Q.10 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 ______.
(A) T
(B) R
(C) S
(D) P

P > T > S > R > U > Q is the complete height order from tallest to shortest.​

This ranking satisfies all observations: S taller than R, Q shortest, U taller than only Q, and T taller than S but not tallest (P is tallest).​

Logical Breakdown

Start with Observation II: Q is shortest, so Q ranks 6th.​

Observation III places U taller than only one (Q), so U ranks 5th: U > Q.​

Observation I gives S > R. Observation IV states T > S but T not tallest, so someone (later P) > T > S.​

R fits between S and U (no contradictions), yielding P (1st) > T (2nd) > S (3rd) > R (4th) > U (5th) > Q (6th).​

Key Question Analysis

Three students taller than R (P, T, S).​

This matches three students shorter than S (R, U, Q).​

Option Evaluation

Option (A) T: Four students shorter than T (S, R, U, Q)—not equal to 3. Incorrect.​

Option (B) R: Two students shorter than R (U, Q)—not equal to 3. Incorrect.​

Option (C) S: Three students shorter than S (R, U, Q)—matches exactly. Correct.​

Option (D) P: Five students shorter than P (all others)—not equal to 3. Incorrect.​

The six students heights puzzle challenges logical reasoning skills essential for competitive exams like GATE CSE and CSIR NET Life Sciences general aptitude sections.​

In this classic logic puzzle, students P, Q, R, S, T, and U have distinct heights and share four key observations about their relative heights.​

Mastering such taller shorter puzzles builds deduction skills for ranking-based questions in entrance tests.

Puzzle Observations Explained

• Observation I: S > R (S ranks above R).​

• Observation II: Q shortest (Q at bottom).​

• Observation III: U taller than only one student (U second-shortest).​

• Observation IV: T > S, T not tallest (T above S, someone above T).​

These clues form inequality chains leading to a unique order.

Step-by-Step Height Ranking Solution

1. Place Q at 6th (shortest).​

2. U > only Q, so U 5th.​

3. T > S > R, and P > T (since T not tallest).​

4. R slots between S and U: no other fits.​

Final Order:

Core Question: Taller Than R Matches Shorter Than Whom?

• Taller than R: P, T, S (3 students).​

• Check options:

  Option	Shorter Than This	Count	Matches?
  (A) T	S, R, U, Q	4	No ​
  (B) R	U, Q	2	No ​
  (C) S	R, U, Q	3	Yes ​
  (D) P	T, S, R, U, Q	5	No ​

Answer: (C) S.​

Tips for Similar Heights Logic Puzzles in CSIR NET GATE

• Draw positions 1-6 tallest to shortest.​

• Anchor absolutes (shortest/tallest) first.​

• Chain inequalities: combine overlapping relations.​

• Test placements to eliminate contradictions.​

• Verify counts for “number taller/shorter” directly from ranking.​

Practice these for CSIR NET general aptitude or GATE reasoning to score high.