Aptitude - Average

Exercise :: Average - Data Sufficiency 2

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.


How many marks did Tarun secure in English?


The average mark obtained by Tarun in four subjects including English is 60.


The total marks obtained by him in English and Mathematics together are 170.


The total marks obtained by him in Mathematics and Science together are 180.

A. I and II only
B. II and III only
C. I and III only
D. All I, II and III
E. None of these

Answer: Option E


I gives, total marks in 4 subjects = (60 x 4) = 240.

II gives, E + M = 170

III gives, M + S = 180.

Thus, none of (A), (B), (C), (D) is true.

Correct answer is (E).


In a cricket team, the average age of eleven players in 28 years. What is the age of the captain?


The captain is eleven years older than the youngest player.


The average age of 10 players, other than the captain is 27.3 years.


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

Answer: Option C


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).