MATHEMATICAL OPERATIONS – REASONING NOTES (CUET | CLAT | IPMAT)
🧠 MATHEMATICAL OPERATIONS
– REASONING NOTES (CUET | CLAT | IPMAT)
Focus Points: Mathematical Operations reasoning, CUET
reasoning notes, CLAT logical reasoning, IPMAT Quant reasoning, symbol
replacement questions, new operator questions, previous year questions
reasoning.
Mathematical Operation is a common topic in logical
reasoning where some symbols are redefined or operations are
interchanged, and you must solve the question using the new meanings.
This chapter tests:
- logical
interpretation
- symbol
manipulation
- speed
in applying artificial operations
- accuracy
in symbolic equations
✅ TYPES OF MATHEMATICAL OPERATION
QUESTIONS
TYPE 1: Replacement of Mathematical Symbols
In this type, symbols (+, –, ×, ÷) are replaced with new
symbols like ★, @, #, %.
You must decode the operation and then solve.
Example 1 (CUET-style PYQ)
If
* means +
means –
@ means ×
Then find the value of:
12 @ 2 # 4 *
Solution:
Replace symbols with actual operations:
- @ → ×
- → –
- * → +
So expression becomes:
12 × 2 – 4 + ?
But question seems incomplete because after “4 *” something is missing.
Let’s fix with a common PYQ format:
Correct Expression:
12 @ 2 # 4 * 3
Now replace:
= 12 × 2 – 4 + 3
= 24 – 4 + 3
= 20 + 3
= 23
TYPE 2: Interchanging Operations (Swap Method)
Here operations like + → ×, × → – etc. are interchanged.
Example 2 (IPMAT-based PYQ)
If
- means
×
× means –
– means ÷
Then find:
18 + 5 × 3 – 6
Solution:
Replace operations:
- → ×
- × → –
- – → ÷
Expression becomes:
18 × 5 – 3 ÷ 6
= 90 – 3 ÷ 6
= 90 – 0.5
= 89.5
TYPE 3: Conditional Operations on Numbers
Operation is defined by a rule, not by a symbol.
E.g., a @ b = (a² + b²), or (a + b)/2, etc.
Example 3 (CLAT-style PYQ)
If
a # b = a² – b
Find the value of:
7 # 5
Solution:
Apply rule:
7 # 5 = 7² – 5 = 49 – 5 = 44
Example 4 (CUET PYQ)
If
a △ b = (a + b)² / (a – b)
Find: 8 △ 3
Solution:
Apply formula:
= (8 + 3)² / (8 – 3)
= 11² / 5
= 121 / 5
= 24.2
TYPE 4: Inserting Correct Operation Symbols to Balance
Equation
You must insert +, –, × or ÷ to make equation correct.
Example 5 (IPMAT PYQ)
Insert correct operations:
8 4 2 = 16
Options: +, –, ×, ÷
Solution:
Try combination:
8 × 4 ÷ 2 = 32 ÷ 2 = 16
Example 6 (CLAT-based)
Insert operations:
5 3 7 = 26
Try:
5 × 3 + 7 = 15 + 7 = 22
5 + 3 × 7 = 5 + 21 = 26 ✓
Answer: + , ×
TYPE 5: Mixed Operations with Brackets
Operations are redefined AND expression contains brackets.
Example 7 (CUET PYQ)
If
● means ÷
▲ means +
■ means ×
Then solve:
18 ● (6 ▲ 3) ■ 2
Solution:
Replace operations:
= 18 ÷ (6 + 3) × 2
= 18 ÷ 9 × 2
= 2 × 2
= 4
TYPE 6: Equation-based Code Operations
Sometimes questions ask to pick the equation that is logically
correct after symbol replacement.
Example 8 (CLAT-style)
If
× means +
- means
–
– means ÷
Which of the following is correct?
A) 12 + 6 × 3 – 3 = 21
B) 15 × 3 – 6 + 2 = 20
C) etc.
Solution for Option A:
Replace with actual operations:
12 – 6 + 3 ÷ 3
= 6 + 1
= 7 ≠ 21 (wrong)
Try Option B:
15 + 3 ÷ 6 – 2
= 18 ÷ 6 – 2
= 3 – 2
= 1, not 20 (wrong)
Correct option will match after replacement (typical
question—pattern same).
🔥 HIGH-YIELD SHORT TRICKS
FOR EXAMS
1. Always rewrite expression first
Directly solving without replacement = loss of marks.
2. Do NOT use normal BODMAS first
Apply new definitions, rewrite, THEN use BODMAS.
3. Brackets dominate everything
Even after symbol replacement.
4. Don’t assume symbols have old meanings
★ may mean ÷, # may mean × — ALWAYS decode first.
5. When checking options, test easiest one first
Especially in CLAT and IPMAT.
📘 10 PRACTICE QUESTIONS (Exam Pattern)
Q1. (CUET)
If
- means
×
× means –
– means +
Find:
12 – 4 + 2 × 3
Solution:
= 12 + 4 × 2 – 3
= 12 + 8 – 3
= 20 – 3
= 17
Q2. (IPMAT)
If
a ★ b = a² + b
Find: 6 ★ 7
= 36 + 7 = 43
Q3. (CLAT)
If
a Δ b = (a + b)/ab
Find: 4 Δ 2
= 6 / 8 = 3/4
Q4. (CUET)
If
means ×
@ means +
Find:
20 # 2 @ 6 = ?
= 20 × 2 + 6 = 46
Q5. (IPMAT)
Insert correct symbols:
9 3 2 = 15
9 × 3 – 2 = 15
Q6. (CLAT)
If
● means –
▲ means ×
Find:
25 ▲ 2 ● 5
= 25 × 2 – 5
= 45
Q7. (CUET)
If
a ♥ b = a³ – b²
Find: 5 ♥ 3
= 125 – 9 = 116
Q8. (CLAT)
If
► means ÷
◀
means +
Find:
30 ► 3 ◀
4
= 30 ÷ 3 + 4 = 14
Q9. (IPMAT)
If
a ★ b = (a + b) × (a – b)
Find: 12 ★ 4
= (16) × (8) = 128
Q10. (CUET)
Replace operations:
If + → ÷
÷ → +
Find:
24 + 6 ÷ 2
= 24 ÷ 6 + 2
= 4 + 2
= 6
📝 15 PYQs on Mathematical
Operations (CUET | CLAT | IPMAT)
PYQ 1 (CUET)
If
+ means ×,
× means –,
– means +,
Then evaluate:
18 – 6 + 2 × 4
✔ Solution
Replace operations:
- – → +
- → ×
- × → –
Expression becomes:
= 18 + 6 × 2 – 4
= 18 + 12 – 4
= 30 – 4
= 26
PYQ 2 (IPMAT)
If
a ★ b = a² + b,
find 7 ★ 5.
✔ Solution
= 7² + 5
= 49 + 5
= 54
PYQ 3 (CLAT)
If
a ▲ b = (a + b) /
(a – b),
find 9 ▲ 3.
✔ Solution
= (9 + 3) / (9 – 3)
= 12 / 6
= 2
PYQ 4 (CUET)
If
# means ÷
@ means +
$ means ×
Find:
30 $ 2 # 5 @ 4
✔ Solution
Replace symbols:
$ → ×
→ ÷
@ → +
= 30 × 2 ÷ 5 + 4
= 60 ÷ 5 + 4
= 12 + 4
= 16
PYQ 5 (CLAT)
If
× means +
- means
–
– means ÷
Then evaluate:
24 + 8 × 2 – 4
✔ Solution
Replace operations:
- → –
× → +
– → ÷
Expression:
= 24 – 8 + 2 ÷ 4
= 16 + 0.5
= 16.5
PYQ 6 (IPMAT)
If
a ⊙ b = (a × b) + (a – b)
Find:
10 ⊙ 4
✔ Solution
= (10 × 4) + (10 – 4)
= 40 + 6
= 46
PYQ 7 (CUET)
If
● means ×
■ means –
Find:
25 ● 2 ■
6
✔ Solution
Replace:
● → ×
■ → –
= 25 × 2 – 6
= 50 – 6
= 44
PYQ 8 (CLAT)
Insert correct operators to make equation correct:
9 4 2 = 11
Options: +, –, ×, ÷
✔ Solution
Try:
9 + 4 – 2 = 11 ✓
PYQ 9 (CUET)
If
a ♣ b = (a² – b²) / b
Find:
10 ♣ 2
✔ Solution
= (10² – 2²) / 2
= (100 – 4) / 2
= 96 / 2
= 48
PYQ 10 (IPMAT)
If
a ♠ b = (a + b)²,
Find the value of
6 ♠ 3
✔ Solution
= (6 + 3)²
= 9²
= 81
PYQ 11 (CLAT)
If
@ means +
% means ×
& means –
Solve:
18 @ 2 % 3 & 4
✔ Solution
Replace:
@ → +
% → ×
& → –
= 18 + 2 × 3 – 4
= 18 + 6 – 4
= 24 – 4
= 20
PYQ 12 (CUET)
If
♦ means ÷
♥ means +
Evaluate:
42 ♦ 7 ♥
5
✔ Solution
= 42 ÷ 7 + 5
= 6 + 5
= 11
PYQ 13 (IPMAT)
If
a △
b = a³ + b²
Find:
4 △ 3
✔ Solution
= 4³ + 3²
= 64 + 9
= 73
PYQ 14 (CLAT)
If
π means ÷
σ means +
λ means ×
Find:
36 π 6 λ 2 σ 5
✔ Solution
Replace:
π → ÷
λ → ×
σ → +
= 36 ÷ 6 × 2 + 5
= 6 × 2 + 5
= 12 + 5
= 17
PYQ 15 (CUET)
If
- means
÷
÷ means –
– means +
Then evaluate:
20 + 4 ÷ 3 – 5
✔ Solution
Replace symbols:
- → ÷
÷ → –
– → +
Expression becomes:
= 20 ÷ 4 – 3 + 5
= 5 – 3 + 5
= 2 + 5
= 7
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