GATE CE 2016 Set 1 — Question 8
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Question
Consider the following statements relating to the level of poker play of four players P, Q, R and S.I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to QWhich of the following can be logically inferred from the above statements?(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to QWhich of the following can be logically inferred from the above statements?(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
Correct answer
(D) neither (i) nor (ii)
Solution
Step 1: Analyze the 'always' relationships given in the statements.
- Statement I: P always beats Q ()
- Statement IV: R always loses to Q, which means Q always beats R ()
- Statement II: R always beats S ()
- Statement III: S loses to P only sometimes. This implies that S beats P (or draws) most of the time. This creates a non-transitive relationship where beats , beats , beats , but beats frequently.
- Inference (i): '**P** is likely to beat all the three other players'. Since P loses to S most of the time, we cannot logically infer that P is likely to beat all three players without more specific frequency data, especially since one player () has a winning record against .
- Inference (ii): '**S** is the absolute worst player in the set'. Since S beats the 'best' player P most of the time, S cannot be considered the absolute worst player in the set.
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