What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 152 ÷ 6 + 1617 × 7 – 77 = ?

Correct — C. Rewrite the whole expression with the swaps in place, then apply BODMAS to the rewritten line — never to the printed one.

Swap: + becomes −, − becomes +, × becomes ÷, ÷ becomes ×.

152 ÷ 6 + 1617 × 7 − 77 becomes 152 × 6 − 1617 ÷ 7 + 77.

152 × 6 = 912
1617 ÷ 7 = 231
912 − 231 = 681
681 + 77 = 758 → option (c)

Why the others are wrong

• (a)
  785 — 785 is the digits of 758 in a different order. No route through the swapped expression reaches it — the last line is 681 + 77.
• (b)
  578 — 578 is another reordering of the same digits. Swapping × and ÷ but leaving + and − alone gives 912 + 231 − 77 = 1066, which is not on the list either.
• (d)
  587 — 587 is a third reordering. The check that catches a missed swap is that 152 ÷ 6 is not a whole number, so any route that keeps that division has gone wrong.

An operator-interchange question is two tasks stacked. First rewrite the expression symbol by symbol under the stated swaps. Only then evaluate.

Doing both at once is where the marks go. The rewritten line here, 152 × 6 − 1617 ÷ 7 + 77, is an ordinary BODMAS sum: both multiplications and divisions first, then the addition and subtraction left to right.

1617 ÷ 7 dividing exactly, to 231, is a quiet signal that the swap was applied correctly.

Key facts

• After the swap the expression is 152 × 6 − 1617 ÷ 7 + 77, which evaluates to 758.
• BODMAS applies to the swapped expression, never to the expression as printed.
• 1617 ÷ 7 = 231 exactly, and 152 ÷ 6 does not divide exactly.

Common traps

• Evaluating strictly left to right after the swap, which turns 912 − 1617 into a negative running total
• Swapping one pair of operators and forgetting the other pair
• Reading the instruction as an interchange of numbers, which is the different stem set at Reasoning Q.16 of this paper

No directly related past PYQ was found.