Solving the Competitive Examination Data Problem

The problem asks us to determine the number of states in the year 2021 where the count of female candidates who qualified in the competitive examination exceeded 5000. To solve this, we need to use the data provided in Table 1 and Table 2.

First, let's find the total number of candidates who qualified from all states (A-F) in the year 2021 using Table 2.

• Total Appeared candidates in 2021: 142000
• Percentage (%) Qualified from States A-F in 2021: 45%

So, the total number of candidates who qualified in 2021 is:

\[ \text{Total Qualified in 2021} = \text{Total Appeared} \times \frac{\text{Percentage Qualified}}{100} \]

\[ \text{Total Qualified in 2021} = 142000 \times \frac{45}{100} = 1420 \times 45 = 63900 \]

Now, we use Table 1 to find the number of qualified candidates from each state and then the number of female qualified candidates for each state in 2021. Table 1 gives the percentage distribution of qualified candidates among the states and the Male to Female ratio for each state.

Let's calculate the number of qualified candidates and female qualified candidates for each state in 2021:

• State A:
  • Qualified from State A = 18% of 63900 = \( \frac{18}{100} \times 63900 = 18 \times 639 = 11502 \)
  • Male:Female ratio = 5:4. Female fraction = \( \frac{4}{5+4} = \frac{4}{9} \)
  • Female Qualified from State A = \( 11502 \times \frac{4}{9} = 1278 \times 4 = 5112 \)
  • Is 5112 > 5000? Yes
• State B:
  • Qualified from State B = 16% of 63900 = \( \frac{16}{100} \times 63900 = 16 \times 639 = 10224 \)
  • Male:Female ratio = 3:1. Female fraction = \( \frac{1}{3+1} = \frac{1}{4} \)
  • Female Qualified from State B = \( 10224 \times \frac{1}{4} = 2556 \)
  • Is 2556 > 5000? No
• State C:
  • Qualified from State C = 12% of 63900 = \( \frac{12}{100} \times 63900 = 12 \times 639 = 7668 \)
  • Male:Female ratio = 7:5. Female fraction = \( \frac{5}{7+5} = \frac{5}{12} \)
  • Female Qualified from State C = \( 7668 \times \frac{5}{12} = 639 \times 5 = 3195 \)
  • Is 3195 > 5000? No
• State D:
  • Qualified from State D = 16% of 63900 = \( \frac{16}{100} \times 63900 = 16 \times 639 = 10224 \)
  • Male:Female ratio = 13:11. Female fraction = \( \frac{11}{13+11} = \frac{11}{24} \)
  • Female Qualified from State D = \( 10224 \times \frac{11}{24} = 426 \times 11 = 4686 \)
  • Is 4686 > 5000? No
• State E:
  • Qualified from State E = 25% of 63900 = \( \frac{25}{100} \times 63900 = \frac{1}{4} \times 63900 = 15975 \)
  • Male:Female ratio = 13:12. Female fraction = \( \frac{12}{13+12} = \frac{12}{25} \)
  • Female Qualified from State E = \( 15975 \times \frac{12}{25} = 639 \times 12 = 7668 \)
  • Is 7668 > 5000? Yes
• State F:
  • Qualified from State F = 13% of 63900 = \( \frac{13}{100} \times 63900 = 13 \times 639 = 8307 \)
  • Male:Female ratio = 8:11. Female fraction = \( \frac{11}{8+11} = \frac{11}{19} \)
  • Female Qualified from State F = \( 8307 \times \frac{11}{19} \approx 437.21 \times 11 \approx 4809.31 \)
  • Is 4809.31 > 5000? No

Summary of Female Qualified Candidates in 2021:

• State A: 5112
• State B: 2556
• State C: 3195
• State D: 4686
• State E: 7668
• State F: Approximately 4809.31

We are looking for the states where the number of female candidates who qualified is more than 5000.

• State A: 5112 > 5000 (Yes)
• State B: 2556 > 5000 (No)
• State C: 3195 > 5000 (No)
• State D: 4686 > 5000 (No)
• State E: 7668 > 5000 (Yes)
• State F: Approximately 4809.31 > 5000 (No)

The states where the number of female candidates who qualified is more than 5000 are State A and State E.

Thus, there are exactly two states where the number of female qualified candidates in 2021 is more than 5000.

Revision Table: Competitive Examination Data Analysis

The states meeting the condition (female qualified > 5000) are A and E. There are 2 such states.

Additional Information: Data Interpretation Skills

Data interpretation questions, like this competitive examination example, require careful reading of tables and charts to extract relevant information. Key skills include:

• Understanding Percentages: Calculating a percentage of a total number is fundamental. Here, 45% of total appeared candidates gives the total qualified, and state-wise percentages of this total qualified number give state-specific qualified counts.
• Working with Ratios: A ratio like M:F represents parts of a whole. To find the number of females, you use the female part divided by the total parts of the ratio, multiplied by the total number for that category (qualified candidates in this case).
• Step-by-Step Calculation: Breaking down the problem into smaller steps makes it manageable. First, find the total qualified; then, find the state-wise qualified; finally, find the gender-wise qualified within each state.
• Careful Comparison: The final step involves comparing the calculated number against a given threshold (5000 in this problem) and counting the occurrences that meet the condition.

It's important to pay close attention to what each table represents (distribution of qualified vs. overall appearance and qualification) and the specific year being asked about (2021 in this case).