**Directions (Qs. 1-3):** Amily Company has its office at the Fourth floor of a multi-storied building in Delhi. There are 5 rooms to be allotted to 5 managers (designated N1 to N5), each of whom will occupy one room. Each room has its own advantages and disadvantages. Some have the sea view, while others are closer to either the lift or the dining room, while some are more spacious. Each of the five managers was asked to rank the room preferences amongst the rooms 401, 402, 403, 404 and 405. Their preferences were recorded as follows:

Some managers did not indicate any preference for some rooms, as they did want to be there under any condition. The company decided to allot rooms to managers in such a way that so that the managers get rooms as per their best preference or close to that.

**Question 1 :Â **If manager X gets his/her 1st choice, then his / her preference ranking isÂ 1Â Â andÂ so on. Management decided to allot rooms so that *the sum of the preference rankings of all the managers is minimized, *what is the total preference ranking for the rooms allotted to all the managers?

A. 5

B. 6

C. 7

D. 8

E. 9

**Question 2 :Â **How many managers would get their rooms as per their best preference?

A. 1

B. 2

C. 3

D. 4

E. 5

**Question 3 :Â **Suppose that Manager N2 decides not to join the new zonal office and Manager N6 takes his place. Manager N6 has the following preference ranking in decreasing order: 401,403,402,404 – in this case what would be the sum of the preference rankings allotted to all the five managers?

A. 5

B. 6

C. 7

D. 8

E. 9

### Answers and Explanations

**Answer 1 :Â (C)**

The sum of the preference rankings is minimized in the arrangement given below. The sum will be 7.

**Answer 2 :Â (C)**

Since three out of five managers have opted for Room No. 402, two of them will have to settle for some other room. Hence, three managers will get rooms as per their first preferences.

**Answer 3 :Â (E)**

The sum of the preference rankings will be 9 in either arrangement shown below.

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