If + = ÷, − = ×, ÷ = +, × = −; then 36 + 6 − 2 × 3 = ?
- (a)6
- (b)15
- (c)13
- (d)9
Answer
Why
Correct — D.
Rule: swap each sign as told (+ → ÷, − → ×, ÷ → +, × → −), then apply BODMAS.
36 + 6 − 2 × 3 becomes
36 ÷ 6 × 2 − 3
36 ÷ 6 = 6, then 6 × 2 = 12
12 − 3 = 9 → option (d)
Why the others are wrong
- (a)6 — 6 is just 36 ÷ 6, the first step. The substituted expression still has × 2 and − 3 to apply: 6 × 2 − 3 = 9.
- (b)15 — 15 is 12 + 3: it keeps the last sign as plus. The stem defines × = −, so the last step is 12 − 3 = 9.
- (c)13 — 13 does not appear at any step of the substituted expression: 36 ÷ 6 = 6, 6 × 2 = 12, 12 − 3 = 9.
Concept
Symbol substitution is rewrite, then evaluate. Change every sign using the key before doing any arithmetic, because the printed signs do not mean what they usually mean.
After the swap, BODMAS applies: ÷ and × first, left to right, then + and −.
36 ÷ 6 × 2 is (36 ÷ 6) × 2 = 12, not 36 ÷ 12 = 3.
Key facts
- Here + means ÷, − means ×, ÷ means + and × means −.
- 36 ÷ 6 × 2 − 3 = 12 − 3 = 9.
- Equal-rank signs (÷ and ×) are worked left to right.
Study next
Common traps
- Grouping 6 × 2 first: 36 ÷ 12 − 3 = 0, which no option offers.
- Substituting some signs and forgetting others, such as leaving × as multiply.
Reasoning Q.23 of this paper uses the same four swaps on 8 ÷ 2 × 3 + 18 − 6, also keyed 9, and 15 Sep 2025, 12:30, Reasoning Q.23 uses them on 48 × 8 ÷ 12 + 4 − 7, keyed 61.
Related PYQs
No directly related past PYQ was found.