GATE AE 2013 • Q56 MCQ • 2 Marks Propulsion

Propulsion

Compressors and Turbines

Subtopic: Centrifugal Compressors

Question Statement:

If $3 \le X \le 5$ and $8 \le Y \le 11$, then which of the following options is TRUE?

Options:

  • (A) $\frac{3}{5} \le \frac{X}{Y} \le \frac{8}{5}$
  • (B) $\frac{3}{11} \le \frac{X}{Y} \le \frac{5}{8}$
  • (C) $\frac{3}{11} \le \frac{X}{Y} \le \frac{8}{5}$
  • (D) $\frac{3}{5} \le \frac{X}{Y} \le \frac{8}{11}$

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2013 Q.56)** **1. Interval Arithmetic for Ratios of Positive Numbers**: Given $X \in [3, 5]$ and $Y \in [8, 11]$ where all bounds are strictly positive: - The minimum possible value of $\frac{X}{Y}$ occurs when numerator $X$ is at its minimum and denominator $Y$ is at its maximum: $$\left(\frac{X}{Y}\right)_{\min} = \frac{X_{\min}}{Y_{\max}} = \frac{3}{11}$$ - The maximum possible value of $\frac{X}{Y}$ occurs when numerator $X$ is at its maximum and denominator $Y$ is at its minimum: $$\left(\frac{X}{Y}\right)_{\max} = \frac{X_{\max}}{Y_{\min}} = \frac{5}{8}$$ **2. Conclusion**: $$\frac{3}{11} \le \frac{X}{Y} \le \frac{5}{8}$$ - **Official Answer Key**: **B**
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