Q. Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false.
True Statement: One of P and Q was selected for the job.
False Statement: At least one of R and S was selected for the job.
True Statement: At most two of R, S and T were selected for the job.
Which of the following conclusions can be drawn?
1. At least four were selected for the job.
2. S was selected for the job.
Select the correct answer using the code given below:
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Correct Answer: (d) Neither 1 nor 2
Question from UPSC Prelims 2023 CSAT
Explanation :
Five candidates P, Q, R, S and T – Job Selection
The statements provide the following information:
– One of P and Q was selected for the job. This statement is true, which means either P or Q was selected.
– At least one of R and S was selected for the job. This statement is false, which implies neither R nor S was selected.
– At most two of R, S and T were selected for the job. This statement is true. But we already know from the second statement that neither R nor S was selected, so at most two people could be selected from R, S, and T. Therefore, at most, T was selected for the job.
So, the possible selections for the job could be P and T, or Q and T but no more than 2 individuals were selected. Therefore, the statement “At least four were selected for the job” is incorrect.
We also know that S was not selected for the job based on the second statement. Therefore, the statement “S was selected for the job” is also false.
Hence, the correct answer is (d) Neither 1 nor 2.
