Some members of the basketball team are members of the chess club

Question

Some members of the basketball team are members of the chess club, but no members of the basketball team are members of the debate society.

If the statements above are true, which of the following may be drawn from them?

A Some members of the chess club are not members of the basketball team.
B No members of the chess club are members of the debate society.
C Some members of the chess club are members of the debate society.
D No members of the debate society are members of the chess club .
E Some members of the chess club are not members of the debate society

What shall be the approach for such question?

pqhai · Accepted Answer

Some members of the basketball team are members of the chess club, but no members of the basketball team are members of the debate society.

If the statements above are true, which of the following may be drawn from them?

A Some members of the chess club are not members of the basketball team.
Wrong. Maybe all chess members are member of basketball team.

B No members of the chess club are members of the debate society.
Wrong. Maybe some chess members are member of debate society.

C Some members of the chess club are members of the debate society.
Wrong. Maybe No members of chess club are members of debate society.

D No members of the debate society are members of the chess club .
Wrong. Maybe some debate society are members of chess club.

E Some members of the chess club are not members of the debate society
  Correct.   They are the people who are  members of both chess and basketball team . Because
All basketball = No debate society
Some chess = some basketball
=> Some chess = No debate society

Hope it helps.

daboo343 · Answer

From the diagram it is clear that only E is possible

keats · Answer

I have made the same Venn diagram as  daboo343  However, I see that both (A) and (E) can be true. How do I eliminate one and reach the correct answer.

Abhishek009 · Answer

You can eliminate option (E) if you consider CASE 1
  
Can you state - Some members of the chess club are not members of the debate society : Definitely no becasue here " Non member of Chess club is a member of Debate society " OR " Non member of Debate society is a member of Chess club "

However if you consider CASE 2 
  
You can state option (E) Some members of the chess club are not members of the debate society

Remember a conclusion is one which holds true in all the possible combination or arrangement, so we may eliminate option (E)

keats · Answer

Abhishek009  : Thank you for response.

I see that Case 2 infact tells me that option (E) is not correct. From Case 2 Venn, it is clear that some of the members of chess club are members of debate society (some part of black overlaps with green)

And if I am not mistaken E is the answer. Why are you trying to disprove it?

abhimahna · Answer

A cannot be inferred out of the information given.

We are given that some members of Basketball club are also the members of chess club.

So, say Total basket ball members = 100

Total Chess members = 50.

Now, it may happen that All these 50 members are out of those 100 only. So, we cannot directly say that some chess members are not basket ball members.

E is the Best answer.

keats · Answer

abhimahna  Thank you for the response. Can you help me explain the case with Venn. Just options (A) and (E). For me, option (E) is coming out as an answer when I look at both the Venn.

PS: I am assuming what logically flows from the argument is a "must be true" case.

abhimahna · Answer

ok. so, you made me do some drawing after so many years. :-D

Look at the diagrams below. A is out as per the diagram on the left and E is correct as per the diagram on the right. Also, please note that we are given " Some members of chess are members of basketball" - (1) And " NO member of basketball is a member of Debate". Doesn't that mean those common members at the statement (1) won't be member of Debate society? Lets take another example, Say You and I are members of Both Chess and Basket Ball. Now, We have a condition that NO ONE from basket ball team could participate in debate, what would you infer out of that??

keats · Answer

abhimahna

The first Venn on the left seals it. I have understood where I was going wrong. I missed the possibility of drawing the case where all the members of the chess club can be a part of the basketball club. This will rule out option A.

However, if I look at Venn 1, and see (E) Some members of the chess club are not members of the debate society
The above option gets incorrect because from the Venn 1, it is clear that all the members of the chess club are not members of debate society (The circle of chess club is completely inside basketball and there is no overlap of chess with debate)

abhimahna · Answer

Keats bro, You are again missing something here. Lets take another example, I have 10 members in chess club and as per my diagram on the left, I can say NONE is a member of debate club. If None is a member, then it would obviously mean some are also not. Notice the words NOT in both. I am not saying "None is a member of debate club, so Some are member of debate club." BUT I am saying the same thing. "None is a member of debate club, so some are not a Member of debate club" This is a logical deductions concept frequently tested on exams like CAT,SAT but sometimes tested on GMAT. I would suggest go through the below link and try solving all the questions given. https://www.indiabix.com/logical-reasoni ... troduction

keats · Answer

I see abhimahna I understand your point. Thanks for bearing with me :-D

I have never prepared for CAT and somehow such type of problems give me hard time. However, I understand now when you say 'None of the members in the Chess Club are a part of Debate Club will ensure that some of the members of the Chess Club are obviously not the part of Debate Club.'

baalok88 · Answer

hello, 
Please advise me on the attached question. I have drawn an explanatory diagram. 
I clearly believe that if there's no relation given between 'Debate Soc' members and Chess members, we can not draw any relation between them.

will be a great help if this is sorted for such an easy question.

DmitryFarberMPrep · Answer

baalok88 , let's look at that intersection of "basketball" and "chess" in your diagram. What do we know about those people? They are in both clubs, right? What else do we know about them? We know nothing else about the chess club, but we know that none of the basketball players are in the debate society. That must apply to  these  basketball players, too!

So, looking at E, we know that there must at least be some chess players who are not in the debate society. Which ones? Those who are also on the basketball team.

By the way, A represents a common trap. The word "some" does not preclude "all." If I say "some of my friends have long hair," that just means that I have at least one long-haired friend. However, it could certainly be that  all  of my friends are long-haired. In short, when we say "some X are Y," that does not imply "some X are  not  Y." For instance, it is correct to say "some countries have capitals" or "some people have DNA," even though ALL countries have capitals and ALL people have DNA.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: E

The premises given can be expressed like this: Some B => C; no B => D. To link them together, we need the term they have in common (B) to come AFTER the arrow in one statement and BEFORE the arrow in the other, so we need to consider how we could rewrite each premise. Some B => C can be written as Some C => B – you can always ‘flip’ a particular (“Some”) singular statement – and no B => D can be rewritten as B => not D. (You can always transfer a negative to the other side of a statement, universal or particular.) This gives us Some C => B and B => not D, meaning that (E) is the best answer choice.

Fdambro294 · Answer

Very simply.....

Some members of the basketball team are members of the chess team.

These “some” members of both basketball AND chess will NEVER be members of the debate team.

Why? Because we are told NOT ONE Single basketball player is part of Debate. This includes the “some” who do Basketball AND Chess.

Correct Answer
-E-

Definitively, without a doubt, there must be “some” members of the chess team (those who are ALSO playing basketball) that are NOT part of the debate team

Posted from my mobile device

Dhwanii · Answer

Even I thought that the case all 50 are out of 100, still how can we correctly infer E ? For E TO BE TRUE, case of all 50 are out of 100 cannot be considered

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Some members of the basketball team are members of the chess club

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