What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 1064 × 2 – 653 ÷ 2 + 89 = ?

Correct — A. Apply the interchange first, then BODMAS.

Given: 1064 x 2 - 653 / 2 + 89
After swapping + with - and x with /: 1064 / 2 + 653 x 2 - 89

Divide: 1064 / 2 = 532
Multiply: 653 x 2 = 1306
Add: 532 + 1306 = 1838
Subtract: 1838 - 89 = 1749, which is option (a).

Why the others are wrong

• (b)
  1497 — The same four digits in a different order. The swapped line gives 532 + 1306 = 1838 and then 1838 - 89 = 1749; nothing in it yields 1497.
• (c)
  1974 — Another rearrangement of 1, 7, 4 and 9. It is there to catch a transcription slip rather than an arithmetic one.
• (d)
  1947 — Also a rearrangement of the same four digits. Write 1749 down as you compute it and the digit-shuffle options stop being tempting.

Symbol-interchange questions test two things at once: whether you rewrite the line before computing, and whether you then obey BODMAS.

Rewrite the expression on paper with the new signs in place. Doing the swap mentally, term by term as you calculate, is where the marks go.

Then compute in order — brackets, of, division, multiplication, addition, subtraction. Here both the division and the multiplication come before the final addition and subtraction, so 532 and 1306 are found first.

Key facts

• After the interchange the line reads 1064 / 2 + 653 x 2 - 89.
• 1064 / 2 = 532 and 653 x 2 = 1306.
• 532 + 1306 - 89 = 1749.
• BODMAS applies to the rewritten line, never to the printed one.

Common traps

• Swapping only one of the two pairs of signs.
• Working left to right after the swap, which gives 2281.
• Marking a digit-rearrangement of the right answer under time pressure.

No directly related past PYQ was found.