What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 125 ÷ 5 + 1809 × 9 – 14 = ?
- (a)348
- (b)438
- (c)483
- (d)384
Answer
Why
Correct — B. Rewrite the line with the swapped signs first, then apply BODMAS.
Rule: '+' becomes '−', '−' becomes '+', '×' becomes '÷' and '÷' becomes '×'.
125 ÷ 5 + 1809 × 9 − 14 rewrites as 125 × 5 − 1809 ÷ 9 + 14.
125 × 5 = 625
1809 ÷ 9 = 201
625 − 201 + 14 = 438 → option (b)
Why the others are wrong
- (a)348 — 348 would need 1809 ÷ 9 to come out as 291, and 9 × 291 = 2619, not 1809. Multiply a quotient back before you trust it.
- (c)483 — 483 would need the quotient to be 156, but 9 × 156 = 1404.
- (d)384 — 384 would need the quotient to be 255, and 9 × 255 = 2295 — nowhere near 1809.
Concept
One line is testing two separate skills.
First the substitution: rewrite the equation with the swapped signs before touching a number, because a swap applied halfway through is a swap applied wrongly.
Then the arithmetic, which here is a three-digit division. 1809 ÷ 9 = 201, and multiplying back is a two-second check.
The order of operations does not change when the symbols do, so × and ÷ are settled first and 625 − 201 + 14 is worked left to right at the end.
All four options are built from the digits 3, 4 and 8 in some order, so finding your answer on the list is no confirmation of anything.
Key facts
- After the swap the line reads 125 × 5 − 1809 ÷ 9 + 14.
- 1809 ÷ 9 = 201, confirmed by 9 × 201 = 1809.
- 625 − 201 + 14 = 438.
Study next
Common traps
- Swapping only one of the two pairs of signs.
- Trusting the division without multiplying the quotient back.
- Treating BODMAS as addition before subtraction, which turns the tail into 625 − 215 = 410.
The same pair of swaps — '+' with '−' and '×' with '÷' — is printed at 9 Sep 2024, 12:30, Reasoning Q.22 and at 9 Sep 2024, 16:00, Reasoning Q.17, each time on a line of five numbers joined by four signs.
Related PYQs
No directly related past PYQ was found.