What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 4515 × 5 – 431 ÷ 3 + 821 = ?

Correct — D. Change the operators first, then evaluate the new expression by BODMAS.

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

4515 × 5 – 431 ÷ 3 + 821
becomes 4515 ÷ 5 + 431 × 3 – 821
= 903 + 1293 – 821
= 2196 – 821 = 1375 → option (d)

Why the others are wrong

• (a)
  1335 — 1335 would need the last step to read 2196 − 861. The expression subtracts 821, and 2196 − 821 is 1375.
• (b)
  1775 — 1775 would need 2196 − 421. The 8 in 821 is not a 4, so the final subtraction is 821, not 421.
• (c)
  1575 — 1575 demands a running total of 2396 before the subtraction. The two swapped terms give 903 + 1293 = 2196, so 1575 cannot appear.

The instruction changes the operators only. The numbers, and the order they sit in, do not move.

Rewrite the whole line with the new signs before you calculate anything. Trying to hold the swap in your head while computing is where most marks are lost here.

Then apply BODMAS to the rewritten line: division and multiplication are settled first, left to right, and only then the additions and subtractions.

Key facts

• After the swap the line reads 4515 ÷ 5 + 431 × 3 – 821.
• 4515 ÷ 5 = 903 and 431 × 3 = 1293 are the two terms that decide the question.
• BODMAS puts ÷ and × before + and −, whatever order they appear in.

Common traps

• Working left to right after the swap instead of doing ÷ and × first
• Swapping only one of the two pairs of operators
• Rewriting the numbers in a new order along with the signs

No directly related past PYQ was found.