What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 2864 × 4 – 168 ÷ 2 + 69 = ?

Correct — D. Rule: rewrite the expression with the symbols swapped, then evaluate by BODMAS. Plus becomes minus, minus becomes plus, times becomes divide and divide becomes times.

As printed: 2864 x 4 - 168 divided by 2 + 69
After the swap: 2864 divided by 4 + 168 x 2 - 69

Now evaluate, division and multiplication first:
2864 divided by 4 = 716
168 x 2 = 336

Then the addition and subtraction, left to right:
716 + 336 = 1052
1052 - 69 = 983, which is option (d).

Why the others are wrong

• (a)
  938 — 938 is 983 with the last two digits swapped. The final step is 1052 - 69, which ends in 3 because 12 - 9 = 3, so an option ending in 8 fails on the units digit alone.
• (b)
  389 — 389 reverses the digits of 983. Nothing in the working reaches it: the division gives 716, the multiplication gives 336, and their sum less 69 is 983.
• (c)
  839 — 839 is another arrangement of the same three digits. The swapped expression 2864 divided by 4, plus 168 times 2, minus 69 evaluates to exactly one number, and that number is 983.

Symbol-interchange items test two things at once: whether you rewrite the expression before evaluating, and whether you then apply BODMAS correctly.

Do the swap on paper. Rewriting 2864 x 4 - 168 divided by 2 + 69 as 2864 divided by 4 + 168 x 2 - 69 takes a few seconds and removes every chance of accidentally solving the printed expression.

Then evaluate in order. Division and multiplication come first, left to right, and only then addition and subtraction. Skipping that order is what turns a solved question into a lost mark.

Key facts

• After the swap the expression reads 2864 divided by 4, plus 168 times 2, minus 69.
• 2864 divided by 4 is 716 and 168 times 2 is 336.
• BODMAS puts division and multiplication ahead of addition and subtraction.

Common traps

• Evaluating the printed expression and swapping the symbols only in your head
• Doing the addition before the division and the multiplication
• Choosing by the look of the number when all four options share the same digits

No directly related past PYQ was found.