Understanding the PhD Entrance Exam Data

The question provides a table showing the distribution of candidates enrolled and candidates who passed a PhD entrance exam across seven different institutes (A through G). We are given the total number of candidates enrolled (17100) and the total number of candidates who passed (11400). The percentages in the table tell us the proportion of these totals belonging to each institute.

We need to calculate the difference between the number of candidates who passed from institutes E and B combined, and the number of candidates enrolled from institutes F and D combined.

Step-by-Step Calculation

First, let's find the actual number of candidates for each category required for the calculation.

Calculating the Number of Passed Candidates from E and B

According to the table:

• Percentage of candidates who passed from Institute E is 16%.
• Percentage of candidates who passed from Institute B is 18%.

The total number of candidates who passed the exam is 11400.

Number of candidates who passed from Institute E:

\(\text{Passed from E} = 16\% \text{ of } 11400\)

\(\text{Passed from E} = \frac{16}{100} \times 11400\)

\(\text{Passed from E} = 0.16 \times 11400 = 1824\)

Number of candidates who passed from Institute B:

\(\text{Passed from B} = 18\% \text{ of } 11400\)

\(\text{Passed from B} = \frac{18}{100} \times 11400\)

\(\text{Passed from B} = 0.18 \times 11400 = 2052\)

Total number of candidates who passed from E and B together:

\(\text{Passed (E and B)} = \text{Passed from E} + \text{Passed from B}\)

\(\text{Passed (E and B)} = 1824 + 2052 = 3876\)

Calculating the Number of Enrolled Candidates from F and D

According to the table:

• Percentage of candidates enrolled from Institute F is 8%.
• Percentage of candidates enrolled from Institute D is 10%.

The total number of candidates enrolled was 17100.

Number of candidates enrolled from Institute F:

\(\text{Enrolled from F} = 8\% \text{ of } 17100\)

\(\text{Enrolled from F} = \frac{8}{100} \times 17100\)

\(\text{Enrolled from F} = 0.08 \times 17100 = 1368\)

Number of candidates enrolled from Institute D:

\(\text{Enrolled from D} = 10\% \text{ of } 17100\)

\(\text{Enrolled from D} = \frac{10}{100} \times 17100\)

\(\text{Enrolled from D} = 0.10 \times 17100 = 1710\)

Total number of candidates enrolled from F and D together:

\(\text{Enrolled (F and D)} = \text{Enrolled from F} + \text{Enrolled from D}\)

\(\text{Enrolled (F and D)} = 1368 + 1710 = 3078\)

Calculating the Difference

Now, we find the difference between the total passed candidates from E and B and the total enrolled candidates from F and D.

\(\text{Difference} = \text{Passed (E and B)} - \text{Enrolled (F and D)}\)

\(\text{Difference} = 3876 - 3078\)

\(\text{Difference} = 798\)

Sum of passed candidates from E and B = 1824 + 2052 = 3876

Sum of enrolled candidates from F and D = 1368 + 1710 = 3078

Difference = 3876 - 3078 = 798

The number of candidates who passed the exam from E and B together exceeds the number of candidates enrolled from F and D together by 798.

Revision Table: Key Data Points

Additional Information on Percentage Calculations

Understanding percentages is crucial for solving data interpretation questions like this one. A percentage represents a part out of a hundred. To find the value corresponding to a percentage of a total amount, you use the formula:

\(\text{Value} = \left(\frac{\text{Percentage}}{100}\right) \times \text{Total Amount}\)

In this problem, we applied this formula multiple times:

• To find the number of passed candidates from a specific institute, we used the percentage of passed candidates for that institute and the total number of passed candidates (11400).
• To find the number of enrolled candidates from a specific institute, we used the percentage of enrolled candidates for that institute and the total number of enrolled candidates (17100).

Data interpretation questions often require careful reading of the table and the question to ensure you use the correct percentage with the correct total base value (e.g., using percentage of passed with total passed, and percentage of enrolled with total enrolled).