Logical Reasoning – A supermarket has to place 12 items


Slot – 1 – LR

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.
Q.1 In how many different ways can the items be arranged on the shelves?

  1. 4
  2. 2
  3. 8
  4. 1
Answer: 3

Q.2 Which of the following items is not a type of biscuit?

  1. A
  2. L
  3. B
  4. G
Answer: 4

Q.3 Which of the following can represent the numbers of the empty shelves in a possible arrangement?

  1. 1,7,11,12
  2. 1,5,6,12
  3. 1,2,6,12
  4. 1,2,8,12
Answer: 3

Q.4 Which of the following statements is necessarily true?

  1. There are two empty shelves between the biscuits and the candies
  2. All candies are kept before biscuits
  3. All biscuits are kept before candies.
  4. There are at least four shelves between items B and C.
Answer: 4

Solution: Total number of Biscuits = 5
Total number of Candies = 3
So Total number of Savouries = 12 – 5 – 3 = 4
From point iii) and iv) it is clear that D, E, F and K are 4 savouries and are kept in shelves numbered 13,14, 15 and 16 as there is no empty shelf between items of the same type.
From point II), V and VII) I, J and L are of the same type L being in the least numbered shelf among 3.
As from point VI,) C is candy so I, J and L must be Biscuits as there are only 3 candies.
From point V) H is not Biscuits so it must be a candy thus A and B must be Biscuits.
Now Item can be placed as given below.
Case 1) when all biscuits are placed after candies.
Case 2) When all candies are placed after biscuits.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Case 1     C H/G G/H   L A B I/J J/I   D E F K
                                 
Case 2   L A B I/J J/I     C H/G G/H   D E F K

Total 8 cases are possible.
All questions can be answered now.
  1. There are two empty shelves between the biscuits and the candies.
  2. All candies are kept before biscuits.
  3. All biscuits are kept before candies.
  4. There are at least four shelves between items B and C


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