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Average - General Aptitude

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
Q1:

In a cricket team, the average age of eleven players in 28 years. What is the age of the captain?  I. The captain is eleven years older than the youngest player.  II. The average age of 10 players, other than the captain is 27.3 years.  III. Leaving aside the captain and the youngest player, the average ages of three groups of three players each are 25 years, 28 years and 30 years respectively.

A Any two of the three

B All I, II and III

C II only or I and III only

D II and III only

E None of these

ANS:C - II only or I and III only

Total age of 11 players = (28 x 11) years = 308 years.  I. C = Y + 11      C - Y = 11 .... (i) II. Total age of 10 players (excluding captain) = (27.3 x 10) years = 273 years.  Age of captain = (308 - 273) years = 35 years. Thus, C = 35. .... (ii) From (i) and (ii), we get Y = 24 III. Total age of 9 players = [ (25 x 3) + (28 x 3) + (30 x 3)] years = 249 years.  C + Y = (308 - 249) = 59 .... (iii) From (i) and (iii), we get C = 35. Thus, II alone gives the answer. Also, I and III together give the answer.  Correct answer is (C).