Question

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?

• A. Equal number of boys and girls qualified
• B. Equal number of boys and girls appeared for the test
• C. The number of boys who appeared for the test is less than the number of girls who appeared
• D. The number of boys who qualified the test is less than the number of girls who qualified

Hint:

When dealing with percentages in logical reasoning problems, breaking down the total and distributing the values according to the given information helps identify the correct inference.

Answer 1

The Correct Option is D

Let's denote the total number of candidates who appeared for the test as \( N \). - The number of boys who appeared for the test is \( 0.65N \), and the number of girls who appeared is \( 0.35N \). - According to the problem, girls accounted for 60% of the qualified candidates. So, the number of girls who qualified the test is \( 0.60Q \), where \( Q \) is the total number of candidates who qualified the test. - This means the number of boys who qualified the test is \( 0.40Q \) because boys account for the remaining 40% of the qualified candidates. Now, let’s analyze the total number of qualified candidates \( Q \): - The total number of qualified candidates is the sum of the number of boys and girls who qualified. Therefore: \[ Q = 0.40Q + 0.60Q \] This implies that the total number of qualified candidates is distributed between boys and girls according to the given ratios. Since girls account for a higher percentage of qualified candidates, the number of boys who qualified the test is less than the number of girls who qualified. Thus, the correct inference is (D): The number of boys who qualified the test is less than the number of girls who qualified.