Multiple choice

Directions: Each of the following questions consists of a question followed by three statements I, II and Ill. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the age of a class teacher? I. There are 11 students in the class. II. The average age of the students and the teacher is 14 years. III. The average age of the teacher and the students is 3 years more than that of the students.

  1. Both I and III

  2. Both l and ll

  3. II and either I or III

  4. All I, II and III

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let T be the teacher's age and S be the sum of students' ages. Statement I gives the number of students (11). Statement II provides (S+T)/12 = 14, which is S+T = 168. Statement III provides (S+T)/12 = (S/11) + 3. With all three, we have a system of equations that allows solving for T.

AI explanation

To find the teacher's age, we must first establish an equation using the overall average age, which requires knowing both the number of people and the average age difference. Statement II gives the combined average age of the students and teacher as 14, yielding a total age of 14 times the total number of people. Statement I explicitly provides the number of students as 11, which is needed to find the students' total age before computing the teacher's age. While statement III offers the relative average difference, it still requires the explicit student count from statement I to be useful. Therefore, all statements I, II, and III are necessary to successfully solve the problem.

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