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CAT 2019 Slot 1 DILR · Set 4 of 8Logical ReasoningModerate DifficultyQ13–Q16 · 4 MCQ

CAT 2019 Slot 1 DILR Set 4: Arrangements (4 Questions) with Solutions

The Arrangements set from the official CAT 2019 Slot 1 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2019 Slot 1 DILR · Questions 13–16
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.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q13. Arrangements

MCQ · +3 / −1
In how many different ways can the items be arranged on the shelves?
  1. A) 4
  2. B) 1
  3. C) 2
  4. D) 8
Correct Answer
D) 8
Step-by-step solution
📌 Core Concept
Place the clusters (savouries, biscuits, candies) using the empty-shelf rules, then count the orderings the clues leave open.
🔢 Step-by-Step Solution
1
Clue 4 puts K in shelf 16. Savouries come after all biscuits and candies, so K is a savoury. D, E, F are consecutive and increasing, so the savouries are D, E, F, K in shelves 13 to 16.
2
Shelf 12 must be empty, because different types need a gap. That leaves 8 items (5 biscuits, 3 candies) in shelves 1 to 11, and 16 - 12 = 4 shelves are empty in total.
3
Clue 6 says C is a candy preceded by two empty shelves, so C starts the candy cluster. Clue 7 says L is preceded by exactly one empty shelf, so L starts a cluster. L cannot start the candy cluster (C does) or the savoury cluster (D does), so L starts the biscuit cluster.
4
Clue 5 makes J the same type as L, so J is a biscuit. Clues 1 and 2 add A, B and I, J, so the biscuits are L, A, B, I, J. The candies are C, G, H, and H is a candy because it differs from L's type. The savoury group is D, E, F, K.
5
With 4 empty shelves in total, only two layouts work:
Layout P: empties at 1, 2, then candies at 3 to 5, empty 6, biscuits at 7 to 11, empty 12.
Layout Q: empty 1, biscuits at 2 to 6, empties 7 and 8, candies at 9 to 11, empty 12.
6
In each layout the biscuit order is forced as L, A, B, then I and J in either order. That gives 2 ways.
7
C is first among the candies, and G and H can swap. That gives 2 ways.
8
Each layout gives 2×2=42 \times 2 = 4 arrangements, so the total is 4+4=84 + 4 = 8.
Quick Check
The two layouts are the only ones with exactly 4 empty shelves that satisfy clues 6 and 7, so 2×4=82 \times 4 = 8.
Correct Answer: D

Q14. Arrangements

MCQ · +3 / −1
Which of the following items is not a type of biscuit?
  1. A) B
  2. B) A
  3. C) L
  4. D) G
Correct Answer
D) G
Step-by-step solution
📌 Core Concept
Sort the 12 items into three clusters (biscuits 5, candies 3, savouries 4) using the clues about cluster starts and pairs.
🔢 Step-by-Step Solution
1
Clue 3 puts D, E, F in consecutive shelves after all biscuits and candies, and clue 4 puts K in shelf 16. The savouries number 12 - 5 - 3 = 4, so they are D, E, F and K. The remaining items A, B, C, G, H, I, J, L are the 5 biscuits and 3 candies.
2
Clue 6 says C is a candy preceded by two empty shelves. The shelf before C is empty, so C is the first shelf of the candy cluster.
3
Clue 7 says L is preceded by exactly one empty shelf. An empty shelf before L means L is the first item of a cluster. L is not a savoury, and the candy cluster already starts with C, so L starts the biscuit cluster. L is therefore a biscuit.
4
Clue 5 says J is the same type as L, so J is a biscuit. Clue 2 puts I in the shelf next to J. Different types need an empty shelf between them, so I is in J's cluster and is also a biscuit.
5
Clue 5 also says H is a different type from L and J, so H is not a biscuit. H is not a savoury, so H is a candy.
6
So far the biscuits are L, J, I and the candies are C, H. A and B are in consecutive shelves (clue 1), so they are the same type. If both were candies, the candies would be C, H, A, B, which is 4 and too many. So A and B are biscuits, which makes the five biscuits L, J, I, A, B.
7
The three candies are therefore C, H and the one item left, G.
Why Not the Others
B: biscuit, from step 6.
A: biscuit, from step 6.
L: biscuit, from step 3.
G: the third candy, from step 7, so it is not a biscuit.
Quick Check
Biscuits A, B, I, J, L (5), candies C, G, H (3), savouries D, E, F, K (4) match the counts given.
Correct Answer: D

Q15. Arrangements

MCQ · +3 / −1
Which of the following can represent the numbers of the empty shelves in a possible arrangement?
  1. A) 1,7,11,12
  2. B) 1,2,8,12
  3. C) 1,2,6,12
  4. D) 1,5,6,12
Correct Answer
C) 1,2,6,12
Step-by-step solution
📌 Core Concept
The only layouts that satisfy all the clues give two possible sets of empty shelves. Match the options to them.
🔢 Step-by-Step Solution
1
D, E, F, K occupy 13 to 16, so shelf 12 is empty. That leaves three more empty shelves among 1 to 11.
2
C is a candy preceded by two empty shelves, and L is a biscuit preceded by exactly one empty shelf. Together these leave two valid layouts:
Candies in 3 to 5 and biscuits in 7 to 11, with empties 1, 2, 6, 12.
Biscuits in 2 to 6 and candies in 9 to 11, with empties 1, 7, 8, 12.
3
Option C (1, 2, 6, 12) matches the first layout.
Why Not the Others
1, 7, 11, 12: the gap before the candies would be 7 to 10, which is not possible.
1, 2, 8, 12: this does not fit either layout.
1, 5, 6, 12: this does not fit either layout, and it gives no consistent block sizes.
Correct Answer: C

Q16. Arrangements

MCQ · +3 / −1
Which of the following statements is necessarily true?
  1. A) There are at least four shelves between items B and C.
  2. B) There are two empty shelves between the biscuits and the candies.
  3. C) All candies are kept before biscuits.
  4. D) All biscuits are kept before candies.
Correct Answer
A) There are at least four shelves between items B and C.
Step-by-step solution
📌 Core Concept
Check each statement against both valid layouts. A statement is necessarily true only if it holds in both.
🔢 Step-by-Step Solution
1
The savouries D, E, F, K sit in shelves 13 to 16. Shelf 12 is empty. The biscuits are L, A, B, I, J, with L first. The candies are C, G, H, with C first.
2
Layout P has empties at 1 and 2, candies at 3 to 5, empty 6, biscuits at 7 to 11, empty 12. Here C is in shelf 3 and B is in shelf 9. The shelves between them are 4 to 8, which is 5 shelves.
3
Layout Q has empty 1, biscuits at 2 to 6, empties 7 and 8, candies at 9 to 11, empty 12. Here B is in shelf 4 and C is in shelf 9. The shelves between them are 5 to 8, which is 4 shelves.
4
In both layouts there are at least four shelves between B and C, so option A is necessarily true.
Why Not the Others
B: in Layout P only one empty shelf (6) separates the candies and biscuits.
C: in Layout Q the biscuits come before the candies.
D: in Layout P the candies come before the biscuits.
Correct Answer: A
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CAT 2019 Slot 1 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Kozhikode

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