Mathematical Operations Quiz: Reasoning Practice
10 timed questions on symbol substitution, BODMAS, sign interchange, choosing signs and hidden-rule operations like a # b. Each solved step by step.
Mathematical Operations Quiz: Reasoning Practice
Tip: use keys 1-4 to answer, Enter for next.
Answers to the starter quiz
Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.
If + means ×, × means −, − means ÷ and ÷ means +, find the value of 18 − 6 + 4 ÷ 3 × 5.
- 12
- 8
- 10
- 14
Answer: 10. Substitute first: 18 ÷ 6 × 4 + 3 − 5. Then BODMAS: 3 × 4 = 12, and 12 + 3 − 5 = 10.
If P means +, Q means −, R means × and S means ÷, find 24 S 4 P 6 R 3 Q 5.
- 19
- 21
- 17
- 13
Answer: 19. It becomes 24 ÷ 4 + 6 × 3 − 5 = 6 + 18 − 5 = 19.
Which two signs must be interchanged to make this equation correct? 16 × 4 + 3 ÷ 2 − 5 = 5
- + and −
- × and +
- ÷ and −
- × and ÷
Answer: × and ÷. Swapping × and ÷ gives 16 ÷ 4 + 3 × 2 − 5 = 4 + 6 − 5 = 5. The other swaps give 67.5, 17 and 66.6.
If 3 # 4 = 25 and 5 # 12 = 169, then 6 # 8 = ?
- 196
- 100
- 48
- 14
Answer: 100. a # b = a² + b²: 9 + 16 = 25 and 25 + 144 = 169. So 36 + 64 = 100.
If 7 $ 3 = 46 and 5 $ 2 = 23, then 9 $ 4 = ?
- 81
- 85
- 77
- 72
Answer: 77. a $ b = a² − b: 49 − 3 = 46 and 25 − 2 = 23. So 81 − 4 = 77.
If '×' means addition, '÷' means subtraction, '+' means multiplication and '−' means division, find 20 × 8 ÷ 8 − 4 + 2.
- 24
- 26
- 20
- 28
Answer: 24. It becomes 20 + 8 − 8 ÷ 4 × 2. Division and multiplication first: 8 ÷ 4 × 2 = 4. Then 20 + 8 − 4 = 24.
Choose the signs, in order, to fill the blanks: 12 _ 4 _ 3 _ 5 = 4
- ×, ÷, −
- ÷, +, −
- −, ×, ÷
- ÷, ×, −
Answer: ÷, ×, −. 12 ÷ 4 × 3 − 5 = 9 − 5 = 4. The others give 11, 1 and 9.6.
If 4 → 18 and 6 → 38 under the same rule, then 9 → ?
- 81
- 83
- 85
- 79
Answer: 83. The rule is n² + 2: 16 + 2 = 18 and 36 + 2 = 38. So 81 + 2 = 83.
If 2 @ 3 = 10 and 4 @ 5 = 36, then 6 @ 7 = ?
- 91
- 84
- 72
- 78
Answer: 78. a @ b = a × (a + b): 2 × 5 = 10 and 4 × 9 = 36. So 6 × 13 = 78.
If 'A' means '÷', 'B' means '+', 'C' means '×' and 'D' means '−', find 36 A 6 C 3 B 4 D 2.
- 18
- 22
- 20
- 16
Answer: 20. It becomes 36 ÷ 6 × 3 + 4 − 2. Left to right for ÷ and ×: 6 × 3 = 18. Then 18 + 4 − 2 = 20.
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