# 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.