Select the number that will come in the place of the question mark(?), if ‘+’ and ‘ – ‘ are interchanged and ‘×’ and ‘÷’ are interchanged 11 ÷ 8 – 78 × 6 + 37 = ?

Correct — B. Rewrite the line with the symbols exchanged, then apply BODMAS to the new line.

Given: 11 ÷ 8 – 78 × 6 + 37
After swapping + with – and × with ÷: 11 × 8 + 78 ÷ 6 – 37

Divide first: 78 ÷ 6 = 13
Multiply: 11 × 8 = 88
Now left to right: 88 + 13 = 101
Then 101 – 37 = 64, which is option (b).

Why the others are wrong

• (a)
  62 — 62 would need 78 ÷ 6 to come out as 11 rather than 13. The division is exact — 78 ÷ 6 = 13 — so this falls two short.
• (c)
  58 — 58 would need 78 ÷ 6 read as 7, giving 88 + 7 – 37. The correct quotient is 13, so this misses by six.
• (d)
  71 — 71 requires either 11 × 8 taken as 95 or the 37 subtracted as 30. The swapped line says 88 + 13 – 37, and that is 64.

A symbol-interchange item has two separate steps and both are marked.

Step one is textual. Rewrite the expression with the symbols exchanged — 11 ÷ 8 – 78 × 6 + 37 becomes 11 × 8 + 78 ÷ 6 – 37. Write it out. Do not try to hold the swap in your head while calculating.

Step two is ordinary BODMAS on the new line: multiplication and division before addition and subtraction, then left to right.

The swap changes which operations carry priority, and that is the entire point of the question.

Key facts

• Swapping + with – and × with ÷ turns 11 ÷ 8 – 78 × 6 + 37 into 11 × 8 + 78 ÷ 6 – 37.
• In the rewritten line 11 × 8 = 88 and 78 ÷ 6 = 13, and 88 + 13 – 37 = 64.
• BODMAS is applied after the swap, never before it.

Common traps

• Applying BODMAS to the printed line and swapping the symbols afterwards
• Swapping only one of the two named pairs
• Working strictly left to right after the swap and losing the priority of × and ÷

No directly related past PYQ was found.