If + = ×, − = +, × = ÷; then 10 + 2 − 4 × 2 = ?
- (a)10
- (b)19
- (c)22
- (d)24
Answer
Why
Correct — C. Rule: replace each sign as told, then apply BODMAS.
Printed: 10 + 2 − 4 × 2
Substituted: 10 × 2 + 4 ÷ 2
Division and multiplication first: 4 ÷ 2 = 2, 10 × 2 = 20
Then addition: 20 + 2 = 22 → option (c)
Why the others are wrong
- (a)10 — 10 is not the value of 10 × 2 + 4 ÷ 2 under BODMAS, which gives 22, or under strict left-to-right working, which gives 12.
- (b)19 — 19 matches no order of working: BODMAS gives 22 and left to right gives 12. After substitution the expression has no − sign at all, since − became +.
- (d)24 — 24 is 10 × 2 + 4 with the ÷ 2 dropped. The printed × became ÷, so 4 ÷ 2 = 2 is added, not 4.
Concept
A sign-substitution item has two stages: swap every sign by the table, then evaluate the new expression under BODMAS.
Write the substituted line out in full before calculating. Here + becomes ×, − becomes + and × becomes ÷, so all three printed signs change.
Division and multiplication share a rank and come before addition, so 4 ÷ 2 is worked before it is added to 20.
Working strictly left to right gives (10 × 2 + 4) ÷ 2 = 12, which is not an option. BODMAS, not reading order, decides the value.
Key facts
- Here + stands for ×, − for + and × for ÷.
- 10 × 2 + 4 ÷ 2 = 20 + 2 = 22.
- × and ÷ are worked before + and −.
Study next
Common traps
- Leaving × unconverted, which gives 10 × 2 + 4 × 2 = 28.
- Working left to right, which gives (20 + 4) ÷ 2 = 12.
The same three substitutions are set at 14 Sep 2025, 09:00, Reasoning Q.25, where 6 + 3 − 2 × 1 becomes 6 × 3 + 2 ÷ 1 = 20.
Related PYQs
No directly related past PYQ was found.