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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?

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

Analyzing Test Appearance Data

Boys constituted 65% of the candidates who appeared for the national entrance test.

The percentage of girls who appeared is calculated as:

$ 100\% - 65\% = 35\% $

This indicates that the number of boys who appeared was greater than the number of girls who appeared.

Comparing Qualification Percentages

Girls accounted for 60% of the qualified candidates.

Therefore, the percentage of boys who qualified is:

$ 100\% - 60\% = 40\% $

This means that among the total qualified candidates, girls represent a larger proportion (60%) than boys (40%).

Logical Inference on Qualified Candidates

Based on the qualification breakdown:

  • Number of boys qualified = 40% of total qualified candidates.
  • Number of girls qualified = 60% of total qualified candidates.

Since 60% is greater than 40%, the number of girls who qualified is greater than the number of boys who qualified.

Evaluating Inference Options

  • Option 1 (Equal boys and girls qualified): Incorrect. Qualification percentages are unequal (40% vs 60%).
  • Option 2 (Equal boys and girls appeared): Incorrect. Appearance percentages are unequal (65% vs 35%).
  • Option 3 (Boys appeared < Girls appeared): Incorrect. Boys appeared (65%) were more than girls (35%).
  • Option 4 (Boys qualified < Girls qualified): Correct. Boys constituted 40% and girls 60% of qualified candidates.
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Important Questions from Logical Inferences

  1. Based on the statements in (1) – (4), which option/s is/are correct? 
    (1) Thor has a female sibling 
    (2) Thor has a sister 
    (3) Thor has visited New Delhi 
    (4) Thor has visited India

  2. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. 
    When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college. 
    Based only on the above information, which one of the following statements can be logically inferred with certainty?

  3. Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one's love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person. 

    Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty? 

    (i) In Elvesland, one always declares one's love by gifting a white flower. 

    (ii) In Elvesland, all emotions are declared by gifting flowers. 

    (iii) In Elvesland, sometimes one expresses one's anger by gifting a flower that is not yellow. 

    (iv) In Elvesland, sometimes one expresses one's love by gifting a white flower.

  4. A duck named Donald Duck says “All ducks always lie." 

    Based only on the information above, which one of the following statements can be logically inferred with certainty?

  5. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.
    Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

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