If × stands for addition, ÷ stands for subtraction, + stands for multiplication, and − stands for division, then 7 × 3 ÷ 6 − 4 + 2 = ?
- (a)7
- (b)9
- (c)10
- (d)8
Answer
Why
Correct — A.
Rule: swap each sign for its meaning first, then apply BODMAS.
Substitute: 7 × 3 ÷ 6 − 4 + 2 becomes 7 + 3 − 6 ÷ 4 × 2
Divide: 6 ÷ 4 = 1.5
Multiply: 1.5 × 2 = 3
Add and subtract: 7 + 3 − 3 = 7 → option (a).
Why the others are wrong
- (b)9 — 9 would need 6 ÷ 4 × 2 to equal 1, since 7 + 3 − 1 = 9. Worked left to right it is 1.5 × 2 = 3, not 1.
- (c)10 — 10 is just 7 + 3. It drops the term 6 ÷ 4 × 2 = 3, which still has to be subtracted.
- (d)8 — 8 would need the division-and-multiplication term to be 2. It is 6 ÷ 4 = 1.5, then 1.5 × 2 = 3, so the result is 10 − 3 = 7.
Concept
Symbol substitution has two stages. First rewrite the expression with the real operations, sign by sign, before any arithmetic. Then evaluate with BODMAS: division and multiplication before addition and subtraction, each pair left to right.
Here × becomes +, ÷ becomes −, + becomes × and − becomes ÷. The division 6 ÷ 4 gives a decimal, 1.5, and the multiplication by 2 brings it back to a whole number.
Write the substituted expression out in full before solving, so you never do arithmetic on the old signs.
Key facts
- BODMAS: brackets, orders, division and multiplication, then addition and subtraction.
- Division and multiplication have equal priority and are done left to right.
- 6 ÷ 4 × 2 = 3 when worked left to right.
Study next
Common traps
- Doing the arithmetic on the original signs before substituting
- Working the substituted expression strictly left to right instead of doing division and multiplication first
19 Sep 2025, 09:00, Reasoning Q.9 swaps all four signs with a different key: 16 ÷ 2 − 4 + 3 × 5 becomes 16 × 2 ÷ 4 − 3 + 5 = 10, keyed b.
19 Sep 2025, 16:00, Reasoning Q.9 uses the same two stages with another sign key, and Q.8 with letters for the operations.
Related PYQs
No directly related past PYQ was found.