What will come in place of the question mark (?) in the following equation if ‘+’ and ‘÷’ are interchanged and ‘×’ and ‘–’ are interchanged? 4 − 12 + 3 ÷ 12 × 6 = ?

Correct — D.

Rule: + becomes ÷ and ÷ becomes +; × becomes − and − becomes ×. Rewrite every sign, then apply BODMAS.

4 − 12 + 3 ÷ 12 × 6 becomes 4 × 12 ÷ 3 + 12 − 6.

4 × 12 = 48
48 ÷ 3 = 16
16 + 12 = 28
28 − 6 = 22

That is option (d).

Why the others are wrong

• (a)
  11 — The substituted line runs 48, 16, 28, 22. Eleven appears at no stage of it, and halving a total is not one of the operations the swap produces.
• (b)
  46 — Swapping only × and − leaves 4 × 12 + 3 ÷ 12 − 6, which comes to 42.25 — not even a whole number, so that half-done swap does not reach 46 either.
• (c)
  13 — Thirteen would need the line to finish below 16, but after 4 × 12 ÷ 3 = 16 the remaining steps add 12 and subtract 6, a net gain that can only raise the total.

An interchange item is a rewrite, not a mental trick. Change every occurrence of both pairs, write the new line down, and evaluate only then.

Two pairs move here, so all four signs change: the minus becomes a times, the plus becomes a divide, the divide becomes a plus and the times becomes a minus.

BODMAS then fixes the order: 4 × 12 ÷ 3 is settled before the addition and the subtraction are touched.

Key facts

• The rewritten line is 4 × 12 ÷ 3 + 12 − 6, which equals 22.
• Both named pairs change everywhere they occur, not only at their first appearance.
• Multiplication and division share a rank and are worked left to right.

Common traps

• Swapping one pair and forgetting the second
• Reading the rewritten line strictly left to right and ignoring BODMAS
• Rewriting the signs but matching the old running total to the nearest option

No directly related past PYQ was found.