Question
Download Solution PDFComprehension
Direction: There are six steps on. a staircase leading from the ground floor to the first floor. Denote the first step by 1, second by 2, and so on. There are four people P, Q, R and S. No two people can be on the same step.
I. P is two steps below R.
II. Q is on the next step to S.
III. R is two steps below S.
If T joined P, Q, R, and S, and T was on the third step, and Q was on a higher step than T, which step must be vacant?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFAs per the given question,
There are six steps on. a staircase leading from the ground floor to the first floor. Denote the first step by 1, second by 2, and so on. There are four people P, Q, R and S. No two people can be on the same step.
- P is two steps below R.
So, P can be on ground floor as there is nothing mention about P's step.
- R is two steps below S.
There are three possibilities:
| Steps | People | ||
| Case I | Case II | Case III | |
| First floor | |||
| 6 | S | ||
| 5 | S | ||
| 4 | R | S | |
| 3 | R | ||
| 2 | P | R | |
| 1 | P | ||
| Ground Floor | P | ||
- Q is on the next step to S.
| Steps | People | ||
| Case I | Case II | Case III | |
| First Floor | Q | ||
| 6 | S | Q | |
| 5 | S | Q | |
| 4 | R | S | |
| 3 | R | ||
| 2 | P | R | |
| 1 | P | ||
| Ground Floor | P | ||
If T is on third place and Q was on a higher step than T, then 'first' step must be vacant.
| Steps | People | ||
| Case I | Case II | Case III | |
| First Floor | Q | ||
| 6 | S | Q | |
| 5 | S | Q | |
| 4 | R | S | |
| 3 | T | R | T |
| 2 | P | R | |
| 1 | P | ||
| Ground Floor | P | ||
So, this condition is possible in Case I and Case III.
Now, 2nd and 4th step is filled in both the cases and 6th step is filled in case I. So, it will not be a definite case.
Hence, "First step" must be vacant both the cases.
Last updated on May 8, 2025
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