GATE AG 2020 • Q10 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Data Interpretation

Question Statement:

Bar chart gives enrollment (thousands) for School P and Q, 2014–2018: P = 3,5,5,6,4; Q = 4,7,8,7,5. Find the ratio of the average number of students in P to the average of the difference of students enrolled in P and Q.

Options:

  • (A) 8 : 23
  • (B) 23 : 8
  • (C) 23 : 31
  • (D) 31 : 23

Official Answer Key:

B

Step-by-Step Solution & Explanation

• **Given Enrollment (thousands):** - School P: 2014=3, 2015=5, 2016=5, 2017=6, 2018=4. Total = $3+5+5+6+4 = 23$. Average $P = \frac{23}{5} = 4.6$. - School Q: 2014=4, 2015=7, 2016=8, 2017=7, 2018=5. Total = $4+7+8+7+5 = 31$. • **Year-wise Differences $(Q - P)$:** - 2014: $4 - 3 = 1$ - 2015: $7 - 5 = 2$ - 2016: $8 - 5 = 3$ - 2017: $7 - 6 = 1$ - 2018: $5 - 4 = 1$ - Total difference $= 1 + 2 + 3 + 1 + 1 = 8$. Average difference $= \frac{8}{5} = 1.6$. • **Ratio Required:** $\frac{\text{Average of } P}{\text{Average difference}} = \frac{23/5}{8/5} = \frac{23}{8} = 23 : 8$. • **Conclusion:** The required ratio is $23 : 8$. **Correct Answer: B**.

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