If '+' means '×', '−' means '÷', '×' means '+', then 4 − 2 × 3 + 6 = ?
- (a)12
- (b)6
- (c)5
- (d)20
Answer
Why
Correct — D.
Rule: '+' → ×, '−' → ÷, '×' → +, then BODMAS.
4 − 2 × 3 + 6
→ 4 ÷ 2 + 3 × 6
Division: 4 ÷ 2 = 2
Multiplication: 3 × 6 = 18
Addition: 2 + 18 = 20 → option (d).
Why the others are wrong
- (a)12 — 12 comes from converting only the '−': 4 ÷ 2 × 3 + 6 = 6 + 6. The '×' and '+' must change too, giving 4 ÷ 2 + 3 × 6 = 20.
- (b)6 — 6 is smaller than the product 3 × 6 = 18 inside the rewritten expression. Adding 4 ÷ 2 = 2 to 18 cannot give less than 18.
- (c)5 — 5 is 4 ÷ 2 + 3, adding the 3 before it is multiplied. BODMAS multiplies first: 3 × 6 = 18, then 2 + 18 = 20.
Concept
This is a three-sign substitution: no meaning is given for '÷' and none is needed, since '÷' does not appear. Rewrite every sign before calculating.
The printed 4 − 2 × 3 + 6 becomes 4 ÷ 2 + 3 × 6. BODMAS then works the division and the multiplication before the addition.
Working left to right instead gives (4 ÷ 2 + 3) × 6 = 30, which no option prints.
Key facts
- Here '+' means ×, '−' means ÷ and '×' means +.
- 4 − 2 × 3 + 6 rewrites to 4 ÷ 2 + 3 × 6 = 20.
- Worked left to right without BODMAS, the same rewrite gives 30.
Study next
Common traps
- Converting the '−' but leaving '×' and '+' as printed, which gives 12
- Evaluating left to right after substituting
13 Sep 2024, 16:00, Reasoning Q.17 sets a similar substitution by interchanging '+' with '×' and '−' with '÷': 27 − 6 + 4 × 8 ÷ 6 becomes 27 ÷ 6 × 4 + 8 − 6, keyed 20.
Related PYQs
No directly related past PYQ was found.