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Test Level 3: Averages - 2 - CAT MCQ


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10 Questions MCQ Test - Test Level 3: Averages - 2

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Test Level 3: Averages - 2 - Question 1

Read the following and answer the questions that follow.
If 5 people are transferred from A to B and another independent set of 5 people are transferred back from B to
A, then after this operation (Assume that the set transferred from B to A contains none from the set of students that
came to B from A)

What will happen to B’s average?

Detailed Solution for Test Level 3: Averages - 2 - Question 1

Will always decrease since the net value transferred from B to A will be higher than the net value transferred
from A to B.

Test Level 3: Averages - 2 - Question 2

Read the following and answer the questions that follow.
If 5 people are transferred from A to B and another independent set of 5 people are transferred back from B to
A, then after this operation (Assume that the set transferred from B to A contains none from the set of students that
came to A from B)

At the end of the 2 steps mentioned above (in the direction) what could be the maximum value of the average of class B?

Detailed Solution for Test Level 3: Averages - 2 - Question 2

The maximum possible value for B will happen when the A to B transfer has the maximum possible value and the reverse transfer has the minimum possible
value.

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Test Level 3: Averages - 2 - Question 3

Read the following and answer the questions that follow.
If 5 people are transferred from A to B and another independent set of 5 people are transferred back from B to
A, then after this operation (Assume that the set transferred from B to A contains none from the set of students that
came to B from A)

Q. What can be said about A’s average?

Detailed Solution for Test Level 3: Averages - 2 - Question 3

Since the lowest score in Class B is 23 which is more than the highest score of any student in class A. Hence, A’s average will always increase.

Test Level 3: Averages - 2 - Question 4

Read the following:
There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20,
25 and 30, respectively. If the three classes are represented by A, B and C and you have the following information about the three classes, answer the questions that follow:
A → Highest score 22, Lowest score 18
B → Highest score 31, Lowest score 23
C → Highest score 33, Lowest score 26

If five students are transferred from A to B.

Q. What will happen to the average score of A?

Detailed Solution for Test Level 3: Averages - 2 - Question 4

Cannot say since there is no indication of the values of the numbers which are transferred.

Test Level 3: Averages - 2 - Question 5

Read the following:
There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20,
25 and 30, respectively. If the three classes are represented by A, B and C and you have the following information about the three classes, answer the questions that follow:
A → Highest score 22, Lowest score 18
B → Highest score 31, Lowest score 23
C → Highest score 33, Lowest score 26

If five students are transferred from A to B.

Q. What will happen to the average score of A?

Detailed Solution for Test Level 3: Averages - 2 - Question 5

The effect on A will depend on the profile of the people who are transferred. Hence, anything can
happen.

Test Level 3: Averages - 2 - Question 6

Read the following:
There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20,
25 and 30, respectively. If the three classes are represented by A, B and C and you have the following information about the three classes, answer the questions that follow:
A → Highest score 22, Lowest score 18
B → Highest score 31, Lowest score 23
C → Highest score 33, Lowest score 26

If five students are transferred from A to B.

Q. Which of these can be said about the average score of B?

Detailed Solution for Test Level 3: Averages - 2 - Question 6

If C increases, then the average of C goes up from 30. For this to happen it is definite that the average of B should drop.

Test Level 3: Averages - 2 - Question 7

Read the following:
There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20,
25 and 30, respectively. If the three classes are represented by A, B and C and you have the following information about the three classes, answer the questions that follow:
A → Highest score 22, Lowest score 18
B → Highest score 31, Lowest score 23
C → Highest score 33, Lowest score 26

If five students are transferred from A to B.

Q. What will happen to the average score of B?

Detailed Solution for Test Level 3: Averages - 2 - Question 7

Definitely decrease, since the highest marks in Class A is less than the lowest marks in Class B.

Test Level 3: Averages - 2 - Question 8

Read the following and answer the questions that follows.
In the island of Hoola Boola Moola, the inhabitants have a strange process of calculating their average incomes and expenditures. According to an old legend prevalent on that island, the average monthly income had to be calculated on the basis of 14 months in a calendar year while the average monthly expenditure was to be calculated on the basis of 9 months per year. This would lead to people having an underestimation of their savings since there would be an underestimation of the income and an overestimation of the expenditure per month.

If the minister for economic affairs decided to reverse the process of calculation of average income and average expenditure, what will happen to the estimated savings of a person living on Hoola Boola Moola island?

Detailed Solution for Test Level 3: Averages - 2 - Question 8

Monthly estimates of income is reduced as the denominator
is increased from 12 to 14 at the same time the monthly estimate of expenditure is increased as the denominator is reduced from 12 to 9. Hence, the savings will be underestimated

Test Level 3: Averages - 2 - Question 9

Read the following and answer the questions that follow.
If 5 people are transferred from C to B, further, 5 more people are transferred from B to A, then 5 are transferred from A to B and finally, 5 more are transferred from B to C.

What is the maximum possible average achieved by class C?

Detailed Solution for Test Level 3: Averages - 2 - Question 9

The maximum possible value for C will be achieved when the transfer from C is of five 26’s and the
transfer back from B is of five 31’s. Hence, difference is totals will be +25. Hence, max. average =
(900 + 25)/30 = 30.833.
[Note here that 900 has come by 30*30]

Test Level 3: Averages - 2 - Question 10

Read the following and answer the questions that follow.
If 5 people are transferred from C to B, further, 5 more people are transferred from B to A, then 5 are transferred from A to B and finally, 5 more are transferred from B to C.

Q. What is the maximum possible average of class B?

Detailed Solution for Test Level 3: Averages - 2 - Question 10

For the maximum possible value of Class B the following set of operations will have to hold:
Five 33’s are transferred from C to B, whatever goes from B to A comes back from A to B, then
five 23’s are transferred from B to C. This leaves us with:
Increase of 50 marks → average increases by 2 to 27.

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