Which number will come in the place of the question mark (?) in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 27 × 3 + 4 ÷ 2 − 7 = ?

Correct — D. Rewrite the line with the symbols exchanged before computing anything. Every + becomes a −, every − becomes a +, every × becomes a ÷ and every ÷ becomes a ×.

27 × 3 + 4 ÷ 2 − 7
becomes 27 ÷ 3 − 4 × 2 + 7

Rule: apply BODMAS to the rewritten line, not left to right.

27 ÷ 3 = 9
4 × 2 = 8
9 − 8 + 7 = 8

The value is 8 — option (d).

Why the others are wrong

• (a)
  10 — 10 is the value of the line with only × and ÷ swapped: 27 ÷ 3 + 4 × 2 − 7 comes to 9 + 8 − 7. The stem exchanges the plus and the minus as well.
• (b)
  9 — 9 is 27 ÷ 3 and nothing further. The rest of the rewritten line still has to be settled: − 4 × 2 takes eight away and + 7 puts seven back.
• (c)
  6 — 6 appears if the tail is read as one bracketed lump, 9 − (8 + 7) = −6, and the minus sign is then dropped. The rewritten line carries no bracket, so the + 7 stands on its own.

Two things happen in this item and candidates routinely do only one.

First, rewrite the line with the symbols exchanged. Do it on paper — the rewritten line is the real question, and holding the swap in your head while evaluating the original is where the marks go.

Second, evaluate that line by BODMAS rather than left to right. Division and multiplication are settled before addition and subtraction, so 27 ÷ 3 and 4 × 2 are computed first and only then combined.

Key facts

• After the interchange the line reads 27 ÷ 3 − 4 × 2 + 7.
• BODMAS settles 27 ÷ 3 = 9 and 4 × 2 = 8 before any addition or subtraction.
• 9 − 8 + 7 = 8, the keyed value.

Common traps

• Exchanging one pair of symbols and forgetting the other pair
• Evaluating the rewritten line strictly left to right
• Treating everything after the minus sign as a single bracketed quantity

No directly related past PYQ was found.