Find the two signs to interchange to correct the equation. 30 − 12 ÷ 3 × 2 + 4 = 122
- (a)÷ and −
- (b)− and ×
- (c)× and +
- (d)÷ and +
Answer
Why
Correct — B.
Rule: swap the two signs, rewrite the line, then solve it by BODMAS (÷ and × before + and −).
Swap − and ×: 30 × 12 ÷ 3 − 2 + 4
30 × 12 = 360
360 ÷ 3 = 120
120 − 2 + 4 = 122 ✓
The line balances → option (b).
Why the others are wrong
- (a)÷ and − — ÷ and − gives 30 ÷ 12 − 3 × 2 + 4 = 2.5 − 6 + 4 = 0.5, nowhere near 122.
- (c)× and + — × and + gives 30 − 12 ÷ 3 + 2 × 4 = 30 − 4 + 8 = 34, not 122.
- (d)÷ and + — ÷ and + gives 30 − 12 + 3 × 2 ÷ 4 = 30 − 12 + 1.5 = 19.5, not 122.
Concept
Read the printed line first: 30 − 12 ÷ 3 × 2 + 4 = 30 − 8 + 4 = 26, far short of 122.
A target that large needs a multiplication acting on a big number. Swapping − and × turns 30 − 12 into 30 × 12 = 360, and the rest of the line brings it down to 122. Estimating like this tells you which option to check first.
× and ÷ share a rank, so 30 × 12 ÷ 3 is 120 whichever you do first: 360 ÷ 3 and 30 × 4 both give 120.
Key facts
- BODMAS: brackets, then orders, then ÷ and × left to right, then + and − left to right.
- The printed line, 30 − 12 ÷ 3 × 2 + 4, equals 26.
- After the swap, 30 × 12 ÷ 3 − 2 + 4 = 122.
Study next
Common traps
- Working left to right without BODMAS, doing 30 − 12 before 12 ÷ 3
- Swapping the signs in your head instead of rewriting the whole line
10 Sep 2024, 09:00, Reasoning Q.16 asks the same question and keys the same pair, − and ×: 18 × 23 − 455 ÷ 7 + 28 = 414 − 65 + 28 = 377.
Related PYQs
No directly related past PYQ was found.