Identify the correct pair of signs to interchange. 12 × 2 + 6 ÷ 3 − 8 = 8

Correct — D.
Rule: swap the two signs, then work the new expression with BODMAS.

Swap × and +: 12 + 2 × 6 ÷ 3 − 8
Multiply and divide: 2 × 6 ÷ 3 = 4
Add and subtract: 12 + 4 − 8 = 8, which matches → option (d).

Why the others are wrong

• (a)
  + and − — + and − gives 12 × 2 − 6 ÷ 3 + 8 = 24 − 2 + 8 = 30. The product 12 × 2 survives the swap and keeps the total far above 8.
• (b)
  × and ÷ — × and ÷ gives 12 ÷ 2 + 6 × 3 − 8 = 6 + 18 − 8 = 16. Moving the × onto 6 × 3 makes the total too large.
• (c)
  ÷ and − — ÷ and − gives 12 × 2 + 6 − 3 ÷ 8 = 24 + 6 − 0.375 = 29.625, not even a whole number, let alone 8.

A sign-interchange item gives an equation that is false as printed and asks which two signs, swapped, make it true. As printed, 12 × 2 + 6 ÷ 3 − 8 = 24 + 2 − 8 = 18, not 8.

Test each pair: swap the two signs, then work the new expression with BODMAS. The × and + swap is the one that brings it to 8.

Key facts

• As printed, 12 × 2 + 6 ÷ 3 − 8 works out to 18.
• After swapping × and +, 12 + 2 × 6 ÷ 3 − 8 = 12 + 4 − 8 = 8.
• Division and multiplication are done before addition and subtraction.

Common traps

• Working the swapped expression left to right, which gives (12 + 2) × 6 ÷ 3 − 8 = 20 and makes the right swap look wrong
• Accepting a swap because it gives a whole number, as options (a) and (b) do, without checking that it equals 8

No directly related past PYQ was found.