What will come in place of the question mark (?) in the following equation if ‘÷’ and ‘−’ are interchanged and ‘×’ and ‘+’ are interchanged? 2 × 16 ÷ 36 + 42 − 6 = ?

Correct — C. Rule: swap the symbols first, then apply BODMAS to the new line. Here division trades with subtraction, and multiplication trades with addition.

2 × 16 ÷ 36 + 42 − 6
becomes 2 + 16 − 36 × 42 ÷ 6

Multiplication and division first, left to right.
36 × 42 = 1512
1512 ÷ 6 = 252

Then addition and subtraction, left to right.
2 + 16 = 18
18 − 252 = −234 — option (c)

Why the others are wrong

• (a)
  −280 — The multiply-divide block is 252, not 298. Since 36 × 42 = 1512 and 1512 ÷ 6 = 252, the line lands on 18 − 252, which is −234.
• (b)
  −246 — 264 is not reachable here. After the swap the only product available is 36 × 42 = 1512, and dividing by 6 gives 252, so the running total 18 is reduced by 252.
• (d)
  −216 — −216 is 18 nearer zero than it should be. The sum 2 + 16 = 18 has to be reduced by the full block of 252, and 18 − 252 = −234.

Symbol-interchange questions test two things at once: whether you rewrite the expression before computing, and whether you then apply BODMAS to the rewritten line rather than working left to right.

Write the new expression out in full. Doing the swap in your head, one operator at a time, is where the marks go.

Note which pairs are swapped. Here it is division with subtraction and multiplication with addition, not the commoner plus-with-minus and times-with-divide.

Key facts

• After the swap the line reads 2 + 16 − 36 × 42 ÷ 6.
• 36 × 42 = 1512, and 1512 ÷ 6 = 252.
• BODMAS applies to the rewritten line, so the product and quotient are settled before the addition.

Common traps

• Applying BODMAS to the printed line and swapping the symbols afterwards
• Working the rewritten line strictly left to right instead of settling multiplication and division first

No directly related past PYQ was found.