What will come in place of the question mark (?) in the following equation, if ‘×’ is replaced by ‘÷’, ‘÷’ is replaced by ‘+’, ‘+’ is replaced by ‘×’ and ‘−’ remains unchanged? 42 × 3 ÷ 4 + 9 − 17 = ?

Correct — A. Rewrite the line under the new symbols first, then evaluate it with ordinary BODMAS.

Rule: x becomes ÷, ÷ becomes +, + becomes x, and − is untouched.

So 42 × 3 ÷ 4 + 9 − 17 rewrites as 42 ÷ 3 + 4 × 9 − 17.

42 ÷ 3 = 14
4 × 9 = 36
14 + 36 = 50
50 − 17 = 33 → option (a)

Why the others are wrong

• (b)
  30 — 30 is what 42 ÷ 3 × 4 − 9 − 17 gives. That reading turns ÷ into a multiplication and + into a minus; the instruction sends ÷ to + and + to x.
• (c)
  23 — 23 sits beside 23.5, which is what the untouched line 42 × 3 ÷ 4 + 9 − 17 comes to. The substitution has to be made before any arithmetic.
• (d)
  29 — 29 would need 42 ÷ 3 to come to 10, or 4 × 9 to come to 32. The three terms of the rewritten line are 14, 36 and 17.

Symbol-substitution items are two tasks stacked. First rewrite the expression under the given mapping; second evaluate the rewritten line by BODMAS. Trying to do both in one pass is where the marks go.

The mapping here is a three-way cycle, not an interchange: × goes to ÷, ÷ goes to +, + goes to x. Only the minus stays put.

A cycle is harder than a swap because applying it twice does not undo it, so there is no symmetry to fall back on. Write the new line out in full before touching a number.

Key facts

• Under this mapping, 42 × 3 ÷ 4 + 9 − 17 becomes 42 ÷ 3 + 4 × 9 − 17.
• BODMAS applies to the rewritten line, so 42 ÷ 3 and 4 × 9 are settled before any addition.
• The three terms of the rewritten line are 14, 36 and 17, giving 33.

Common traps

• Working left to right after the swap, which gives 145 here.
• Applying the mapping backwards, so + becomes ÷ instead of x.
• Applying two legs of the cycle and dropping the third — × to ÷ and ÷ to +, with the + left alone — which turns the line into 42 ÷ 3 + 4 + 9 − 17 = 10.

No directly related past PYQ was found.