Multiple choice

Directions: In the following problem, a question is followed by three statements I, II and III. Read the question and the statements carefully and choose which statements are required to answer the question. How many boys are there in the class? I. The number of boys is 20 more than the number of girls. II. The average weight of boys is 40 kg and that of girls is 30 kg. III. The average weight of all the students of the class is 36 kg.

  1. I and II only

  2. II and III only

  3. All I, II and III

  4. Either I and II, or II and III

  5. The question cannot be answered even using all the statements together.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be boys and G be girls. (I) B = G + 20. (II) Average weight of boys = 40, girls = 30. (III) Average weight of class = 36. The total weight is 40B + 30G = 36(B + G). This gives 40B + 30G = 36B + 36G, so 4B = 6G, or 2B = 3G. Combining with B = G + 20, we can solve for B and G. All three are needed.

AI explanation

All three statements are required to establish the number of boys in the class. Letting the number of boys be B and the number of girls be G, the overall average weight equation from statements II and III is (40B + 30G) / (B + G) = 36. This equation simplifies to 4B = 6G, meaning the ratio of boys to girls is needed to find the exact count. Statement I provides the exact relationship needed by establishing B = G + 20, allowing you to solve the simultaneous equations for the definitive count of boys. Without all three statements, the exact number of boys remains unsolvable.

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