What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘–‘ are interchanged and ‘×’ and ‘÷’ are interchanged? 25 + 3 ÷ 9 −14 × 2 = ?
- (a)5
- (b)7
- (c)12
- (d)0
Answer
Why
Correct — A. Rewrite the line with the symbols swapped, then apply BODMAS to what you have written.
Swap + with − throughout, and swap × with ÷ throughout.
So 25 + 3 ÷ 9 − 14 × 2 rewrites as 25 − 3 × 9 + 14 ÷ 2.
3 × 9 = 27
14 ÷ 2 = 7
25 − 27 = −2
−2 + 7 = 5 → option (a)
Why the others are wrong
- (b)7 — 7 is 14 ÷ 2 standing on its own. It survives only if 25 − 3 × 9 is taken as zero instead of −2.
- (c)12 — 12 is 25 − 27 + 14, which stops one step early. The swapped line still carries ÷ 2 on that last term.
- (d)0 — 0 is 25 − 27 + 2, which uses the bare 2 rather than 14 ÷ 2 = 7.
Concept
The instruction changes the symbols, not the numbers and not their order. Rewrite the line first — the rewriting is the question, and the arithmetic that follows is ordinary.
On the rewritten line, multiplication and division come first, left to right, and only then addition and subtraction. Skipping the rewrite and swapping mentally as you go is where most marks are lost.
This line goes negative in the middle. 25 − 27 is −2, and the +7 that follows brings it back to 5 — a step candidates often drop by treating the total as a magnitude.
Key facts
- The swapped line is 25 − 3 × 9 + 14 ÷ 2.
- Multiplication and division are done before addition and subtraction on that line.
- 25 − 27 + 7 = 5.
Study next
Common traps
- Working left to right and never applying BODMAS.
- Swapping the numbers instead of the symbols.
- Dropping the sign when 25 − 27 turns negative.
The same double swap is set at 09 Sep 2024, 09:00, Reasoning Q.1 (4515 × 5 − 431 ÷ 3 + 821) and again at 23 Sep 2024, 09:00, Reasoning Q.4 (63 × 7 ÷ 13 − 64 + 42).
Related PYQs
No directly related past PYQ was found.