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Q77·CSAT · Prelims 2023

True/False statements logic puzzle for candidates

ReasoningLogical PuzzlesInequality logicHard

Question

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?

1At least four were selected for the job.
2S was selected for the job.

Options

a

1 only

b

2 only

c

Both 1 and 2

d

Neither 1 nor 2

Answer

Explanation

Analyze the conditions by decoding the specified true/false values systematically :

Step 1: The statement "At least one of R and S was selected" is given as FALSE[cite: 4426, 4482]. Negating a false existential statement means that neither R nor S was selected for the job (R = 0, S = 0). This immediately invalidates Conclusion 2 ("S was selected") [cite: 4431, 4510].

Step 2: Evaluate the true statements with this knowledge:

"One of P and Q was selected" is TRUE \implies exactly 1 person from \{P, Q\} is selected [cite: 4425, 4481].
"At most two of R, S and T were selected" is TRUE[cite: 4427, 4499]. Since R=0 and S=0, this statement simplifies to T \le 2, which provides no contradiction since T is a single individual (can be 0 or 1).

Total possible selections = 1 (from P/Q) + 0 (R) + 0 (S) + T (0 or 1) = maximum of 2 people. This completely disproves Conclusion 1 ("At least four were selected")[cite: 4429, 4507]. Neither conclusion follows[cite: 4436, 4534].

Negating an existential proposition ("at least one is true" is FALSE) automatically binds all individual component variables within that set to exactly zero.

Answer: (d).

Question details

Year

2023

Paper

CSAT

Question

Q77

Section

Logical & Analytical Reasoning

Sub-topic

Logical Puzzles

Type

Inequality logic

Difficulty

Hard

Source hint

Logical deduction

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