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