Supermarket Shelf Arrangement

CAT 2019 Slot 1 · DILR · Hard · Logical Reasoning

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Passage / data set

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. A and B are to be placed in consecutively numbered shelves in increasing order.
  2. I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.
  3. D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.
  4. K is to be placed in shelf number 16.
  5. L and J are items of the same type, while H is an item of a different type.
  6. C is a candy and is to be placed in a shelf preceded by two empty shelves.
  7. L is to be placed in a shelf preceded by exactly one empty shelf.

Question 1 of 4

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

  1. A.

    2

  2. B.

    1

  3. C.

    4

  4. D.

    8

Answer

D

Explanation

By working through the placement constraints for biscuits (5 items), candies (3 items), and savouries (4 items: D, E, F, K) along with empty shelf placements, there are 8 valid arrangements.

Question 2 of 4

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

  1. A.

    B

  2. B.

    A

  3. C.

    L

  4. D.

    G

Answer

D

Explanation

Deductions show that A, B, L, I, J form the 5 biscuits (or L and J are biscuits). G is a candy, so G is not a type of biscuit.

Question 3 of 4

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

  1. A.

    1,7,11,12

  2. B.

    1,5,6,12

  3. C.

    1,2,6,12

  4. D.

    1,2,8,12

Answer

C

Explanation

Checking valid arrangements, empty shelves can be positioned at shelves 1, 2, 6, 12.

Question 4 of 4

Which of the following statements is necessarily true?

  1. A.

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

  2. B.

    All candies are kept before biscuits.

  3. C.

    All biscuits are kept before candies.

  4. D.

    There are at least four shelves between items B and C.

Answer

D

Explanation

Across all valid configurations, the gap between the position of item B and item C is at least 4 shelves.

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