GATE CS 2022 Q.7: Data Interpretation and Graphs

In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.

Which one of the following is the correct logical inference based on the information provided in the above passage?

Equal number of boys and girls qualified

Equal number of boys and girls appeared for the test

The number of boys who appeared for the test is less than the number of girls who appeared

The number of boys who qualified the test is less than the number of girls who qualified

Official answer and solution

Official answer: D
From: Official GATE 2022 answer key

Solution

Compare the proportions of qualified candidates based on the given percentages.

Let $Q$ be the total number of candidates who qualified the entrance test ( $Q > 0$ ).

The passage states that girls accounted for 60% of the qualified candidates:

\text{Qualified girls} = 0.60 \times Q

Since candidates are categorized into boys and girls, boys account for the remaining $100\% - 60\% = 40\%$ of the qualified candidates:

\text{Qualified boys} = 0.40 \times Q

Comparing the two quantities: $0.40 Q < 0.60 Q$ . Hence, the number of boys who qualified the test is strictly less than the number of girls who qualified.

Final answer

Option (D)

Common trap

Confusing the percentage of test-takers who are boys (65%) with the percentage of qualified candidates who are boys (40%).

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

Source

Paper: GATE 2022 Computer Science and Information Technology (CS)
Question: 7 of 65
Section: General Aptitude

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