If '+' means '×', '×' means '−', '−' means '÷', then 10 − 5 + 3 × 2 = ?
- (a)1
- (b)2
- (c)3
- (d)4
Answer
Why
Correct — D.
Rule: swap every symbol first, then apply BODMAS.
10 − 5 + 3 × 2 becomes 10 ÷ 5 × 3 − 2
Divide: 10 ÷ 5 = 2
Multiply: 2 × 3 = 6
Subtract: 6 − 2 = 4 → option (d).
Why the others are wrong
- (a)1 — 1 is not reachable once the swaps are right. 10 ÷ 5 × 3 is 6, and the expression then subtracts just 2, leaving 4.
- (b)2 — 2 comes from subtracting first: 3 − 2 = 1, then 10 ÷ 5 × 1 = 2. BODMAS does the × before the −, giving 6 − 2.
- (c)3 — 3 comes from turning the last '×' into '÷': 10 ÷ 5 × 3 ÷ 2 = 3. The key sends '×' to '−', and it is '−' that becomes '÷'.
Concept
A symbol-substitution item tests two things in order. First, rewrite the whole expression with the new meanings, symbol by symbol, before calculating anything.
Second, evaluate the rewritten expression by BODMAS: division and multiplication before addition and subtraction, and within each pair, left to right.
Convert every symbol from the original expression in one pass. The swaps chain (+ becomes ×, and × becomes −), so re-reading a symbol you have already converted turns + into − by mistake.
Key facts
- Key for this item: + → ×, × → −, − → ÷.
- BODMAS: ÷ and × first, left to right, then + and −.
- 10 ÷ 5 × 3 is (10 ÷ 5) × 3 = 6, not 10 ÷ 15.
Study next
Common traps
- Doing the subtraction before the multiplication, which gives 2
- Evaluating 10 ÷ 5 × 3 as 10 ÷ 15
- Converting a symbol twice because the swaps chain (+ → × → −)
14 Sep 2025, 12:30, Reasoning Q.24 uses the identical three swaps on 20 + 5 × 2 − 10, which becomes 20 × 5 − 2 ÷ 10 = 100 − 0.2, keyed 99.8.
19 Sep 2025, 09:00, Reasoning Q.23 redefines all four signs: 20 + 5 × 4 − 2 becomes 20 − 5 ÷ 4 × 2 = 17.5, the keyed answer.
Related PYQs
No directly related past PYQ was found.