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CAT Exam 2021 Slot 2 Solved Paper

Instructions [29 - 34 ]
Ten objects 01 , 021 , …, 010 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.

	01	02	03	04	05	06	07	08	09	010
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 if X values Y’‌s bundle more than X’‌s own bundle.
For example, hypothetically suppose Amar’s bundle consists of 01 and 02 , and Barat’s bundle consists of 03 and 04 . 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 01 , 02 and 03 were given to three different people.
3. Objects 01 and 08 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 : 30

Total: 66

Who among the following envies someone else?

Barat
Charles
Amar
Elise

Validate

Solution:

We have the following table :

	01	02	03	04	05	06	07	08	09	010
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

010 is given to Elise and 09 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 01 or 05 or 07
Case 1 :
01 is given to Elise
Now the total valuation of 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, 07 will be given to him
so we get
Bharat - 09 and 07 and Elise - 010 and 01
For Charles to have valuation 16
the only way =8+8
so we can say 08 is given to Charles along with either 02 03 .( 01 and 08 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 02 or 03 and 05
Now we are left with 04 and 06
So if Disha receives 04 and 06
The valuation of Disha will be 5+3=8 which is not an odd number
so this case is discarded.

Case 2 :
Elise receives 05 or 07 .
Now Valuation of Elise = 16.
And Elise receives 010 and

Bharat received 09 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 07 .
So Elise received 05 .
So we have
Bharat - 09 , 07
Elise - 010 , 05 .
Now as we know 01 , 02 and 03 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 08 will be given to Charles, and he cannot have 01 , also he cannot have 02 because if he has 02 he will value Bharat’s bundle as 17 and will envy him which is not possible so Charles will have 03 , 08
Now Amar will have 02 and Disha will have 01 .
Now Amar will not have 04 because in that case Charles will envy Amar and is not possible so we can say Amar will have 06 and Disha will have 04 .
So we have the following :
Amar - 02 , 06
Bharat - 09 , 07
Charles - 03 08
Disha - 01 , 04
Elise - 010 05
So Amar envies someone else

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