XAT 2018 Question 67
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XAT
Sum of the ages of the 6 friends is the square of a prime number.
Statement I states that all the members were aged between 50 and 85 years. There are 6 friends in total. Therefore, the sum of the ages can vary from 6*50 to 6*85. Sum of the ages of the 6 persons should lie between 300 and 510. 361 is the only square of a prime number (19) in the given range. Therefore, statement I alone is sufficient to answer the question.
Statement II states that the standard deviation of their ages is 4.6. SD gives us how much the values deviate from the mean. We cannot obtain the mean using the SD. Therefore, statement II alone is insufficient to answer the question without knowing the values in the data set.
Therefore, option A is the right answer.