Multiple choice

[CAT 1994] The question is followed by two statements, I and II. Mark the answer as per the given conditions. What is the average weight of the 3 new team members who are recently included into the team? I. The average weight of the team increases by 20 kg. II. The 3 new men substitute earlier members whose weights are 64 kg, 75 kg and 66 kg.

  1. Statement I alone is required to answer the question, but not statement II.

  2. Statement II alone is required to answer the question, but not statement I.

  3. Cannot be answered even with the help of both the statements taken together.

  4. Both statements I and II together are needed to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let n be the number of team members. Let S be the sum of weights. New average = (S - 64 - 75 - 66 + W1 + W2 + W3) / n. We have two unknowns (n and the sum of new weights) and only one equation from the average increase. We cannot determine the average weight of the 3 new members.

AI explanation

Let the original team size be n and the new members' average weight be W. From statement one, the total weight increase is 20n, meaning the new members weigh 205 kg plus the replaced members, which equals 205 kg plus 205 kg, a tautology giving no new data. Because statement one only provides a proportional relationship without the original team size, it is impossible to calculate the sum of the three new weights. Therefore, the question cannot be answered even with both statements taken together.

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