Find the value of 11 − {(3 ÷ 4) of 8 − 4̅ ̅−̅ ̅8̅}.

Correct — D. The expression is 11 − {(3 ÷ 4) of 8 − 4 − 8}, with a bar over the 4 − 8. That bar is a vinculum and it is resolved before anything else (the V in VBODMAS).

Vinculum: 4 − 8 = −4
Bracket: 3 ÷ 4 = 3⁄4
Of: 3⁄4 of 8 = 6

Inside the braces: 6 − (−4) = 6 + 4 = 10

Last step: 11 − 10 = 1 → option (d).

Why the others are wrong

• (a)
  −1 — −1 is the keyed value with its sign flipped, which is what a candidate gets by finishing as 10 − 11 instead of 11 − 10.
• (b)
  3 — 3 needs the braces to come to 8. With the bar resolved they come to 6 − (−4) = 10, and no correct ordering of these terms produces 8.
• (c)
  2 — 2 would need the braces to come to 9. With the bar honoured they come to 6 − (−4) = 10, and ignoring it gives 6 − 4 − 8 = −6, so no reading lands on 2.

VBODMAS is BODMAS with a V in front for vinculum, the bar drawn over part of an expression. The bar binds tighter than any bracket, so what sits under it is collapsed to a single number first.

Here that number is negative: 4 − 8 = −4. The braces then read 6 − (−4), and subtracting a negative adds, which is where the value 10 comes from.

Miss the bar and you read the tail as two loose subtractions instead of one bracketed quantity, and the whole expression changes value.

Key facts

• A vinculum is resolved before brackets — it is the V that precedes BODMAS.
• Subtracting a negative adds: 6 − (−4) = 10.
• The braces total 10, so the expression is 11 − 10 = 1.

Common traps

• Ignoring the bar and reading 4 − 8 as two separate subtractions.
• Getting the braces right and forgetting that 11 still has to have them subtracted.
• Reading (3 ÷ 4) of 8 as 3 ÷ (4 of 8), which is 3⁄32.

No directly related past PYQ was found.