Mathematical Operations: Symbol Substitution, Interchange and Number Patterns
Mathematical Operations: Symbol Substitution, Interchange and Number Patterns
Mathematical-operations questions test BODMAS under a disguise: the signs are renamed, swapped or hidden, or the numbers follow an invented operation. The method never changes: rewrite the expression in ordinary signs first, then calculate with BODMAS. Number matrices ask for the rule linking rows or columns.
1. Method Box
| Type | Method |
|---|---|
| Symbols renamed (× means +, A means ÷) | Rewrite the whole expression with real signs, then BODMAS |
| Two signs to interchange | Swap each option's pair in the left side and evaluate; only one balances |
| Two signs and two numbers to interchange | Swap both pairs, then evaluate |
| Fill * with signs | Test each option left to right; the equality sign usually sits before the last number |
| Invented operation (3 # 4 = 25) | Try a² + b², (a + b)², ab + a + b, digit joins; confirm on every given example |
| Number matrix | Check row rules first (product, sum), then column rules (equal sums of pairs) |
BODMAS after rewriting: brackets, of, ÷ and × left to right, + and − left to right
Always confirm a rule on two given examples before using it
✗ After replacing signs, compute left to right | ✓ BODMAS still applies: × and ÷ before + and −
✗ 3 # 4 = 25 so the rule is (3 + 4)² − 24 | ✓ Prefer the simplest rule that fits every example: 3² + 4² = 25
हिंदी नोट: गणितीय संक्रियाओं में पहले चिह्न बदलकर पूरा व्यंजक सामान्य रूप में लिखिए, फिर BODMAS लगाइए। संख्या आव्यूह में पहले पंक्ति का नियम, फिर स्तंभ का नियम देखिए।
Exam Pointer: Verified NTPC patterns: renamed operators evaluated with BODMAS (April 2016 CBT-1, June 2025 Graduate CBT-1), interchanging two signs, or two signs and two numbers (two 2022 CBT-2 shifts), and number matrices with a row or column rule (two January 2021 CBT-1 shifts). Fill-the-signs and invented-operation questions had no verified NTPC shift and are tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Renamed operators
[PYQ: NTPC Graduate CBT-1 5-Jun-2025 Shift-1 | NTPC CBT-1 19-Apr-2016 Shift-2]
EXAM LEVEL
Q. If × means +, + means ÷, − means × and ÷ means −, find 12 × 18 + 6 − 4 ÷ 5.
Rewritten: 12 + 18 ÷ 6 × 4 − 5. BODMAS: 18 ÷ 6 = 3, 3 × 4 = 12, so 12 + 12 − 5 = 19.
Answer: 19
EXAMATLAS LEVEL
Q. If A means +, B means −, C means × and D means ÷, find 36 D 4 C 5 A 18 B 7 C 3.
Rewritten: 36 ÷ 4 × 5 + 18 − 7 × 3. Then 36 ÷ 4 = 9, 9 × 5 = 45 and 7 × 3 = 21, so 45 + 18 − 21 = 42.
Answer: 42
Pattern 2: Interchanging signs (and numbers)
[PYQ: NTPC CBT-2 9-May-2022 Shift-1 | NTPC CBT-2 13-Jun-2022 Shift-2]
EXAM LEVEL
Q. Which two signs must be interchanged to make 15 + 3 × 4 − 8 ÷ 2 = 45 correct?
As written the left side is 15 + 12 − 4 = 23. Swapping + and × gives 15 × 3 + 4 − 8 ÷ 2 = 45 + 4 − 4 = 45. (Other swaps give 7, 14, 2, 14.5 and −0.25.)
Answer: + and ×
EXAMATLAS LEVEL
Q. Which two signs and which two numbers must be interchanged to make 20 − 4 × 3 + 12 ÷ 6 = 78 correct? (a) − and ×, 3 and 6 (b) + and ÷, 4 and 12 (c) − and +, 3 and 4 (d) × and ÷, 20 and 12
(a) gives 20 × 4 − 6 + 12 ÷ 3 = 80 − 6 + 4 = 78. (b) gives 20 − 12 × 3 ÷ 4 + 6 = 17, (c) gives 20 + 3 × 4 − 12 ÷ 6 = 30, and (d) gives 12 − 4 ÷ 3 + 20 × 6 ≈ 130.7.
Answer: (a)
Pattern 3: Filling the * with signs
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Choose the signs for 6 * 4 * 3 = 21. (a) ×, − (b) +, × (c) −, + (d) ×, +
(a) 24 − 3 = 21. (b) 6 + 12 = 18, (c) 2 + 3 = 5, (d) 24 + 3 = 27.
Answer: (a)
EXAMATLAS LEVEL
Q. Choose the signs, in order, to replace each * in 24 * 6 * 3 * 2 * 14. (a) ÷, ×, +, = (b) ×, ÷, −, = (c) +, ×, ÷, = (d) ÷, +, ×, =
(a) 24 ÷ 6 × 3 + 2 = 4 × 3 + 2 = 14. (b) 144 ÷ 3 − 2 = 46. (c) 24 + 18 ÷ 2 = 33. (d) 4 + 6 = 10.
Answer: (a)
Pattern 4: Invented operations
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. If 3 # 4 = 25 and 5 # 12 = 169, find 6 # 8.
3² + 4² = 25 and 5² + 12² = 169, so 6 # 8 = 36 + 64 = 100.
Answer: 100
EXAMATLAS LEVEL
Q. If 7 © 3 = 1021 and 6 © 5 = 1130, find 9 © 4.
7 + 3 = 10 and 7 × 3 = 21, written together; 6 + 5 = 11 and 6 × 5 = 30. So 9 © 4 = 13 followed by 36.
Answer: 1336
Pattern 5: Number matrices
[PYQ: NTPC CBT-1 8-Jan-2021 Shift-2 | NTPC CBT-1 31-Jan-2021 Shift-1]
EXAM LEVEL
Q. Rows: (4, 5, 20), (6, 3, 18), (7, ?, 56). Find ?.
In each row the third number is the product of the first two: 7 × ? = 56, so ? = 8.
Answer: 8
EXAMATLAS LEVEL
Q. Rows: (3, 4, 2, 10), (5, 6, 7, 23), (4, 9, ?, 29). Find ?.
Test on the first two rows: 3 × 4 − 2 = 10 and 5 × 6 − 7 = 23, so the fourth number is first × second − third. A sum rule fails (5 + 6 + 7 = 18). For the last row, 36 − ? = 29, so ? = 7.
Answer: 7
60-Second Revision
- Rewrite renamed signs first, then BODMAS.
- Interchange questions: swap the pair in the left side and evaluate each option.
- Invented operations: confirm the rule on every given example.
- Matrices: test the rule on two complete rows or columns before solving.