Test Index

CAT Exam 2021 Slot 2 Solved Paper

Instructions [29 - 34 ]

Ten objects

0_1

0_{21}

, …,

0_{10}

were distributed among Amar, Barat, Charles, Disha, and Elise. Each item went to exactly one person. Each person got exactly two of the items, and this pair of objects is called her/his bundle.

The following table shows how each person values each object.

	$0_1$	$0_2$	$0_3$	$0_4$	$0_5$	$0_6$	$0_7$	$0_8$	$0_9$	$0_{10}$
Amar	4	9	9	3	7	3	8	7	9	5
Bharat	5	9	7	5	5	3	6	8	10	8
Chales	8	8	8	3	6	4	5	8	9	6
Disha	8	8	8	5	5	3	6	4	9	8
Elise	6	8	9	5	6	5	6	3	7	10

The value of any bundle by a person is the sum of that person’s values of the objects in that bundle. A person

X

envies another person

Y

X

values

\text{Y's}

bundle more than

\text{X's}

own bundle.

For example, hypothetically suppose Amar’s bundle consists of

0_1

and

0_2

, and Barat’s bundle consists of

0_3

and

0_4

. Then Amar values his own bundle at

4 + 9 = 13

and Barat’s bundle at

9 + 3 = 12

. Hence Amar does not envy Barat. On the other hand, Barat values his own bundle at

7 + 5 = 12

and Amar’s bundle at

5 + 9 = 14

. Hence Barat envies Amar.

The following facts are known about the actual distribution of the objects among the five people.

1. If someone’s value for an object is 10, then she/he received that object.

2. Objects

0_1

0_2

and

0_3

were given to three different people.

3. Objects

0_1

and

0_8

were given to different people.

4. Three people value their own bundles at 16. No one values her/his own bundle at a number higher than 16.

5. Disha values her own bundle at an odd number. All others value their own bundles at an even number.

6. Some people who value their own bundles less than 16 envy some other people who value their own bundle at 16. No one else envies others.

Question : 31 of 66

Marks: +1, -0

What is Amar’s value for his own bundle?

Your Answer:

Validate

Solution:

We have the following table :

	$0_1$	$0_2$	$0_3$	$0_4$	$0_5$	$0_6$	$0_7$	$0_8$	$0_9$	$0_10$
Amar	4	9	9	3	7	3	8	7	9	5
Bharat	5	9	7	5	5	3	6	8	10	8
Chales	8	8	8	3	6	4	5	8	9	6
Disha	8	8	8	5	5	3	6	4	9	8
Elise	6	8	9	5	6	5	6	3	7	10

0_10

is given to Elise and

0_9

is given to Bharat .

Now as Elise values his own bundle at an even number so the only two objects which can be given to Elise is

0_1

0_5

0_7

Case 1 :

0_1

is given to Elise

Now the total valuation of

\text{Elise} = 12

Valuation of Disha is an odd number

So we can say Amar , Bharat and Charles values their bundles at 16.

So for Bharat the valuation to be 16,

0_7

will be given to him

so we get

Bharat -

0_9

and

0_7

and Elise -

0_10

and

0_1

For Charles to have valuation 16

the only way

= 8+8

so we can say

0_8

is given to Charles along with either

0_2

0_3

0_1

and

0_8

cannot be together )

Now for Amar to have a valuation of 16

the only way possible

= 9 + 7

Now so we can say

Amar will receive either

0_2

0_3

and

0_5

Now we are left with

0_4

and

0_6

So if Disha receives

0_4

and

0_6

The valuation of Disha will be

5+3 =8

which is not an odd number

so this case is discarded.

Case 2 :

Elise receives

0_5

0_7

Now Valuation of Elise = 16.

And Elise receives

0_10

and

\frac{0_5}{0_7}

Bharat received

0_9

and we know the evaluation of Bharat is an even number and the minimum even number possible for valuation of Bharat is 16 and no one can have evaluation more than 16 so Bharat received

0_7

So Elise received

0_5

So we have

Bharat -

0_9

0_7

Elise -

0_10

0_5

Now as we know

0_1

0_2

and

0_3

are given to three different persons so they are Amar, Charles and Disha .

Now As per Amar

he values Bharat at 17 so he envy him

So Amar will value his bundle less than 16

So the only possibility for Amar to value his bundle less than

16 = 12 =9+3

Now we can say Charles will have 16 as his own valuation so he will get

8+8

Now

0_8

will be given to Charles, and he cannot have

0_1

, also he cannot have

0_2

because if he has

0_2

he will value Bharat’s bundle as 17 and will envy him which is not possible so Charles will have

0_3

0_8

Now Amar will have

0_2

and Disha will have

0_1

Now Amar will not have

0_4

because in that case Charles will envy Amar and is not possible so we can say Amar will have

0_6

and Disha will have

0_4

So we have the following :

Amar -

0_2

0_6

Bharat -

0_9

0_7

Charles -

0_3

0_8

Disha -

0_1

0_4

Elise -

0_10

0_5

So Amar's own valuation

= 9+3 =12

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