"If the given symbols mean: '+' means 'divided by' '−' means 'multiplied by' '×' means 'minus' '÷' means 'plus' Then, find the value of the following expressions: 12 + 3 − 8 × 2 ÷ 1=?
- (a)17
- (b)31
- (c)46
- (d)67
Answer
Why
Correct — B.
Rule: replace every symbol first, then apply BODMAS.
Map: + → ÷, − → ×, × → −, ÷ → +
12 + 3 − 8 × 2 ÷ 1 becomes 12 ÷ 3 × 8 − 2 + 1
Divide: 12 ÷ 3 = 4
Multiply: 4 × 8 = 32
Subtract: 32 − 2 = 30
Add: 30 + 1 = 31 → option (b).
Why the others are wrong
- (a)17 — 17 would need 12 ÷ 3 × 8 to equal 18. It equals 4 × 8 = 32, and 32 − 2 + 1 = 31.
- (c)46 — 46 would need 12 ÷ 3 × 8 to equal 47. It equals 4 × 8 = 32, and 32 − 2 + 1 = 31.
- (d)67 — 67 would need 12 ÷ 3 × 8 to equal 68. It equals 4 × 8 = 32, and 32 − 2 + 1 = 31.
Concept
Symbol-substitution items redefine the operators. Rewrite the whole expression with the new meanings before any arithmetic, then follow BODMAS: division and multiplication left to right, then addition and subtraction.
Write the mapping out once: + → ÷, − → ×, × → −, ÷ → +. Converting from a written map stops a symbol being converted twice or left as printed.
Calculating with the printed symbols gives 12 + 3 − 16 = −1, which is not an option: a sign the swap has not been made.
Key facts
- BODMAS: division and multiplication left to right, then addition and subtraction left to right.
- Under this legend × means minus and ÷ means plus.
- Convert every symbol in one pass before calculating.
Study next
Common traps
- Converting × to − and then converting that − again to ×
- Doing 3 × 8 before 12 ÷ 3, which turns 12 ÷ 3 × 8 into 12 ÷ 24
15 Sep 2025, 12:30, Reasoning Q.23 uses the same four-symbol legend: 48 × 8 ÷ 12 + 4 − 7 becomes 48 − 8 + 12 ÷ 4 × 7 = 61 (keyed d).
Related PYQs
No directly related past PYQ was found.