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:

1. A. 1 only
2. B. 2 only
3. C. Both 1 and 2
4. D. Neither 1 nor 2

Answer: D

Explanation

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.