Mathematical Operations Questions with Solutions
These questions hand you a fake rulebook — "+ means ÷", "− means ×" — and ask you to compute an expression using the swapped meanings. The trick is purely mechanical: substitute carefully, then apply the normal order of operations. Here’s the approach, four fully worked examples sharing one symbol key, and a few to try yourself.
The approach, quickly
- First, rewrite the whole expression substituting every symbol with its NEW meaning — do this as one clean pass before calculating anything, so you don’t re-read the swapped meaning mid-calculation and make an error.
- Once substituted, solve using the normal order of operations: multiplication and division first (left to right), then addition and subtraction (left to right) — exactly like Simplification/BODMAS.
- Multiplication and division rank equally with each other, and addition and subtraction rank equally with each other — neither one in a pair automatically goes before the other.
- Double-check your substitution against the key once more before calculating — mixing up which symbol maps to which is the single most common mistake here, not the arithmetic itself.
Worked examples
1. If '+' means '÷', '−' means '×', '×' means '+', and '÷' means '−', find the value of: 20 + 4 − 3 × 6 ÷ 2
Solution
- Substitute: 20 ÷ 4 × 3 + 6 − 2.
- Division and multiplication first: 20 ÷ 4 = 5, then 5 × 3 = 15.
- Addition and subtraction: 15 + 6 = 21, then 21 − 2 = 19.
Answer: 19
2. Using the same key ('+'='÷', '−'='×', '×'='+', '÷'='−'), find the value of: 15 × 5 ÷ 10 − 2 + 4
Solution
- Substitute: 15 + 5 − 10 × 2 ÷ 4.
- Multiplication and division first: 10 × 2 = 20, then 20 ÷ 4 = 5.
- Addition and subtraction: 15 + 5 = 20, then 20 − 5 = 15.
Answer: 15
3. Using the same key, find the value of: 12 + 6 − 4 × 3 ÷ 2
Solution
- Substitute: 12 ÷ 6 × 4 + 3 − 2.
- Division and multiplication first: 12 ÷ 6 = 2, then 2 × 4 = 8.
- Addition and subtraction: 8 + 3 = 11, then 11 − 2 = 9.
Answer: 9
4. Using the same key, find the value of: 18 − 6 + 4 × 2 ÷ 1
Solution
- Substitute: 18 × 6 ÷ 4 + 2 − 1.
- Multiplication and division first: 18 × 6 = 108, then 108 ÷ 4 = 27.
- Addition and subtraction: 27 + 2 = 29, then 29 − 1 = 28.
Answer: 28
Try these yourself
Substitute using the same key, apply the order of operations, then check against the answer.
1. Using the same key ('+'='÷', '−'='×', '×'='+', '÷'='−'), find the value of: 24 + 8 − 2 × 5 ÷ 1
Answer: 10
2. Using the same key, find the value of: 16 + 8 × 6 − 2 ÷ 5
Answer: 9
3. Using the same key, find the value of: 16 + 4 − 3 × 2 ÷ 1
Answer: 13
Where this comes up
Mathematical Operations (symbol substitution) is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.
Practice more Mathematical Operations questions
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