Question

How many children are there in the class? Statement (I): The sum of the ages of all the children in the class and the class teacher is 262 years. Statement (II): The total ages of the children in the class is 240 years and the average age is 16 years.

• A. Statement I alone is sufficient, but Statement II alone is not sufficient.
• B. Statement II alone is sufficient, but Statement I alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Even both statements together are not sufficient.

Hint:

If total value and average value are known, divide the total by the average to find the number of observations.

Answer 1

The Correct Option is B

Concept: Average age is given by \[ \text{Average Age} = \frac{\text{Total Age}}{\text{Number of Individuals}}. \] Thus, \[ \text{Number of Individuals} = \frac{\text{Total Age}}{\text{Average Age}}. \]

Step 1: Analyze Statement (I). The total age of children and teacher together is \[ 262. \] The teacher's age is unknown. Hence children's total age is unknown. Number of children cannot be determined. Statement (I) is insufficient.

Step 2: Analyze Statement (II). Given: \[ \text{Total age}=240 \] and \[ \text{Average age}=16. \] Therefore \[ \text{Number of children} = \frac{240}{16} = 15. \] A unique value is obtained. Statement (II) alone is sufficient.