If '+' means '×', '×' means '−', '−' means '÷', then 20 + 5 × 2 − 10 = ?
- (a)89
- (b)67
- (c)78.89
- (d)99.8
Answer
Why
Correct — D. Swap the signs first, then apply BODMAS.
Rule: + becomes ×, × becomes −, − becomes ÷.
20 + 5 × 2 − 10 becomes 20 × 5 − 2 ÷ 10
Multiply: 20 × 5 = 100
Divide: 2 ÷ 10 = 0.2
Subtract: 100 − 0.2 = 99.8
That is option (d).
Why the others are wrong
- (a)89 — 89 is a whole number, but the working takes 2 ÷ 10 = 0.2 away from 100, so the answer must end in .8.
- (b)67 — 67 is far below 100 − 0.2. Once + becomes ×, the expression starts from 20 × 5 = 100, and just 0.2 is subtracted.
- (c)78.89 — 78.89 has a .89 part that no step here produces. The one fraction in the working is 2 ÷ 10 = 0.2, and 100 − 0.2 = 99.8.
Concept
A sign-substitution item has two stages. First rewrite the expression with the new meanings, changing each sign once. Then evaluate it with BODMAS: division and multiplication before addition and subtraction.
Here the code turns 20 + 5 × 2 − 10 into 20 × 5 − 2 ÷ 10. The ÷ joins 2 and 10 before the subtraction happens, which is where the 0.2 comes from.
Working left to right after the swap gives (100 − 2) ÷ 10 = 9.8, which is not an option. That is the signal that the order of operations was skipped.
Key facts
- After substitution, 20 + 5 × 2 − 10 reads 20 × 5 − 2 ÷ 10.
- BODMAS does division and multiplication before subtraction.
- 20 × 5 − 2 ÷ 10 = 100 − 0.2 = 99.8.
Study next
Common traps
- Changing signs in a chain, so a + that became × is then turned into −.
- Working left to right after substituting, which gives 9.8.
The same three-sign code returns at 17 Sep 2025, 16:00, Reasoning Q.23, where 10 − 5 + 3 × 2 becomes 10 ÷ 5 × 3 − 2 = 4.
19 Sep 2025, 09:00, Reasoning Q.23 uses a four-sign code on 20 + 5 × 4 − 2 and also ends in a decimal, 17.5.
Related PYQs
No directly related past PYQ was found.