GATE CS 2016 Set 1 Q.8 (GA Q.8): Analytical and Logical Reasoning

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 Q

Which 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

(i) only

(ii) only

(i) and (ii)

neither (i) nor (ii)

Official answer and solution

Official answer: D
From: Official GATE 2016 answer key

Solution

Evaluate the transitive and intransitive relationships given by the four poker statements.

List the pairwise relationship facts:

Statement I: $P$ always beats $Q$ ( $P > Q$ )
Statement II: $R$ always beats $S$ ( $R > S$ )
Statement IV: $R$ always loses to $Q$ , meaning $Q$ always beats $R$ ( $Q > R$ )
Combining these three: $P$ beats $Q$ , $Q$ beats $R$ , and $R$ beats $S$ ( $P > Q > R > S$ in deterministic pairwise matchups).

Now examine Statement III: 'S loses to P only sometimes'.
This means that $S$ does not always lose to $P$ ; in fact, $S$ wins against $P$ at least some of the time (or even most of the time).

Because $S$ can beat $P$ , the relation is not strictly transitive across the set of players:

(i) 'P is likely to beat all the three other players' cannot be inferred because $P$ does not reliably beat $S$ .
(ii) 'S is the absolute worst player in the set' cannot be inferred because $S$ beats $P$ (who beats everyone else in direct matches) a significant portion of the time.

Therefore, neither (i) nor (ii) can be logically inferred.

Final answer

Common trap

Assuming transitivity from $P > Q > R > S$ and ignoring Statement III which introduces an intransitive loop where $S$ defeats $P$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2016 Computer Science and Information Technology (CS) Session 1
Question: 8 of 65, printed as GA Q.8
Section: General Aptitude

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