If |-2X + 9| = 3, then a possible value of -(X^2 - 6) would be: A. 30 B. -30 C. -42 D. 42

GATE 2013 · General Aptitude · Absolute Value · medium

Answer: When X = 6, -(X^2 - 6) = -30. Answer: B.

1. Split the absolute value equation into two cases: Case 1: -2X + 9 = 3 => -2X = -6 => X = 3. Case 2: -2X + 9 = -3 => -2X = -12 => X = 6.
2. Evaluate -(X^2 - 6) for X = 3: -(3^2 - 6) = -(9 - 6) = -(3) = -3. This value does not appear in the answer options.
3. Evaluate -(X^2 - 6) for X = 6: -(6^2 - 6) = -(36 - 6) = -(30) = -30. This matches option B.