Multiple choice

Directions: In the following problem, a question is followed by three statements numbered (I), (II), and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. How many students are there in the group? I. Average age of the students in the group is 10 years. II. If a new student of age 4 years is added to the group, then the average age becomes 9 years. III. Three students in the group are 12 years of age, two of the students in the group are 7 years of age.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statement II and either statement I or statement III

  4. All three statements

  5. None of the statements
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A Correct answer
Explanation

Let n be the number of students and S be the sum of their ages. I: S/n = 10, so S = 10n. II: (S + 4)/(n + 1) = 9, so S + 4 = 9n + 9. Substituting S = 10n: 10n + 4 = 9n + 9, so n = 5. Statements I and II are sufficient.

AI explanation

By combining statements one and two, we let the total age of the group be T and the number of students be N. Statement one gives the equation T divided by N equals 10, and statement two gives the equation T plus 4 divided by N plus 1 equals 9. Solving these simultaneous equations, we substitute T as 10N to get 10N plus 4 equals 9N plus 9, which results in N equaling 5 students. Statement three provides no information about the total number of students or the overall total age, making only statements one and two sufficient to answer the question.

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