Which number will come in the place of the question mark (?) in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 14 − 45 × 5 + 6 ÷ 3 = ?

Correct — A. Rule: every + becomes -, every - becomes +, every x becomes ÷ and every ÷ becomes x, applied to the printed line before any arithmetic.

14 - 45 x 5 + 6 ÷ 3 becomes 14 + 45 ÷ 5 - 6 x 3.

45 ÷ 5 = 9
6 x 3 = 18
14 + 9 = 23
23 - 18 = 5

So the question mark stands for 5, which is option (a).

Why the others are wrong

• (b)
  3 — 3 comes out of no reading of the line. Swap only + and - and the value is 237; swap only x and ÷ and it is 23. Neither slip produces 3.
• (c)
  4 — 4 appears nowhere in the working. Both sub-results are exact — 45 ÷ 5 = 9 and 6 x 3 = 18 — so 14 + 9 - 18 leaves no room for 4.
• (d)
  6 — 6 sits one above the answer and is there to catch an unfinished line. Complete it: 14 + 9 = 23, then 23 - 18 = 5.

An operator-interchange item has two separate jobs, and only the second is arithmetic.

Job one is rewriting. Apply the swaps the question names to every occurrence of each sign, and write the new line out rather than holding it in your head.

Job two is evaluation, under BODMAS. Division and multiplication resolve first, then the additions and subtractions run left to right.

Key facts

• The instruction swaps signs in pairs, + with - and x with ÷, across the whole expression.
• After the swap the line reads 14 + 45 ÷ 5 - 6 x 3.
• Under BODMAS the division and multiplication resolve first to 9 and 18, giving 14 + 9 - 18 = 5.

Common traps

• Swapping + with x instead of the pairs the question actually names.
• Evaluating the rewritten line left to right instead of by BODMAS.
• Applying the swap to only the first occurrence of each sign.

No directly related past PYQ was found.