Interchange two signs to correct. 50 ÷ 5 + 8 − 6 × 2 = 56

Correct — D.
Rule: swap the two signs, then solve with BODMAS (÷ and × before + and −).

Swap − and ×:
50 ÷ 5 + 8 × 6 − 2
= 10 + 48 − 2
= 56 ✓ → option (d).

Why the others are wrong

• (a)
  ÷ and − — Swapping ÷ and − gives 50 − 5 + 8 ÷ 6 × 2 = 45 + 8⁄3 ≈ 47.67, not 56.
• (b)
  + and − — Swapping + and − gives 50 ÷ 5 − 8 + 6 × 2 = 10 − 8 + 12 = 14, far short of 56.
• (c)
  ÷ and × — Swapping ÷ and × gives 50 × 5 + 8 − 6 ÷ 2 = 250 + 8 − 3 = 255, far above 56.

A sign-interchange item gives a false equation and asks which pair of signs, swapped, makes it true. Swap each option's pair in turn and evaluate with BODMAS: ÷ and × first, left to right, then + and −.

As printed, the left side is 10 + 8 − 12 = 6. The target is 56, so look for a swap that builds a large product: putting × between 8 and 6 gives 48.

Key facts

• Evaluate ÷ and × before + and −, working left to right among signs of equal rank.
• As printed, 50 ÷ 5 + 8 − 6 × 2 equals 6.
• With − and × swapped, 50 ÷ 5 + 8 × 6 − 2 = 10 + 48 − 2 = 56.

Common traps

• Solving left to right after the swap instead of doing ÷ and × first
• Reading 8 ÷ 6 × 2 as 8 ÷ 12: signs of equal rank go left to right, so it is (8 ÷ 6) × 2

No directly related past PYQ was found.