If '+' means '÷', '−' means '×', '×' means '+', and '÷' means '−', then 18 + 6 − 2 × 3 = ?
- (a)9
- (b)6
- (c)5
- (d)15
Answer
Why
Correct — A.
Rule: swap each sign for its meaning, then apply BODMAS.
18 + 6 − 2 × 3 becomes 18 ÷ 6 × 2 + 3
Divide: 18 ÷ 6 = 3
Multiply: 3 × 2 = 6
Add: 6 + 3 = 9 → option (a).
Why the others are wrong
- (b)6 — 6 is where the working stands one step early: 18 ÷ 6 × 2 = 6. The swapped expression still ends + 3, which makes 9.
- (c)5 — 5 fits neither order of the ÷ and ×. Left to right gives 9, and 18 ÷ (6 × 2) + 3 gives 1.5 + 3 = 4.5.
- (d)15 — 15 is 3 × (2 + 3): it adds before multiplying. BODMAS takes 3 × 2 = 6 first and then adds 3, giving 9.
Concept
When all four signs are redefined, rewrite the full expression before calculating. Swapping as you go makes it easy to swap a sign twice or not at all.
After the swap, BODMAS applies as usual: ÷ and × first, left to right, then + and −.
Here that means 18 ÷ 6 = 3, then 3 × 2 = 6, and then + 3 = 9.
Key facts
- Here + means ÷, − means ×, × means + and ÷ means −.
- 18 + 6 − 2 × 3 becomes 18 ÷ 6 × 2 + 3 = 9.
- ÷ and × are worked left to right before any + or −.
Study next
Common traps
- Adding 2 + 3 before multiplying, which gives 3 × 5 = 15.
- Stopping at 18 ÷ 6 × 2 = 6 and forgetting the + 3.
17 Sep 2025, 16:00, Reasoning Q.23 runs the same routine on 10 − 5 + 3 × 2, which becomes 10 ÷ 5 × 3 − 2, keyed 4.
15 Sep 2025, 09:00, Reasoning Q.20 swaps the signs with a different table: 7 × 3 ÷ 4 + 20 − 5 becomes 7 − 3 + 4 ÷ 20 × 5, keyed 5.
Related PYQs
No directly related past PYQ was found.