− (− 3)(− 2 − 8 − 4) ÷ [3 5 + (− 2)(− 1)] = ?

Question

− (− 3)(− 2 − 8 − 4) ÷ [3 5 + (− 2)(− 1)] = ?

1. A. 35
2. B. -34
3. C. -41
4. D. -2 (Correct answer)

Correct Answer

Option D — -2

Detailed Solution & Explanation

The correct answer is -2.

Key Points

• $-(-3)(-2 - 8 - 4) \div [3\{5 + (-2)(-1)\}]$
• Simplify the first bracket:
  • $-2 - 8 - 4 = -14$
• Resolve the leading signs: $-(-3) = +3$, so the numerator becomes:
  • $3 \times (-14) = -42$
• Simplify the denominator, innermost first:
  • $(-2)(-1) = +2$
  • $\{5 + 2\} = 7$
  • $[3 \times 7] = 21$
• Divide:
  • $-42 \div 21 = \mathbf{-2}$

Shortcut Trick

• Settle the sign before computing the magnitude. The numerator has three negative factors in effect ($-$, $-3$, $-14$): an odd count of negatives at the top and none at the bottom means the answer is negative. That alone eliminates option A (35), leaving only a magnitude check.

Additional Information

• Sign rules for multiplication and division:
  • $(-) \times (-) = (+)$ and $(+) \times (-) = (-)$
  • An even number of negative factors gives a positive result; an odd number gives a negative result.
• Bracket priority order: innermost first — parentheses $(\ )$, then braces $\{\ \}$, then square brackets $[\ ]$.
• The most frequent mistake here is reading $-(-3)$ as $-3$ instead of $+3$, which flips the final sign.