GATE CS 2019 Q.7 (GA Q.7): Quantitative Aptitude

In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of

Inverted triangle (Teachers), tall rectangle (Administrators) whose top overlaps the triangle's right corner, and circle (Researchers) overlapping the bottom of the rectangle. Region counts: Teachers only 70; Teachers and Administrators 10; Administrators only 20; Administrators and Researchers 20; Researchers only 40.

0 to 15

16 to 30

31 to 45

46 to 60

Official answer and solution

Official answer: C
From: Official GATE 2019 answer key

Solution

Calculate the total number of individuals and the number of administrators from the given Venn diagram regions.

From the Venn diagram:

Teachers only (Triangle only) = 70
Researchers only (Circle only) = 40
Administrators only (Rectangle only) = 20
Teachers and Administrators intersection (Triangle $\cap$ Rectangle) = 10
Researchers and Administrators intersection (Circle $\cap$ Rectangle) = 20

The total number of people is:

N_{\text{total}} = 70 + 40 + 20 + 10 + 20 = 160

The total number of administrators is the sum of all regions within the rectangle:

N_{\text{admin}} = 20 + 10 + 20 = 50

The percentage of administrators among the total population is:

P = \frac{50}{160} \times 100\% = \frac{5}{16} \times 100\% = 31.25\%

The value $31.25\%$ lies in the range of 31 to 45 (Option C).

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2019 Computer Science and Information Technology (CS)
Question: 7 of 65, printed as GA Q.7
Section: General Aptitude

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