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Question

Difficulty: EasyData Sufficiency

What is the average age of a class of 20 students?

Statement I: The sum of the ages of all 20 students in the class is 300 years.
Statement II: The age of the youngest student in the class is 12 years.

  1. Statement I alone is sufficient to answer the question, while Statement II alone is not sufficient.Answer
  2. B
    Statement II alone is sufficient to answer the question, while Statement I alone is not sufficient.
  3. C
    Either Statement I alone or Statement II alone is sufficient to answer the question.
  4. D
    Neither Statement I nor Statement II is sufficient to answer the question.
  5. E
    Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.

Answer

Statement I alone is sufficient to answer the question, while Statement II alone is not sufficient.
The correct choice highlights that Statement I alone provides the total sum of ages for the 20 students. Since average equals total sum divided by the number of items (Average=30020=15\text{Average} = \frac{300}{20} = 15), Statement I alone is sufficient. Statement II only tells us the age of one specific student, which does not allow us to compute the average for all 20 students.

Step-by-Step Solution

1
Analyze the core formula needed to solve the question
The average age of a group is calculated using the formula: Average Age=Sum of ages of all studentsTotal number of students\text{Average Age} = \frac{\text{Sum of ages of all students}}{\text{Total number of students}}. The total number of students is given as 2020.
Understanding the required parameters helps evaluate statement sufficiency.
2
Evaluate Statement I individually
Statement I gives the sum of ages =300= 300 years. Average Age=30020=15\text{Average Age} = \frac{300}{20} = 15 years. Thus, Statement I alone yields a unique answer and is sufficient.
Determines if Statement I provides enough data on its own.
3
Evaluate Statement II individually
Statement II gives the age of the youngest student =12= 12 years. This tells us nothing about the remaining 1919 students, so we cannot determine the sum or the average age. Thus, Statement II alone is not sufficient.
Determines if Statement II provides enough data on its own.

Key Concept

Data Sufficiency - Evaluation of Individual Statements in Average Calculations
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Topics

Data Sufficiency

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