Aptitude - Average - Discussion

Discussion Forum : Average - Data Sufficiency 1 (Q.No. 3)
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.

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)

Discussion:
7 comments Page 1 of 1.

ASAN said:   1 decade ago
How to use multiply rule Finding used in teacher age ?

Jyoti said:   1 decade ago
Why average age of x+1 is x+1 years?

Gowrishankar said:   1 decade ago
I can't understand this problem.

No one said:   1 decade ago
Let the average age of all the children be A and the number of students be n. Then we have to find A.

Now (I) says -
T = n; where T = teacher's age. It's clear that we can't find A from (I).

(II) says that the average increases by 1 if we include the teacher's age too.

So,
(n * A + T) / (n + 1) = A + 1;

Again, can't be solved.

Now we must check whether (I) and (II) together can be sufficient. For that, put T = n from (I) into (II) as follows -

(n * A + n) / (n + 1) = A + 1
n * ( A + 1) / (n + 1) = (A + 1)
n / (n + 1) = 1;

The last condition we arrived at, can NOT be satisfied with any real number(or any number for that matter).

So, Even both combined cannot provide a solution. Hence, the answer should be (D).

Anindya said:   1 decade ago
Say avg age of 5 people is 6. Then the total age of 5 people is:
5*6=30.

Similarly average age when teacher is included=x+1 and the no. of persons concerned=x+1.

So total age of the persons involved = (x+1)*(x+1).

Now from condition I, avg age of the students = [(total age)/x] which is equal to x.

So total age of all the students = x*x =x^2.

So subtraction of total age of (teacher +students) and the total age of students gives the age of teacher.
(1)

Shashi said:   9 years ago
Let number of children be x.
So, Age of teacher = x years

Let Avg age of children be y years.
So, Sum of the age of children = xy years.

Acc to Question,

(xy + x)/(x + 1) = y + 1.

=> x(y + 1)/(x + 1) = y + 1.
=> x/(x + 1) = (y + 1)/(y + 1).
=> x/(x + 1) = 1.
=> x = x + 1.
=> x - x = 1.
=> 0 = 1

Now, this is a contradiction, So answer should be D
(1)

Kallu said:   6 years ago
How we can get avg of x+1=x+1?

By including both conditions we are getting -ve avg ie not possible. So, D is the answer.

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