Simplify 21 − [6 + 7 − {3.22 − (1.1 × 0.2)}].

Correct — A. Work outward from the innermost grouping, in BODMAS order.

Parentheses first:
1.1 × 0.2 = 0.22

Then the braces:
3.22 − 0.22 = 3

Then the square bracket:
6 + 7 = 13
13 − 3 = 10

Finally the subtraction standing outside it:
21 − 10 = 11 → option (a).

Why the others are wrong

• (b)
  13 — 13 would need the bracket to come to 8, since 21 − 8 = 13. The bracket is 6 + 7 − 3 = 10. Note that 13 is the value of 6 + 7 by itself, so the brace has simply never been subtracted.
• (c)
  12 — 12 would need the bracket to equal 9, which means a brace worth 4. The brace is 3.22 − 0.22, and that is exactly 3.
• (d)
  10 — 10 is the value of the square bracket itself — the answer to the second-last step. The expression still has 21 minus that bracket to go, which gives 11.

BODMAS with three levels of grouping. The rule is not left-to-right but innermost-first: parentheses ( ), then braces { }, then brackets [ ], and only then whatever stands outside.

Within a level, multiplication and division come before addition and subtraction — which is why 1.1 × 0.2 is resolved before the 3.22 is touched at all.

The decimals are cosmetic. 1.1 × 0.2 = 0.22 was chosen to cancel the 0.22 in 3.22 and leave a whole 3, so a brace that is not a whole number means a slipped decimal place.

Key facts

• Grouping is resolved innermost first: parentheses, then braces, then square brackets.
• 1.1 × 0.2 = 0.22, so the brace {3.22 − (1.1 × 0.2)} is exactly 3.
• The square bracket is 6 + 7 − 3 = 10, and 21 − 10 = 11.

Common traps

• Stopping at the bracket value of 10 and marking it.
• Multiplying 1.1 × 0.2 as 0.02 or as 2.2, either of which breaks the clean 3.
• Distributing the outer minus wrongly as 21 − 6 − 7 − 3, which gives 5.

No directly related past PYQ was found.