SSC Mathematical Operations Reasoning Questions with Answers

Mathematical operations is a favourite topic of the SSC reasoning section. The question changes the meaning of signs or gives a hidden number pattern, and you must use the new rules carefully. If you replace the signs first and then apply BODMAS, the questions become simple arithmetic. This practice paper gives you 21 questions with answers and short solutions.

Types of Mathematical Operations Questions

• Symbol replacement: the meanings of +, -, x and / are changed.
• Number patterns: a hidden rule links the numbers (for example a^2 + b^2).
• Missing signs: you choose the signs that make the equation true.
• Interchange: signs and numbers are interchanged before solving.

Rules and Shortcut Tricks

• Replace first, solve later: rewrite the whole expression with the real signs before calculating.
• Apply BODMAS only after the replacement.
• For pattern questions, test simple rules: sum, difference, product, squares and their combinations on the first example.
• Check that the rule also works for the second example.
• For missing signs, try division and multiplication first because they change the value the most.
• Write the new expression on a fresh line to avoid mistakes.

Set 1: Symbol Replacement (Q1–Q7)

Q1. If + means x, x means -, - means / and / means +, find 6 + 4 - 2 x 5 / 3.
Answer: 10
Solution: 6 x 4 / 2 - 5 + 3 = 12 - 5 + 3 = 10.

Q2. If + means -, - means +, x means / and / means x, find 18 x 3 + 4 / 2 - 5.
Answer: 3
Solution: 18 / 3 - 4 x 2 + 5 = 6 - 8 + 5 = 3.

Q3. If A means +, B means -, C means x and D means /, find 12 A 8 C 3 B 6 D 2.
Answer: 33
Solution: 12 + 8 x 3 - 6 / 2 = 12 + 24 - 3 = 33.

Q4. If x means + and + means x, find 5 x 3 + 4.
Answer: 17
Solution: 5 + 3 x 4 = 5 + 12 = 17.

Q5. If - means x and x means -, find 10 - 4 x 6.
Answer: 34
Solution: 10 x 4 - 6 = 34.

Q6. If / means - and - means /, find 24 - 6 / 2.
Answer: 2
Solution: 24 / 6 - 2 = 4 - 2 = 2.

Q7. If P means x, Q means /, R means + and S means -, find 16 Q 4 P 3 R 5 S 2.
Answer: 15
Solution: 16 / 4 x 3 + 5 - 2 = 12 + 5 - 2 = 15.

Set 2: Number Patterns (Q8–Q14)

Q8. If 3 * 4 = 25 and 5 * 12 = 169, find 8 * 15.
Answer: 289
Trick: The rule is a^2 + b^2, so 64 + 225 = 289.

Q9. If 2 # 3 = 13 and 4 # 5 = 41, find 6 # 7.
Answer: 85
Solution: The rule is a^2 + b^2, so 36 + 49 = 85.

Q10. If 5 @ 3 = 16 and 6 @ 2 = 16, find 7 @ 4.
Answer: 22
Solution: The rule is 2 x (a + b), so 2 x 11 = 22.

Q11. If 6 $ 2 = 8 and 9 $ 3 = 12, find 12 $ 4.
Answer: 16
Solution: The rule is a + b, so 12 + 4 = 16.

Q12. If 7 ? 2 = 51 and 6 ? 3 = 39, find 8 ? 5.
Answer: 69
Solution: The rule is a^2 + b, so 64 + 5 = 69.

Q13. If 8 * 2 = 4 and 18 * 3 = 6, find 27 * 9.
Answer: 3
Solution: The rule is a / b, so 27 / 9 = 3.

Q14. If 4 + 3 = 19 and 5 + 2 = 27 in a code, find 6 + 1.
Answer: 37
Solution: The rule is a^2 + b, so 36 + 1 = 37.

Set 3: Interchange and Missing Signs (Q15–Q21)

Q15. Interchange the signs + and x and the numbers 2 and 3 in 3 + 2 x 4. Find the value.
Answer: 10
Solution: New expression: 2 x 3 + 4 = 10.

Q16. Interchange the signs + and - and the numbers 3 and 5 in 5 + 3 - 2. Find the value.
Answer: 0
Solution: Signs: 5 - 3 + 2. Numbers: 3 - 5 + 2 = 0.

Q17. Which signs fill the blanks in 12 * 4 * 3 = 9 (using / and x)?
Answer: / and x
Solution: 12 / 4 x 3 = 3 x 3 = 9.

Q18. Which signs fill the blanks in 15 * 5 * 2 = 5?
Answer: / and +
Solution: 15 / 5 + 2 = 3 + 2 = 5.

Q19. Find the value of 8 + 6 x 2 - 4.
Answer: 16
Solution: 6 x 2 = 12, so 8 + 12 - 4 = 16.

Q20. If + means /, / means x, x means - and - means +, find 36 + 4 / 3 x 5 - 2.
Answer: 24
Solution: 36 / 4 x 3 - 5 + 2 = 27 - 5 + 2 = 24.

Q21. If A = 2, B = 3 and C = 4, find A x B + C.
Answer: 10
Solution: 2 x 3 + 4 = 10.

Common Mistakes in Mathematical Operations

• Solving with the old meaning of a sign.
• Not rewriting the whole expression after replacement.
• Ignoring BODMAS after the replacement.
• Testing the pattern on only one example.
• Forgetting to interchange both the signs and the numbers.
• Making calculation errors with negative numbers.

How to Practice These 21 Questions

1. Always write the new expression first.
2. Practise 15 questions daily.
3. Learn squares up to 25 for pattern questions.
4. Solve each set in 7 minutes.

Related Topics to Study Next

• SSC Simplification Questions
• SSC Reasoning Practice Set
• Odd One Out Questions
• SSC Algebra Questions

Frequently Asked Questions

What is a mathematical operations question?

It is a reasoning question in which the meaning of the signs is changed or a hidden number rule is used.

How do I solve symbol replacement questions?

Replace each symbol with its new meaning, write the new expression and then apply BODMAS.

How do I find the pattern in number questions?

Test sum, difference, product, squares and their combinations on the first example and confirm with the second.

What is the interchange of signs?

You swap two given signs everywhere in the expression before solving.

What is BODMAS?

It is the order of operations: Brackets, Orders, Division, Multiplication, Addition and Subtraction.

Which sign should I try first in missing sign questions?

Division and multiplication, because they change the value the most.

How many such questions come in SSC exams?

One or two questions per shift in the reasoning section.

Is it a scoring topic?

Yes. After replacing the signs, it is just arithmetic.

What should I do if the pattern does not work for the second example?

Try another rule. The pattern must work for all given examples.

How can I improve speed?

Memorise squares and practise with a timer.

Can I do it in my head?

Simple replacement questions can be done mentally, but write the new expression for safety.

How should I prepare mathematical operations for SSC exams?

Learn the types, practise daily and solve previous year questions.