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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?

  1. Equal number of boys and girls qualified
  2. Equal number of boys and girls appeared for the test
  3. The number of boys who appeared for the test is less than the number of girls who appeared
  4. The number of boys who qualified the test is less than the number of girls who qualified
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Lets assume, total number of student is $100.$

Now, boys constituted of $65\%$ of appeared students.

So total number of boys who appeared  $= 65.$

Total number of girls who appeared$=100-65=35.$

Now, Girls accounted for $60\%$ of qualified students.

So, no of girls who qualified $=0.6X$ where $X$ is the total number of qualified students and number of boys who qualified $=0.4X$

So, options A, B and C are false and correct answer is D.
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Option A, FALSE because the qualification ratio is $40:60.$

OPTION B, FALSE because the appearance ratio is $65:35.$

OPTION C, FALSE because clearly more boys than girls appeared in the test.

OPTION D, TRUE because qualification percentage is independent of appearance percentage and clearly more girls qualified $(60\%).$

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Based on the information provided in the passage, boys constituted 65% of those who appeared for the national entrance test. Girls therefore accounted for the remaining 35% of candidates who appeared for the test. Since girls accounted for 60% of the qualified candidates, it follows that they were more successful in the test than boys, who must have accounted for less than 60% of the qualified candidates. Therefore, the correct logical inference based on the information provided is that the number of boys who qualified the test is less than the number of girls who qualified.

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

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If $T$ is the total number of students, and $X$ is the total number of qualified students,

Qualification rate of girls $ =\frac{ 0.6X}{0.35T}$

Qualification rate of boys $= \frac{0.4X}{0.65T}$

The first one is clearly the winner here and it is independent of both $T$ (total number of candidates) and $X$ (total number of qualified candidates).
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It would not be correct to say that the qualification rate of girls is "clearly the winner" and is "independent of both T and X". In order to determine which group had a higher qualification rate, we would need to know the values of T and X. Without knowing these values, it is not possible to determine which group had a higher qualification rate.
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@gatecse Sir, looks like ChatGPT had given GATE 2022 xD

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