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Aptitude - Average

Exercise : Average - Data Sufficiency 1
Directions to Solve

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

  • Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
  • Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
1.

The average age of P, Q, R and S is 30 years. How old is R?

I. 

The sum of ages of P and R is 60 years.

 II. 

S is 10 years younger than R.

I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Answer: Option
Explanation:

P + Q + R + S = (30 x 4)      P + Q + R + S = 120 .... (i)

 I. P + R = 60 .... (ii)

II. S = (R - 10) .... (iii)

From (i), (ii) and (iii), we cannot find R.

Correct answer is (D)

2.

How many candidates were interviewed everyday by the panel A out of the three panels A, B and C?

I. 

The three panels on average interview 15 candidates every day.

 II. 

Out of a total of 45 candidates interviewed everyday by the three panels, the number of candidates interviewed by panel A is more by 2 than the candidates interviewed by panel c and is more by 1 than the candidates interviewed by panel B.

I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Answer: Option
Explanation:

 I. Total candidates interviewed by 3 panels = (15 x 3) = 45.

II. Let x candidates be interviewed by C.

Number of candidates interviewed by A = (x + 2).

Number of candidates interviewed by B = (x + 1).

x + (x + 2) + (x + 1) = 45

3x = 42

x = 14

Hence, the correct answer is (B).

3.

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.

I alone sufficient while II alone not sufficient to answer
II alone sufficient while I alone not sufficient to answer
Either I or II alone sufficient to answer
Both I and II are not sufficient to answer
Both I and II are necessary to answer
Answer: Option
Explanation:

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)

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