If '×' = '−', '−' = '+', '/' = '×', '+' = '÷', which equation is correct?
- (a)12 × 4 − 2 + 8 / 4 = 11
- (b)18 − 6 × 3 + 2 / 2 = 13
- (c)14 + 7 − 3 / 2 × 1 = 16
- (d)20 − 4 + 8 / 2 × 1 = 20
Answer
Why
Correct — D.
Rule: swap × → −, − → +, / → ×, + → ÷, then apply BODMAS.
Option (d): 20 − 4 + 8 / 2 × 1 becomes 20 + 4 ÷ 8 × 2 − 1
Divide: 4 ÷ 8 = 0.5
Multiply: 0.5 × 2 = 1
Then: 20 + 1 − 1 = 20 ✓
The left side equals the stated 20 → option (d).
Why the others are wrong
- (a)12 × 4 − 2 + 8 / 4 = 11 — 12 × 4 − 2 + 8 / 4 becomes 12 − 4 + 2 ÷ 8 × 4. Since 2 ÷ 8 × 4 = 1, it equals 9, not 11.
- (b)18 − 6 × 3 + 2 / 2 = 13 — 18 − 6 × 3 + 2 / 2 becomes 18 + 6 − 3 ÷ 2 × 2. Since 3 ÷ 2 × 2 = 3, it equals 21, not 13.
- (c)14 + 7 − 3 / 2 × 1 = 16 — 14 + 7 − 3 / 2 × 1 becomes 14 ÷ 7 + 3 × 2 − 1 = 2 + 6 − 1, which is 7, not 16.
Concept
In a which-equation-is-correct item, convert each option's left side with the new meanings, evaluate it by BODMAS, and compare it with the number on the right.
Here / stands for ×, while the printed × now means −. Write the four swaps once before touching any option, so no symbol is converted twice.
Option (d) passes through a fraction, 4 ÷ 8 = 0.5, before landing on a whole number. A fraction mid-way is not a sign of a wrong option.
Key facts
- Under this legend / means × and × means −.
- Division and multiplication run left to right: 4 ÷ 8 × 2 = 1.
- Only the left side is converted, and the number after = is the target.
Study next
Common traps
- Doing × before ÷ in 4 ÷ 8 × 2, which gives 4 ÷ 16 = 0.25 and makes (d) look false
- Rejecting an option because a step produces a fraction
15 Sep 2025, 12:30, Reasoning Q.24 uses the identical legend and keys 16 / 2 + 4 − 1 × 3 = 6, which becomes 16 × 2 ÷ 4 + 1 − 3 = 6 (keyed c).
Related PYQs
No directly related past PYQ was found.