Set 7 : Square Layout

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:



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.

1. How many individuals in this layout can be reached by just one individual?

1. 3
2. 5
3. 7
4. 8

EXPLANATION

Answer: 7

Hence, the answer is “7”.

2. Which of the following is true for any individual at a platform of height 1m in this layout?

1. They can be reached by all the individuals in their own row and column.
2. They can be reached by at least 4 individuals.
3. They can be reached by at least one individual.
4. They cannot be reached by anyone.

EXPLANATION

Answer: They cannot be reached by anyone.

Hence, the answer is “They cannot be reached by anyone”.

Choice D is the correct answer.

3. We can find two individuals who cannot be reached by anyone?

1. the last row
2. the fourth row
3. the fourth column
4. the middle column

EXPLANATION

Answer: the fourth column

Hence, the answer is “the fourth column”.

Choice C is the correct answer.

4. Which of the following statements is true about this layout?

1. Each row has an individual who can be reached by 5 or more individuals
2. Each row has an individual who cannot be reached by anyone
3. Each row has at least two individuals who can be reached by an equal number of individuals
4. All individuals at the height of 9 m can be reached by at least 5 individuals

EXPLANATION

Hence, the answer is “Each row has at least two individuals who can be reached by an equal number of individuals”.

Choice C is the correct answer.