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Year

CAT 2019

Section

Data

Topic

Linear Arrangements

Difficulty

Hard

Question

Slot-1

Read the passage and answer the questions below.

Passage:

A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.

The following additional facts are known.

  1. AA and BB are to be placed in consecutively numbered shelves in increasing order.

  2. II and JJ are to be placed in consecutively numbered shelves both higher numbered than the shelves in which AA and BB are kept.

  3. DD, EE and FF are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.

  4. KK is to be placed in shelf number 16.

  5. LL and JJ are items of the same type, while HH is an item of a different type.

  6. CC is a candy and is to be placed in a shelf preceded by two empty shelves.

  7. LL is to be placed in a shelf preceded by exactly one empty shelf.

Question 1

In how many different ways can the items be arranged on the shelves?

8

4

2

1

Question 2

Which of the following items is not a type of biscuit?

L

A

B

G

Question 3

Which of the following can represent the numbers of the empty shelves in a possible arrangement?

1,7,11,121,7,11,12

1,5,6,121,5,6,12

1,2,6,121,2,6,12

1,2,8,121,2,8,12

Question 4

Which of the following statements is necessarily true?

All biscuits are kept before candies.

There are two empty shelves between the biscuits and the candies.

All candies are kept before biscuits.

There are at least four shelves between items BB and CC.

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