Q47. 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:

Let's analyze the given statements: 1. True Statement 1: 'One of P and Q was selected.' This means exactly one of P or Q is selected. 2. False Statement: 'At least one of R and S was selected.' Since this is false, its negation is true: 'Neither R nor S was selected.' So, R is NOT selected and S is NOT selected.

3. True Statement 2: 'At most two of R, S and T were selected.' This means the number of selected candidates from {R, S, T} is 0, 1, or 2. Combining these deductions: - From (2), R and S are not selected (0 candidates from R, S).

- From (1), exactly one of P or Q is selected (1 candidate). - From (3), since R and S are not selected, this statement implies that at most two of T were selected. As there is only one T, this means T can either be selected or not selected (0 or 1 candidate from T).

Therefore, the total number of selected candidates can be 1 (if T is not selected) or 2 (if T is selected). Now, evaluate the conclusions: Conclusion 1: 'At least four were selected for the job.' This is incorrect, as a maximum of 2 candidates can be selected.

Conclusion 2: 'S was selected for the job.' This is incorrect, as we deduced that S was NOT selected. Thus, neither Conclusion 1 nor Conclusion 2 follows. This question tests logical deduction and careful interpretation of quantifiers, a common challenge in CSAT.