What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 1205 × 5 + 35 – 197 ÷ 18 = ?

Correct — C. Rewrite the line with the swaps on paper before calculating anything.

Rule: every + becomes −, every − becomes +, every × becomes ÷ and every ÷ becomes ×.

1205 × 5 + 35 − 197 ÷ 18 becomes 1205 ÷ 5 − 35 + 197 × 18.

Now apply BODMAS to the new line:
1205 ÷ 5 = 241
197 × 18 = 3546
241 − 35 + 3546 = 206 + 3546 = 3752 → option (c)

Why the others are wrong

• (a)
  3284 — 3284 would require the product 197 × 18 to be 3078. It is 3546, and the swapped line worked straight through gives 241 − 35 + 3546 = 3752.
• (b)
  3482 — 3482 would require the product 197 × 18 to be 3276. It is 3546, and the swapped line gives 241 − 35 + 3546 = 3752.
• (d)
  3824 — Adding the 35 instead of subtracting it gives 241 + 35 + 3546 = 3822, and 3824 is not even that. After the swap, the + printed before 35 has become a −.

Symbol-interchange questions test order of operations twice over. First rewrite the expression with the swaps physically in place, because doing the substitution in your head one operator at a time is where the marks go.

Then apply BODMAS to the new line and not to the printed one. Division and multiplication are settled before addition and subtraction, and a subtraction followed by an addition is worked from left to right.

The swap is stated in the stem, never marked on the expression, so the rewrite is always your job.

Key facts

• After the swap the line reads 1205 ÷ 5 − 35 + 197 × 18.
• 1205 ÷ 5 = 241 and 197 × 18 = 3546.
• Under BODMAS the swapped line evaluates to 241 − 35 + 3546 = 3752.

Common traps

• Swapping the operators correctly and then evaluating from left to right
• Swapping one pair of operators and forgetting the other pair

No directly related past PYQ was found.