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Mathematical Operations

General Intelligence & Reasoning · Series, Analogy & Coding

Useful for: SSC CGL, Railway RRB, KVS, NVS, OTET, UGC NET, EMRS, OSSC RHT — Regular High School Teacher

and 15 more exams

CSIR NET, Central Univ./IIT/NIT Faculty, Junior Teacher, OPSC Assistant Professor, OPSC PGT, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Arts, OSEPA Upper Primary — Science, OSSSC Govt Physical Education Teacher (PET), OSSSC Govt TGT Arts, OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM, Sainik Schools, Special OTET, SSB Lecturer / PGT

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Overview

Symbolic operation items redefine arithmetic signs or ask for a hidden rule linking numbers; rewriting before calculating avoids errors.

Key points

Substitute every symbol before calculating.
Apply BODMAS after substitution.
Hidden-rule items: test sum, difference, product, squares, a × b + a, a² + b.
Balance-type items: interchange two signs to make the equation true.
Check the rule on all given examples.

Explanation

If more than one rule fits one example, test the next example.
Inequality-symbol items: combine through a common term.
Keep a small table of the symbol meanings.
Negative results are possible; do not reject them automatically.

Step by step

Rewrite.
Calculate with BODMAS.
Verify.

Examples

If "+" means "×" and "−" means "+", then 6 + 3 − 4 = 6 × 3 + 4 = 22.
Rule a × b + a: a = 4, b = 5 → 24.
If ÷ means + and + means ÷, then 12 + 3 ÷ 4 = 12 ÷ 3 + 4 = 4 + 4 = 8.

Traps and advanced points

Trap: Calculating with old symbols.
Trap: Skipping BODMAS.
Trap: Fitting a rule to only one example.

Quick revision

Rewrite first.
BODMAS after substitution.
Test rules on all examples.

Practice MCQs

If “+” means “×” and “×” means “+”, evaluate 106 + 8 × 8.
1. 864
2. 872
3. 848
4. 856
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Answer: (d) 856. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 17 + 9 × 9.
1. 153
2. 171
3. 180
4. 162
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Answer: (d) 162. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 28 + 2 × 2.
1. 58
2. 60
3. 62
4. 56
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Answer: (a) 58. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 39 + 4 × 4.
1. 164
2. 160
3. 168
4. 156
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Answer: (b) 160. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 50 + 6 × 6.
1. 318
2. 312
3. 300
4. 306
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Answer: (d) 306. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 55 + 2 × 2.
1. 112
2. 114
3. 110
4. 116
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Answer: (a) 112. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 41 + 6 × 6.
1. 252
2. 264
3. 246
4. 258
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Answer: (a) 252. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 23 + 6 × 6.
1. 156
2. 150
3. 138
4. 144
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Answer: (d) 144. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 100 + 2 × 2.
1. 200
2. 202
3. 204
4. 206
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Answer: (b) 202. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 93 + 4 × 4.
1. 372
2. 376
3. 384
4. 380
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Answer: (b) 376. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 89 + 9 × 9.
1. 810
2. 819
3. 828
4. 801
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Answer: (a) 810. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 71 + 9 × 9.
1. 648
2. 666
3. 657
4. 639
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Answer: (a) 648. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 101 + 3 × 3.
1. 303
2. 309
3. 306
4. 312
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Answer: (c) 306. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 35 + 9 × 9.
1. 315
2. 342
3. 333
4. 324
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Answer: (d) 324. Replace symbols first, then apply normal BODMAS.
If “+” means “×” and “×” means “+”, evaluate 109 + 2 × 2.
1. 218
2. 224
3. 220
4. 222
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Answer: (c) 220. Replace symbols first, then apply normal BODMAS.