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Six students $\text{P, Q, R, S, T and U}$, with distinct heights, compare their heights and make the following observations.

  • $\text{Observation I}$: $\text{S}$ is taller than $\text{R}$.
  • $\text{Observation II}$: $\text{Q}$ is the shortest of all.
  • $\text{Observation III}$: $\text{U}$ is taller than only one student.
  • $\text{Observation IV}$: $\text{T}$ is taller than $\text{S}$ but is not the tallest

The number of students that are taller than $\text{R}$ is the same as the number of students shorter than ____________.

  1. $\text{T}$
  2. $\text{R}$
  3. $\text{S}$
  4. $\text{P}$
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2 Answers

Best answer
10 votes
10 votes

Let us arrange people in decreasing order of heights:

By looking at each observation, we fill these stars $:*,*,*,*,*,*$ where the left-most star corresponds to the tallest person and the rightmost star corresponds to the shortest person.

  1. $\text{S}$ is taller than $\text{R}.$
    So, $\text{S}>\text{R}$
  2. $\text{Q}$ is the shortest of all.
    So, we have
    $*,*,*,*,*,\text{Q}$
  3. $\text{U}$ is taller than only one student.
    So, $\text{U}$ is second tallest. Hence,
    $*,*,*,*,\text{U},\text{Q}$
  4. $\text{T}$ is taller than $\text{S}$ but not tallest.
    $\text{T}$ is taller than $\text{S}$ implies $T> S$.

From observations $i$ and $iv,$ we have $\text{T}>\text{S}>\text{R}.$

Thus, we have one of these possibilities:

  • $*,\text{T},\text{S},\text{R},\text{U},\text{Q}$ or
  • $\text{T},*,\text{S},\text{R},\text{U},\text{Q}$ or
  • $\text{T},\text{S},*,\text{R},\text{U},\text{Q}$ or
  • $\text{T},\text{S},\text{R}*,\text{U},\text{Q}$

But it is mentioned that $\text{T}$ is not the tallest person.

So we are left with only one possibility:

$*,\text{T},\text{S},\text{R},\text{U},\text{Q}$

Since, we have only one student $\text{P}$ left, we fill the blank with $\text{P}$

$\text{P},\text{T},\text{S},\text{R},\text{U},\text{Q}$

  • Number of students taller than $\text{R}=3$ $(\text{P},\text{T},\text{S})$
  • Number of students shorter than $\text{T}=4$
  • Number of students shorter than $\text{R}=2$
  • Number of students shorter than $\text{S}=3$

Hence, option C is the correct answer.

edited by
3 votes
3 votes

P   (Tallest)

T

S

R

U

Q   (shortest)

Number of students taller than R = 3 

Number of students shorter than S =3

Hence  option C is right ans

Answer:

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