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.