Simplify the following expression. (60 + 64 ÷ 4 of 4) × {1000 ÷ ((10 of (3 + 2)) × 2 of 5)} − 28 + (100 × 3 of 3).

Correct — A. In BODMAS 'of' is settled before ÷ and ×, so '4 of 4' is a single product, 16.

First bracket: 4 of 4 = 16, so 64 ÷ 16 = 4, and 60 + 4 = 64

Braces: (3 + 2) = 5, then 10 of 5 = 50 and 2 of 5 = 10
50 × 10 = 500, so 1000 ÷ 500 = 2

Last bracket: 3 of 3 = 9, so 100 × 9 = 900

64 × 2 − 28 + 900 = 128 − 28 + 900 = 1000 → option (a)

Why the others are wrong

• (b)
  100 — 100 is 128 − 28, the running total after the multiplication and the subtraction. The final (100 × 3 of 3) = 900 term has simply been left off.
• (c)
  500 — 500 is the product inside the braces, (10 of 5) × (2 of 5). It is an intermediate figure — the braces are worth 1000 ÷ 500 = 2, not 500.
• (d)
  600 — 600 follows from no reading of the line. The three blocks are worth 64, 2 and 900, and 64 × 2 − 28 + 900 can only come to 1000.

BODMAS ranks the operations: brackets, then 'of', then ÷ and × left to right, then + and −.

'of' is not a second name for multiplication — it binds tighter. So 64 ÷ 4 of 4 is 64 ÷ 16 = 4, not (64 ÷ 4) × 4 = 64. That one choice decides the whole item.

Brackets clear innermost first: (3 + 2) before 10 of 5, and 10 of 5 before the product inside the braces.

Key facts

• 'of' outranks ÷ and ×, so 64 ÷ 4 of 4 = 64 ÷ 16 = 4.
• Read left to right instead, that same bracket comes to 124 and the line ends at 1120.
• The three blocks here are worth 64, 2 and 900.
• Addition and subtraction come last, left to right: 128 − 28 + 900 = 1000.

Common traps

• Reading 64 ÷ 4 of 4 as (64 ÷ 4) × 4 = 64.
• Stopping at 128 − 28 = 100 and never adding the last bracket.
• Turning 2 of 5 into 2 + 5 or into 2⁄5 rather than 10.

No directly related past PYQ was found.