GATE AE 2013 • Q64 MCQ • 2 Marks Aerospace Structures

Aerospace Structures

Aerospace Materials & Fatigue

Subtopic: Fatigue Crack Growth & S-N Curves

Question Statement:

If $|-2X + 9| = 3$, then the possible value of $|-X| - X^2$ would be:

Options:

  • (A) 30
  • (B) -30
  • (C) -42
  • (D) 42

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2013 Q.64)** **1. Solving the Absolute Value Equation**: Given: $$|-2X + 9| = 3$$ This yields two algebraic cases: - **Case 1**: $$-2X + 9 = 3 \implies -2X = -6 \implies X = 3$$ - **Case 2**: $$-2X + 9 = -3 \implies -2X = -12 \implies X = 6$$ **2. Evaluating the Target Expression $|-X| - X^2$**: - For $X = 3$: $$|-3| - 3^2 = 3 - 9 = -6$$ - For $X = 6$: $$|-6| - 6^2 = 6 - 36 = -30$$ Among the given choices, $-30$ is present as Option (B). - **Official Answer Key**: **B**
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