GATE CSE 2016 Set 1 | Question: GA08

Question

Consider the following statements relating to the level of poker play of four players $P,Q,R \ and  \ S$.

1. $P$ always beats $Q$
2. $R$ always beats $S$
3. $S$ loses to $P$ only sometimes.
4. $R$ always loses to $Q$

Which of the following can be logically inferred from the above statements?

1. $P$ is likely to beat all the three other players
2. $S$ is the absolute worst player in the set

• A. (i). only 
• B. (ii) only
• C. (i) and (ii) only'
• D. neither (i) nor (ii)

Comments

I think , the main point in this question is -  "P beats Q" & "Q beats R" does not mean that "P beats R".

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@Himanshu Why is this point not followed? If P is stronger that Q, Q is stronger than R than P should be stronger than R.

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@Swati:-This conclusion that you are using can only be used if we have quantitative data like height.A taller than B,B taller than C, => A taller than C

Now India is stronger team then Bangladesh .

And Bangladesh is stronger than Zimbawe

=> India is stronger than Zimbabwe(this is false)

Unless until we dont know the result of India and Zimbawe,we cant comment anything.

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even i was wondering the same thing

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can anyone explain how p is likely to beat all other  players is false ,because in the options it is given s loses to p sometimes,so p is likely to beat other 3 seems to be correct

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@harshit_josh

It is given that "S loses to P ONLY some times"..

Here the word only is important. This means there are some cases where P wins over Q..

But still we can't conclude that statement 1 is wrong..

If they had given statement that, "P beats all the other 3 players",then that statement had been wrong...

But they had given that "P is likely to beat all the three other players"..

then the reason why that statement is false is given in below comment..

https://gateoverflow.in/39617/gate2016-1-ga08?show=99061#c99061

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means P always beats Q and Q always beats R does not imply that P always beats R from above diagram..

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yes..

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@chirudeepnamini thanks for d explaination..

 

Answer 1

Answer is (D) because

1. $P$ is not likely to beat $S$ because $S$ only sometimes loses to $P$
2. $S$ is not worst player because he is likely to beat $P$

Comments

@Pranavpurkar S loses to P “only sometimes”. P winning over S has a very slight chance. Likely imply it is almost bound to happen.

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Then it is true only in the case when  “P always beats everyone”.?

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Yes

Answer 2

1) P is likely to beat all the three other players : False, there is no reference of P defeating R.

` 2) S is the absolute worst player in the set : False, S may be defeated by P.

Hence, option D.

Answer 3

From Statement 1,2,and 4

Level P>Q>R>S

But from 3rd statement S loses to P only sometimes.Here note that if S beat P then above statements will not hold true. So,statements are contracting each other and no conclusion can be drawn.

So Option D will be answer.

Answer 4

Both statements are wrong because data give is insufficient to conclude any of the statements.

P can beat Q and S but its not given whether P will beat R or not.

S is the worst player. We cant conclude that since all the data required to analyze them are not given like its not given whether S will beat Q or not.

Comments

yes Data is insufficient...

Because of no relation between P and R , can’t comment on truthness of 1^st inference.  And because of no relation between S and Q too can’t comment on truthness of 2^nd inference.