CAT 2017 Slot 1 — DILR Question 21
Answer the following question based on the information given below.
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.
How many individuals in this layout can be reached by just one individual?
Answer & solution
- A
3
- B
5
7
- D
8
Let us check how many people in the grid can reach individuals. Let us do this by moving row wise
Row 1
6 – Can be reached by 1, 2 and 4 in the same row i.e., a total of 3 people
1 – Cannot be reached by anyone
2 – Can be reached by only 1 in the same row on the left
4 – Can be reached by 3 people i.e., 2 and 3 in the same row and 2 in the column below
3 – Cannot be reached by anyone
In a similar way we proceed for the other rows
Row 2
9 – Can be reached by 6, 5, 8 and 7 i.e., of total of 4 people
5 – Can be reached by 1 and 3 i.e., a total of 2 people
3 – Can be reach by 2 and 2 i.e., a total of 2 people
2 – Cannot be reached by anyone
8 – Can be reached by 5 people i.e., 2, 3 and 5 in the same row, 3 in the column above above and 5 in the column below.
Row 3
7 – Can be reached by only 3 in the row below
8 – Can be reached 5, 7, 4, and 6 i.e., total of 4 people
4 – Can be reached by only 3 in the above row
6 – Can be reached only by 4 and 5 in the same row and 4, 2, 1 and 3 in the same column i.e., a total of 6 people
5 – Can only be reached by 2 in the same row below
Row 4
3 – Can only be reached by 1 in the row below
9 – Can be reached by 3 and 5 in the same row and 7 & 8 in the row below and above i.e., a total of 4 people
5 – Can be reached by 1 & 2 in the same row and 4 in the row above
1 – Cannot be reached by anyone
2 – Can be reached only by 1 in the same row
Row 5
1 – Cannot be reached by anyone
7 – Can be reached by 1 and 6 in the same row i.e., a total of 2 people
6 – Can be reached by 5 in the row above and 3 in the same row. i.e., a total of 2 people
3 – Can be reached only by 1 in the row above
9 – Can be reached by 3, 6 and 7 in the same row and 2, 5 and 8 in the rows above i.e., a total of 6 people
Looking at the table we can see the person having height 2 m in the 1st row, people having height 7 m, 4 m and 5 m in the 3rd row, people having height 3 m and 2 m in the 4th row and the person having height 3 m in the 5th row i.e., a total of 7 people can be reached by only one person.
Hence, option (c).