If '×' means '−', '−' means '+', '+' means '÷', then 12 + 6 × 2 − 4 = ?
- (a)4
- (b)8
- (c)6
- (d)10
Answer
Why
Correct — A.
Rule: swap the symbols first, then apply BODMAS.
'×' → '−', '−' → '+', '+' → '÷'
12 + 6 × 2 − 4 becomes 12 ÷ 6 − 2 + 4
Division first: 12 ÷ 6 = 2
Then left to right: 2 − 2 + 4 = 4 → option (a).
Why the others are wrong
- (b)8 — 8 is 2 + 2 + 4, treating the × as +. The rule turns × into −, so the middle step is 2 − 2.
- (c)6 — 6 is 2 + 4, leaving out the − 2 that the × becomes. Every symbol must be swapped before you calculate.
- (d)10 — 10 does not come out of 12 ÷ 6 − 2 + 4 in any order of working. Division first gives 2, and 2 − 2 + 4 = 4.
Concept
A symbol-substitution item gives the operations new signs. Rewrite the whole expression with the real operations before doing any arithmetic, then follow the usual order: division and multiplication before addition and subtraction.
Here the rewrite is 12 ÷ 6 − 2 + 4. Calculating while still swapping symbols mixes old and new signs.
The mapping is one-way. '−' means '+', but that does not make '+' mean '−': the question says '+' means '÷'.
Key facts
- After substitution: 12 ÷ 6 − 2 + 4.
- Division comes before addition and subtraction: 12 ÷ 6 = 2.
- Addition and subtraction then run left to right: 2 − 2 + 4 = 4.
Study next
Common traps
- Reading the mapping both ways: − means +, but + means ÷
- Working the original expression before swapping, which leaves the old signs in play
13 Sep 2025, 12:30, Reasoning Q.25 swaps + and − and turns × into ÷: 50 − 10 + 5 ÷ 5 = 41.
19 Sep 2025, 16:00, Reasoning Q.23 uses × for +, + for − and − for ÷: 8 + 4 − 2 ÷ 2 = 11.
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