What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 99 ÷ 41 + 208 × 2 – 35 = ?

Correct — A. Rewrite the line with the symbols swapped, then apply BODMAS to the new line.

Given: 99 ÷ 41 + 208 × 2 − 35
Swapped: 99 × 41 − 208 ÷ 2 + 35

99 × 41 = 4059 (100 × 41 = 4100, less 41)
208 ÷ 2 = 104
4059 − 104 = 3955
3955 + 35 = 3990 → option (a)

Why the others are wrong

• (b)
  3390 — 3390 falls 600 short. It needs the product 99 × 41 to come out as 3459; the product is 4059, and the rest of the line only takes away 104 and adds 35.
• (c)
  3890 — 3890 follows if 208 ÷ 2 is read as 204 instead of 104 — a dropped hundreds digit. 4059 − 204 + 35 = 3890.
• (d)
  3980 — 3980 needs 99 × 41 to be 4049. It is 4059: 100 × 41 is 4100, and you take away 41, not 51.

An interchange item tests two things, and candidates usually lose it on the second.

Step one is mechanical: rewrite the whole line with every symbol replaced. Do it on paper — reading the swap while you calculate is where the near-miss answers come from.

Step two is BODMAS on the rewritten line. Division and multiplication are settled before addition and subtraction, whatever order they are printed in. The swap changes which symbols sit where; it does not change the order of operations.

Key facts

• After the swap the line reads 99 × 41 − 208 ÷ 2 + 35.
• 99 × 41 = 4059, most quickly as 100 × 41 = 4100 minus 41.
• Multiplication and division outrank addition and subtraction in the rewritten line.

Common traps

• Working the rewritten line left to right instead of applying BODMAS.
• Swapping only one of the two pairs, which gives 4128 here.
• Calculating on the original line and then trying to adjust the answer afterwards.

No directly related past PYQ was found.