Simplify: 13 − [7 − (4 + 7) − {7 − (7 − 4 + 7)} + 14]

Correct — D. Rule: clear brackets from the inside out — round ( ), then curly { }, then square [ ].

(4 + 7) = 11
(7 − 4 + 7) = 10 (left to right, not 7 − 11)
{7 − 10} = −3

[7 − 11 − (−3) + 14] = 7 − 11 + 3 + 14 = 13
13 − 13 = 0 → option (d)

The step that decides the question is − (−3) = + 3: the minus in front of the curly bracket flips the value inside it.

Why the others are wrong

• (a)
  9 — 9 appears nowhere in the chain. It would need the square bracket to come to 4, and no arrangement of signs on its terms 7, 11, 3 and 14 produces 4.
• (b)
  13 — 13 is the square bracket's own value, not the expression's. The final step 13 − [ ] is still owed — getting the bracket right and stopping there is the commonest way to drop this mark.
• (c)
  26 — 26 is 13 + 13 — the bracket added instead of subtracted. The sign standing in front of [ ] is a minus, so the two 13s cancel to zero.

BODMAS fixes the order, and within brackets the innermost pair goes first: round, then curly, then square.

A minus sign standing in front of a bracket multiplies everything inside it by −1. That is where nearly all the marks in this item are won or lost.

Addition and subtraction of equal rank run left to right, so 7 − 4 + 7 is (7 − 4) + 7 = 10, not 7 − (4 + 7) = −4. The paper puts exactly that string inside the innermost bracket.

Key facts

• Innermost brackets are cleared first: round ( ), then curly { }, then square [ ].
• A minus in front of a bracket changes the sign of every term inside it.
• Addition and subtraction of equal precedence work left to right, so 7 − 4 + 7 = 10.
• Here the square bracket comes to 13, and 13 − 13 = 0.

Common traps

• Reading 7 − 4 + 7 as 7 − (4 + 7) and getting −4 where the answer needs 10.
• Leaving − {7 − 10} as −3 instead of flipping it to +3.
• Marking the bracket's value of 13 rather than the expression's value.

No directly related past PYQ was found.