If + = ×, × = +, − = ÷; then 5 + 6 × 2 − 2 = ?

Correct — D.
Rule: replace every sign first, then apply BODMAS.

Substitute: 5 + 6 × 2 − 2 → 5 × 6 + 2 ÷ 2
Divide: 2 ÷ 2 = 1
Multiply: 5 × 6 = 30
Add: 30 + 1 = 31 → option (d).

Why the others are wrong

• (a)
  16 — 16 works the new signs strictly left to right: 5 × 6 = 30, 30 + 2 = 32, 32 ÷ 2 = 16. BODMAS divides before it adds.
• (b)
  2 — 2 is not a value of 5 × 6 + 2 ÷ 2 under any order of working. The possible results are 31, 16, 20 and 35.
• (c)
  12 — 12 cannot be reached either: every order of working 5 × 6 + 2 ÷ 2 gives 16, 20, 31 or 35, and BODMAS gives 31.

A sign-substitution item changes what each symbol means, not the order of operations. Rewrite the whole expression with the new signs, then solve it as ordinary arithmetic.

Here + and × trade meanings, and − becomes ÷. After rewriting, BODMAS applies: division, then multiplication, then addition.

Key facts

• Rewritten, 5 + 6 × 2 − 2 becomes 5 × 6 + 2 ÷ 2.
• BODMAS: division and multiplication before addition and subtraction.
• Working the rewritten signs left to right gives 16, which is also an option.

Common traps

• Solving the printed expression without substituting (5 + 12 − 2 = 15)
• Substituting correctly but working left to right, which gives 16

No directly related past PYQ was found.