What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 69 + 2485 × 5 – 912 ÷ 2 = ?

Correct — A.

Rule: rewrite the expression with the symbols swapped, then solve it by BODMAS.

Both pairs trade places: + with −, and × with ÷.

69 + 2485 × 5 − 912 ÷ 2 rewrites as 69 − 2485 ÷ 5 + 912 × 2.

Division and multiplication first:
2485 ÷ 5 = 497
912 × 2 = 1824

Then left to right:
69 − 497 = −428
−428 + 1824 = 1396, which is option (a).

Why the others are wrong

• (b)
  1936 — 1936 uses the same four digits, 1, 3, 6 and 9, in another order. No stage of the working produces it, so it catches a hurried transcription rather than a wrong method.
• (c)
  1639 — 1639 is a third arrangement of those digits. The working ends at 1396, whose middle digits are 3 then 9, in that order.
• (d)
  1963 — 1963 is a fourth arrangement of the same digits. Once 69 − 497 + 1824 has been done, only 1396 is left standing.

Symbol-interchange items test two things at once: whether you rewrite before you calculate, and whether you then apply BODMAS instead of working left to right.

Do the swap on paper. Rewriting the line as 69 − 2485 ÷ 5 + 912 × 2 takes five seconds and removes every later chance of reaching for an old symbol.

Then order matters: divide and multiply before you add and subtract. Solving the rewritten line strictly left to right gives a number that matches none of the options, which is the designed punishment.

Key facts

• After the swap the expression reads 69 − 2485 ÷ 5 + 912 × 2.
• 2485 ÷ 5 = 497 and 912 × 2 = 1824.
• 69 − 497 + 1824 = 1396.

Common traps

• Applying the swap to only one of the two symbol pairs.
• Working the rewritten line strictly left to right instead of by BODMAS.
• Picking a digit-permutation of the right answer under time pressure.

No directly related past PYQ was found.