Question

These statements provide data that may help answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions. Accordingly, choose the appropriate option given below the questions.

A group of six friends noticed that the sum of their ages is the square of a prime number. What is the average age of the group?

Statement I: All members are between 50 and 85 years of age. Statement II: The standard deviation of their ages is 4.6.

Accepted Answer

A. Sum of ages of 6 friends is the square of a prime number $p^2$. From Statement I, each member is between 50 and 85 years old. Sum of ages is between $6 	imes 50 = 300$ and $6 	imes 85 = 510$. The only square of a prime number in this range is $19^2 = 361$. Therefore, the sum of their ages must be 361, and the average age is $\frac{361}{6}$. Thus, Statement I alone is sufficient. Statement II alone does not provide the sum or mean. Thus, option A is correct.

Data Sufficiency - Average age of group

Explanation

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