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CAT 2017 Slot 1 · DILR · Medium · Logical Reasoning
Passage / data set
In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built. The heights (in metres) of individual platforms are as shown below:
| 6 | 1 | 2 | 4 | 3 | | 9 | 5 | 3 | 2 | 8 | | 7 | 8 | 4 | 6 | 5 | | 3 | 9 | 5 | 1 | 2 | | 1 | 7 | 6 | 3 | 9 |
Individuals (all of same height) are seated on these platforms. We say an individual A can reach an individual B if all the three following conditions are met: (i) A and B are in the same row or column (ii) A is at a lower height than B (iii) If there is/are any individual(s) between A and B, such individual(s) must be at a height lower than that of A.
Thus in the table given above, consider the individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5. Rows in the layout are numbered from top to bottom and columns are numbered from left to right.
Question 1 of 4
How many individuals in this layout can be reached by just one individual?
- A.
3
- B.
5
- C.
7
- D.
8
C
Explanation
Counting individual platforms that satisfy the condition of being reachable by exactly 1 other individual gives 7.
Question 2 of 4
Which of the following is true for any individual at a platform of height 1m in this layout?
- A.
They can be reached by all the individuals in their own row and column.
- B.
They can be reached by at least 4 individuals.
- C.
They can be reached by at least one individual.
- D.
They cannot be reached by anyone.
D
Explanation
Since 1m is the minimum height, condition (ii) requiring A to be at a lower height than B means no one can reach a platform of height 1m. Thus, they cannot be reached by anyone.
Question 3 of 4
We can find two individuals who cannot be reached by anyone in
- A.
the last row
- B.
the fourth row
- C.
the fourth column
- D.
the middle column
C
Explanation
Looking at the fourth column: heights are 4, 2, 6, 1, 3. The platform of height 1 cannot be reached by anyone. Checking the others shows that another platform in column 4 also cannot be reached by anyone.
Question 4 of 4
Which of the following statements is true about this layout?
- A.
Each row has an individual who can be reached by 5 or more individuals
- B.
Each row has an individual who cannot be reached by anyone
- C.
Each row has at least two individuals who can be reached by an equal number of individuals
- D.
All individuals at the height of 9 m can be reached by at least 5 individuals
C
Explanation
Evaluating each row shows that in every row, there are at least two individuals who can be reached by an equal number of individuals.
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