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Average - General Aptitude

Q1:

What is the average age of children in the class?  I. The age of the teacher is as many years as the number of children.  II. Average age is increased by 1 year if the teacher's age is also included.

A I alone sufficient while II alone not sufficient to answer

B II alone sufficient while I alone not sufficient to answer

C Either I or II alone sufficient to answer

D Both I and II are not sufficient to answer

E Both I and II are necessary to answer

ANS:D - Both I and II are not sufficient to answer

Let there be x children. I gives, age of teacher = x years. II gives, average age of (x + 1) persons = (x + 1) years.  Teacher's age = (x + 1) (x + 1) - x2 = (x2 + 1 + 2x) - x2 = (1 + 2x) Thus, teacher's age cannot be obtained.  Correct answer is (D)