GATE CS 2021 Set 2 — Question 10
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Question
Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.Observation I: S is taller than R.
Observation II: Q is the shortest of all.
Observation III: U is taller than only one student.
Observation IV: T is taller than S but is not the tallest.The number of students that are taller than R is the same as the number of students shorter than __________.
Observation II: Q is the shortest of all.
Observation III: U is taller than only one student.
Observation IV: T is taller than S but is not the tallest.The number of students that are taller than R is the same as the number of students shorter than __________.
Correct answer
(C) S
Solution
Let the heights of the six students be represented in descending order: .
1.Observation II: Q is the shortest of all. Thus, .
2.Observation III: U is taller than only one student. Since Q is the shortest, U must be taller than only Q. Thus, .
3.Observation I & IV: We are given and . Combining these, we get .
4.Observation IV: T is not the tallest. The remaining students are P, T, S, and R for positions . Since and T cannot be , the only possible arrangement is:
- The number of students taller than R () is 3 (P, T, and S).
- We need to find a student such that the number of students shorter than them is also 3.
- Looking at the order, the students shorter than S () are R, U, and Q, which totals 3 students.
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