Objects and Bundles

CAT 2021 Slot 2 · DILR · Hard · Data Interpretation

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Passage / data set

Ten objects $o_1, o_2, \dots, o_{10}$ 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:

	$o_1$	$o_2$	$o_3$	$o_4$	$o_5$	$o_6$	$o_7$	$o_8$	$o_9$	$o_{10}$
Amar	4	9	9	3	7	3	8	7	9	5
Barat	5	9	7	5	5	3	6	8	10	8
Charles	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 $o_1$ and $o_2$ , and Barat's bundle consists of $o_3$ and $o_4$ . 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:

If someone's value for an object is 10, then she/he received that object.
Objects $o_1$ , $o_2$ , and $o_3$ were given to three different people.
Objects $o_1$ and $o_8$ were given to different people.
Three people value their own bundles at 16. No one values her/his own bundle at a number higher than 16.
Disha values her own bundle at an odd number. All others value their own bundles at an even number.
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 1 of 6

What BEST can be said about object $o_8$ ?

A.
$o_8$ was given to Disha
B.
$o_8$ was given to Amar, Charles, or Disha
C.
$o_8$ was given to Charles or Disha
D.
$o_8$ was given to Charles

Answer

Explanation

Based on the rules and bundle values, object $o_8$ was definitely given to Charles.

Question 2 of 6

Who among the following envies someone else?

A.
Amar
B.
Barat
C.
Charles
D.
Elise

Answer

Explanation

Amar values his own bundle less than 16 and envies someone who values their bundle at 16.

Question 3 of 6

What is Amar's value for his own bundle?

Answer

Explanation

Amar received $o_5$ and $o_{10}$ or a pair that yields a total value of 12.

Question 4 of 6

Object $o_4$ was given to

A.
Disha
B.
Barat
C.
Charles
D.
Elise

Answer

Explanation

Object $o_4$ was assigned to Disha to satisfy the odd total condition and constraints.

Question 5 of 6

Object $o_5$ was given to

A.
Amar
B.
Elise
C.
Charles
D.
Disha

Answer

Explanation

By deduplication of object distribution across all 5 persons, $o_5$ was given to Elise.

Question 6 of 6

What BEST can be said about the distribution of object $o_1$ ?

A.
$o_1$ was given to Charles or Disha
B.
$o_1$ was given to Charles, Disha, or Elise
C.
$o_1$ was given to Charles
D.
$o_1$ was given to Disha

Answer

Explanation

Analyzing the constraints, $o_1$ must have been given to Disha.

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