quick-score reasoning topics, see our coding decoding tricks for SSC CGL and odd one out classification questions for SSC CGL.
BODMAS Rule for Mathematical Operations Questions
| Step | Operation | How to apply it |
|---|---|---|
| 1 | Brackets | Solve anything inside ( ) first |
| 2 | Orders | Powers and roots, if any |
| 3 | Division and Multiplication | Left to right, whichever comes first |
| 4 | Addition and Subtraction | Left to right, whichever comes first |
Two points that SSC options are built to catch:
- ÷ and × have equal rank. In 18 ÷ 3 × 4, divide first (left to right): 6 × 4 = 24, not 18 ÷ 12.
- + and − have equal rank. In 24 + 6 − 5, go left to right: 30 − 5 = 25.
Types of Mathematical Operations Questions in SSC Exams
| Type | What the question gives | What you do |
|---|---|---|
| Sign substitution | '+' means '×', '−' means '÷' ... | Replace every sign, then BODMAS |
| Letter or symbol coded signs | 'A' means '+', 'B' means '−' ... | Replace each letter with its sign, then BODMAS |
| Interchange two signs | An equation that is wrong as written | Try each pair of signs until LHS = RHS |
| Interchange signs and numbers | Swap two signs and two numbers | Make both swaps, then BODMAS |
| Choose the correct signs | Blanks between numbers | Test each option's sign set |
| Defined operation | a ★ b = a² − b | Put the numbers into the rule |
Sign Interchange Questions with Solutions (Solved Examples)
Example 1: Sign substitution
If '+' means '×', '−' means '÷', '×' means '−' and '÷' means '+', find the value of 18 − 3 + 4 ÷ 6 × 5.
- Rewrite: 18 ÷ 3 × 4 + 6 − 5
- Divide and multiply left to right: 18 ÷ 3 = 6, 6 × 4 = 24
- Add and subtract left to right: 24 + 6 − 5 = 25
Example 2: Letter-coded signs
If 'A' means '+', 'B' means '−', 'C' means '×' and 'D' means '÷', find 36 D 4 C 3 A 8 B 5.
- Rewrite: 36 ÷ 4 × 3 + 8 − 5
- 36 ÷ 4 = 9, 9 × 3 = 27
- 27 + 8 − 5 = 30
Example 3: Which two signs should be interchanged?
Which two signs should be interchanged to make this equation correct? 16 + 8 ÷ 4 − 2 × 3 = 17
As written, the left side is 16 + 2 − 6 = 12, so the equation is wrong. Try each pair:
| Signs swapped | New expression | Value |
|---|---|---|
| + and − | 16 − 8 ÷ 4 + 2 × 3 | 20 |
| + and × | 16 × 8 ÷ 4 − 2 + 3 | 33 |
| + and ÷ | 16 ÷ 8 + 4 − 2 × 3 | 0 |
| − and × | 16 + 8 ÷ 4 × 2 − 3 | 17 |
| − and ÷ | 16 + 8 − 4 ÷ 2 × 3 | 18 |
Answer: − and ×. In the exam, test only the pairs given in the options, starting with the one that changes the biggest term.
Example 4: Interchange of signs and numbers
If '+' and '×' are interchanged and the numbers 4 and 6 are interchanged, find the value of 4 + 6 × 3 − 8 ÷ 2.
- Swap the signs and the numbers: 6 × 4 + 3 − 8 ÷ 2
- 6 × 4 = 24 and 8 ÷ 2 = 4
- 24 + 3 − 4 = 23
Example 5: Choose the correct set of signs
Select the correct combination of signs to replace the blanks in 9 _ 3 _ 4 _ 2 = 10.
| Option | Expression | Value |
|---|---|---|
| ×, −, + | 9 × 3 − 4 + 2 | 25 |
| ÷, ×, − | 9 ÷ 3 × 4 − 2 | 10 |
| +, ÷, × | 9 + 3 ÷ 4 × 2 | 10.5 |
| −, +, × | 9 − 3 + 4 × 2 | 14 |
Answer: ÷, ×, −. Other sign sets (for example +, −, +) also give 10, which is why you should always test the options given rather than search for your own answer.
Example 6: Defined operation
If a ★ b = a² − b, find 7 ★ 3 and (2 ★ 5) ★ 4.
- 7 ★ 3 = 49 − 3 = 46
- 2 ★ 5 = 4 − 5 = −1, then (−1) ★ 4 = 1 − 4 = −3
Example 7: Which equation becomes correct?
If '+' and '−' are interchanged and '×' and '÷' are interchanged, which equation is correct?
| Equation | After interchange | Real value | Correct? |
|---|---|---|---|
| 20 ÷ 4 + 6 × 3 − 2 = 80 | 20 × 4 − 6 ÷ 3 + 2 | 80 | Yes |
| 15 × 3 − 2 ÷ 4 + 6 = 9 | 15 ÷ 3 + 2 × 4 − 6 | 7 | No |
| 24 × 6 + 3 ÷ 2 − 5 = 5 | 24 ÷ 6 − 3 × 2 + 5 | 3 | No |
| 9 ÷ 2 − 8 × 4 + 1 = 17 | 9 × 2 + 8 ÷ 4 − 1 | 19 | No |
How to Solve Mathematical Operations Questions Fast (Step-by-Step)
- Write the code table once (for example + → ×, − → ÷) above the expression.
- Rewrite the full expression with the real signs before calculating anything.
- Circle every × and ÷ and solve them left to right.
- Finish with + and −, left to right.
- For "interchange" questions, check the option pairs only; one bad term usually shows the answer within two tries.
- Check the result is a whole number. SSC answers are almost always integers, so a fraction usually means a slip in substitution.
Common Mistakes in Sign Interchange Questions
- Solving the expression with the printed signs instead of the decoded signs.
- Doing addition before division ("24 + 6 ÷ 3" is 26, not 10).
- Dividing right to left in a chain such as 18 ÷ 3 × 4.
- Forgetting to swap the numbers too when the question swaps both signs and numbers.
- Swapping only the first occurrence of a sign when it appears twice in the expression.
Quick Revision Table: Mathematical Operations Tricks
| Situation | Rule |
|---|---|
| Any coded expression | Decode fully, then BODMAS |
| × and ÷ together | Left to right |
| + and − together | Left to right |
| Interchange two signs | Swap every occurrence of both signs |
| Interchange numbers | Swap every occurrence of both numbers |
| Choose the signs | Test the options, not your own guess |
| Answer is a fraction | Recheck the substitution |
Mathematical Operations Practice Questions with Answers
- If '+' means '÷', '÷' means '+', '−' means '×' and '×' means '−', find 12 + 4 − 6 × 3 ÷ 2. Answer: 17. 12 ÷ 4 × 6 − 3 + 2 = 18 − 3 + 2 = 17.
- If '−' means '÷', '+' means '×', '×' means '+' and '÷' means '−', find 40 − 8 + 2 × 5 ÷ 3. Answer: 12. 40 ÷ 8 × 2 + 5 − 3 = 10 + 5 − 3 = 12.
- If '×' means '+', '÷' means '×' and '+' means '÷' ('−' is unchanged), find 7 × 6 ÷ 3 + 9 − 3. Answer: 6. 7 + 6 × 3 ÷ 9 − 3 = 7 + 2 − 3 = 6.
- If 'P' means '÷', 'Q' means '×', 'R' means '−' and 'S' means '+', find 54 P 6 Q 4 R 10 S 3. Answer: 29. 54 ÷ 6 × 4 − 10 + 3 = 36 − 10 + 3 = 29.
- If '÷' means '−', '×' means '+', '−' means '×' and '+' means '÷', find 63 ÷ 7 × 5 − 4 + 2. Answer: 66. 63 − 7 + 5 × 4 ÷ 2 = 56 + 10 = 66.
- If '+' means '÷', '−' means '×', '×' means '−' and '÷' means '+', find 100 + 25 − 3 × 10 ÷ 5. Answer: 7. 100 ÷ 25 × 3 − 10 + 5 = 12 − 10 + 5 = 7.
For timed practice, take the SSC CGL Mathematical Operations Mock Test 02 and the SSC GD Mathematical Operations Mock Test 01.
Mathematical Operations FAQs
What are mathematical operations questions in reasoning?
They are questions where the usual signs (+, −, ×, ÷) are replaced by other signs, letters or symbols. You decode the signs and then solve the expression by BODMAS.
Which rule is used to solve mathematical operations questions?
BODMAS: brackets, orders, division and multiplication (left to right), then addition and subtraction (left to right). Apply it only after replacing every coded sign.
How do you find which two signs to interchange?
Swap each pair given in the options, every time the sign appears, and recalculate the left side. The pair that makes both sides equal is the answer.
Are mathematical operations asked in SSC MTS and SSC GD?
Yes. The same sign substitution pattern appears in the reasoning sections of SSC MTS, SSC GD, SSC CHSL, SSC CGL and SSC CPO, usually as direct "find the value" questions.
Practice Next
- Topic tests: SSC CGL Mathematical Operations Mock Test 01, SSC CGL Mathematical Operations Mock Test 02 and SSC GD Mathematical Operations Mock Test 01.
- Mixed reasoning: SSC CPO Reasoning Mock Test 02 and SSC MTS Reasoning Sectional Mock Test 07.
- Related notes: coding decoding tricks for SSC CGL, odd one out classification questions for SSC CGL and direction sense questions for SSC CGL.
- Browse all study notes.