The following equation is incorrect. Which two signs should be interchanged to correct the equation? 18 + 6 × 4 − 12 ÷ 3 = 17
- (a)+ and ×
- (b)× and ÷
- (c)+ and −
- (d)− and ÷
Answer
Why
Correct — D.
Rule: swap the two signs, then solve with BODMAS (× and ÷ before + and −).
Swap − and ÷: 18 + 6 × 4 ÷ 12 − 3
6 × 4 = 24, then 24 ÷ 12 = 2
18 + 2 = 20
20 − 3 = 17, the right-hand side → option (d).
Why the others are wrong
- (a)+ and × — Swapping + and × gives 18 × 6 + 4 − 12 ÷ 3 = 108 + 4 − 4 = 108, far from 17.
- (b)× and ÷ — Swapping × and ÷ gives 18 + 6 ÷ 4 − 12 × 3 = 18 + 1.5 − 36 = −16.5, not 17.
- (c)+ and − — Swapping + and − gives 18 − 6 × 4 + 12 ÷ 3 = 18 − 24 + 4 = −2, not 17.
Concept
In a sign-swap question the numbers stay where they are and two signs trade places. Rewrite the equation with the swap, then work it out in BODMAS order: × and ÷ from left to right first, then + and − from left to right.
As printed, the left side is 18 + 24 − 4 = 38, not 17, so a swap is needed.
A quick estimate narrows the search. The target, 17, is just below the first number, 18, so everything after 18 must come to −1. After the swap it does: + 2 − 3 = −1.
Key facts
- BODMAS: × and ÷ first, left to right, then + and −.
- As printed, the left side comes to 38.
- Swapping − and ÷ gives 18 + 6 × 4 ÷ 12 − 3 = 17.
Study next
Common traps
- Working strictly left to right without BODMAS, e.g. adding 18 + 6 before multiplying
- Moving the numbers along with the signs, instead of keeping every number in place
19 Sep 2025, 09:00, Reasoning Q.8 asks the same: 97 × 23 − 18 + 9 ÷ 3 = 66 balances when × and + swap (keyed a).
17 Sep 2025, 12:30, Reasoning Q.5 balances 30 − 12 ÷ 3 × 2 + 4 = 122 by swapping − and × (keyed b).
Related PYQs
No directly related past PYQ was found.