What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 304 × 19 − 101 + 23 ÷ 5 = ?

Correct — D.

Rule: rewrite the line with the signs swapped, then apply BODMAS to the new line.

Printed: 304 × 19 − 101 + 23 ÷ 5
After the swap: 304 ÷ 19 + 101 − 23 × 5

Divide first: 304 ÷ 19 = 16.
Multiply next: 23 × 5 = 115.

Now left to right: 16 + 101 = 117, then 117 − 115 = 2 → option (d).

Why the others are wrong

• (a)
  6 — 6 would need the closing subtraction to be 117 − 111. The swapped line has 23 × 5 = 115 in that slot, and 115 is fixed by the numbers as printed.
• (b)
  21 — 21 is 117 − 96. Nothing in the swapped line produces 96: the only product is 23 × 5 and the only quotient is 304 ÷ 19.
• (c)
  12 — 12 would require 117 − 105, which is the total you reach if the product is read as 21 × 5. Check the numbers as carefully as the signs.

Sign-swap items look like arithmetic and are really a copying test. The printed line is already solvable, which is the trap: candidates evaluate what they see and only afterwards remember the instruction.

Do the substitution on paper as a separate step. Rewrite the whole line with the new signs, then forget the original. BODMAS applies to the rewritten line only.

The numbers are chosen so the division comes out exact. 304 / 19 = 16 is the anchor here, and it tells you your swap was the right way round.

Key facts

• After the swap the line reads 304 ÷ 19 + 101 − 23 × 5.
• 304 ÷ 19 is exactly 16, because 19 × 16 = 304.
• 23 × 5 = 115, and 16 + 101 − 115 = 2.
• BODMAS is applied to the swapped line, never to the line as printed.

Common traps

• Evaluating the line as printed and swapping only at the end.
• Swapping plus and minus but leaving the multiplication and division signs alone.
• Working the swapped line left to right instead of doing division and multiplication first.

No directly related past PYQ was found.