Question

The following charts show percentage youth education/ Job status in five major classification (Diploma, Undergraduate, Post Graduate, Ph.D and Job) in State A and State B. The total youth population in state A is 55750 and in state B 86500. Read the charts carefully and answer the followings.
\includegraphics[width=0.6\textwidth]{27.png}
Which of the following statement/s is/are True ?
Statement I- The total youth pursuing under graduate from both state is 50210.
Statement II- The ratio of youth pursuing Ph.D for state A to State B is 0.75.
Statement III- The youth pursuing Ph.D from state B is higher by 3690.

• A. Only Statement (I) and Statement (II) are true.
• B. Only Statement (II) is true.
• C. Statement (I), Statement (II) and Statement (III) are true.
• D. Only Statement (I) is true.

Hint:

Always calculate the absolute numbers when comparing ratios or differences across pie charts with different total populations, as comparing percentages directly can lead to incorrect conclusions.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a data interpretation problem involving pie charts for two different states (State A and State B).
To evaluate the statements, we must calculate the absolute values of the specified categories using the given percentages and the total populations of each state.
Key Formula or Approach:
- Total Population of State A, \(N_A = 55750\)
- Total Population of State B, \(N_B = 86500\)
- Number of people in a category = \((\text{Percentage of Category}) \times \text{Total Population}\)

Step 2: Detailed Explanation:
Let us calculate the values for each statement systematically:
- Evaluating Statement I:
- Percentage of Undergraduates in State A = \(28\%\)
\[ \text{Undergraduates in State A} = 55750 \times 0.28 = 15610 \]
- Percentage of Undergraduates in State B = \(40\%\)
\[ \text{Undergraduates in State B} = 86500 \times 0.40 = 34600 \]
- Total Undergraduates = \(15610 + 34600 = 50210\).
Therefore, Statement I is true.
- Evaluating Statement II:
- Percentage of Ph.D in State A = \(8\%\)
\[ \text{Ph.D in State A} = 55750 \times 0.08 = 4460 \]
- Percentage of Ph.D in State B = \(10\%\)
\[ \text{Ph.D in State B} = 86500 \times 0.10 = 8650 \]
- Ratio of Ph.D students in State A to State B:
\[ \text{Ratio} = \frac{4460}{8650} \approx 0.515 \]
Therefore, Statement II is false.
- Evaluating Statement III:
- Difference in Ph.D students between State B and State A:
\[ \text{Difference} = 8650 - 4460 = 4190 \]
Therefore, Statement III is false.
Thus, only Statement I is true.

Step 3: Final Answer:
The correct option is (D) Only Statement (I) is true.