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  • In a square layout of size 5m × 5m, 25 equal-sized platforms of different heights are built. The heights (in metres) of individual platforms are as shown below: <table border="1" cellp

In a square layout of size 5m × 5m, 25 equal-sized 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 individuals 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 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.

Row in the layout are numbered from top to bottom and columns are numbered from left to right.

Question :  Which of the following statements is true about this layout?

Option: 1

Each row has an individual who can be reached by S or more individuals.


Option: 2

Each row has an individual who cannot be reached by anyone.


Option: 3

Each row has at least two individuals who can be reached by an equal number of individuals.


Option: 4

All individuals at the height of 9 m can be reached by at least 5 individuals.


Answers (1)

best_answer

The correct answer is 3. Each row has at least two individuals who can be reached by an equal number of individuals.

This is because the following pairs of individuals in each row can be reached by an equal number of individuals:

Row 1: (6, 4)

Row 2: (3, 2)

Row 3: (5, 5)

Row 4: (8, 1)

To see why, let's look at the three conditions given in the problem:

Condition 1: The individuals are in the same row or column.

The individuals in each of the pairs listed above are in the same row.

Condition 2: The individuals are at a lower height than the individual they can be reached by.

The individuals in each of the pairs listed above are at a lower height than the individual they can be reached by.

Condition 3: If there is/are any individual(s) between the two individuals, such individual(s) must be at a height lower than that of the lower individual.

There are no individuals between the individuals in each of the pairs listed above.

Therefore, the pairs of individuals listed above can be reached by an equal number of individuals.

Statement 1 is wrong because no individual in row 1 can be reached by 5 or more individuals.

Statement 2 is wrong because row 3 has no individual who cannot be reached by anyone.

Statement 4 is wrong because the individual at height 9 in column 1 can be reached by only 4 individuals.

Therefore, only statement 3 is correct.

 

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