GATE ECE 2022 | GA Question: 9

Question

In a class of five students $\text{P, Q, R, S}$ and $\text{T},$ only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.

$\text{Statement of P: R}$ has copied in the exam.

$\text{Statement of Q: S}$ has copied in the exam.

$\text{Statement of R: P}$ did not copy in the exam. 

$\text{Statement of S:}$ Only one of us is telling the truth.

$\text{Statement of T: R}$ is telling the truth.

The investigating team had authentic information that $\text{S}$ never lies.

Based on the information given above, the person who has copied in the exam is

• A. $\text{R}$
• B. $\text{P}$
• C. $\text{Q}$
• D. $\text{T}$

Answer 1

Given the statements:

• $\text{Statement of P:  R}$ has copied in the exam.
• $\text{Statement of Q:  S}$ has copied in the exam.
• $\text{Statement of R:  P}$ did not copy in the exam. 
• $\text{Statement of S: }$ Only one of us is telling the truth.
• $\text{Statement of T:  R}$ is telling the truth.

Based on the above statements, we can make the pictorial representation.

$\qquad \begin{array}{ccccc} \underbrace{\text{P}}_{\text{R}\;\Large{\checkmark}} & \underbrace{\text{Q}}_{\text{S}\;\Large{\checkmark}} & \underbrace{\text{R}}_{\text{P}\Large{\times}} & \underbrace{\text{S}}_{\text{Only one is true}}  & \underbrace{\text{T}}_{\text{R is true}} \\\hline  \underbrace{\underbrace{\text{P}}_{\text{R}\;\Large{\checkmark}}}_{{\color{Red}{\text{False}}}} & \underbrace{\underbrace{\text{Q}}_{\text{S}\;\Large{\checkmark}}}_{{\color{Red}{\text{False}}}} & \underbrace{\underbrace{\text{R}}_{\text{P}\Large{\times}}}_{{\color{Red}{\text{False}}}} &\underbrace{\underbrace{\text{S}}_{\text{Only one is true}}}_{{\color{Green}{\text{Always True}}}}  & \underbrace{\underbrace{\text{T}}_{\text{R is true}}}_{{\color{Lime}{\text{True}}}} \\\hline  \underbrace{\text{P}}_{\text{R}\;\Large{\times}} & \underbrace{\text{Q}}_{\text{S}\;\Large{\times}} & \underbrace{\text{R}}_{\text{P}\;\Large{\checkmark}}  & & \end{array}$

$\therefore$ The person who has copied in the exam is ${\color{Blue}{\text{P}.}}$

Correct Answer $:\text{B}$