What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 164 – 173 ÷ 110 + 140 × 5 = ?

Correct — C.

Rule: swap the signs first, then BODMAS on the swapped line. Plus becomes minus, minus becomes plus, × becomes ÷ and ÷ becomes ×.

Printed: 164 − 173 ÷ 110 + 140 × 5
After the swap: 164 + 173 × 110 − 140 ÷ 5

Multiply: 173 × 110 = 19030.
Divide: 140 ÷ 5 = 28.

Then 164 + 19030 = 19194, and 19194 − 28 = 19166 → option (c).

Why the others are wrong

• (a)
  11619 — 11619 would need the product 173 × 110 to be 11483 rather than 19030. It is not even a rearrangement of the answer: it carries three 1s and one 6, where 19166 has two of each.
• (b)
  19616 — 19616 is 450 above the true total, and the only step left after 164 + 19030 is a subtraction of 28. Nothing larger than 19194 can come out of that line.
• (d)
  11916 — 11916 would need 173 × 110 to be 11780. The multiplication is the heavy step here, so check it before you check anything else.

Same instruction as the earlier sign-swap item, but the numbers are large enough that you cannot finish it in your head, and that is deliberate.

All four options are five-digit numbers built from the digits 1, 6 and 9. Size, shape and the leading digit are useless as filters, so there is no way through except doing the arithmetic.

The heavy step is 173 × 110. Take it as 173 × 11 = 1903, then put a zero on the end: 19030. The division 140 ÷ 5 = 28 is trivial once the product is safe.

Key facts

• After the swap the line reads 164 + 173 × 110 − 140 ÷ 5.
• 173 × 110 = 19030, most quickly as 173 × 11 = 1903 with a zero appended.
• 140 ÷ 5 = 28, and 164 + 19030 − 28 = 19166.

Common traps

• Choosing by shape because all four options look alike, instead of finishing the sum.
• Swapping the multiplication and division signs but leaving plus and minus as printed.
• Adding 164 and 173 first because they stand next to each other on the line.

No directly related past PYQ was found.