Out of the 14 people in a group, 3 like to play Badminton, Soccer and

Question

Out of the 14 people in a group, 3 like to play Badminton, Soccer and Volleyball. If there are 7 people in the group who like to play Volleyball and 5 who like to play Badminton and Soccer, what is the number of people who do not like to play any of the 3 games?

A. 2
B. 5
C. 6
D. 7
E. Cannot be determined

A. 2
B. 5
C. 6
D. 7
E. Cannot be determined

chetan2u · Answer

We can draw the circles as shown..

All three games = 3.
So only B+S=5-3=2
V+(any one game only or none)=7-3=4

Total who play game=3+2+4=9.

So, the number of people who do not like to play any of the 3 games = 14-9=5.

B

yashikaaggarwal · Answer

Have you consider people like only Badminton and only Soccer as Null?

Posted from my mobile device

chetan2u · Answer

Yes, because that is what the data suggests.

gurmukh · Answer

Where in the question it is given that only badminton and only soccer each is zero, when there is also option cannot be determined?

NitishJain · Answer

IMO  E

chetan2u : Sir it is given that All three games = 3, and Badminton and Soccer =5, how you deduced that it actually should be 2 (5-3) and why other values as 0.

Can you please help in clarifying doubts.

yashikaaggarwal · Answer

Bunuel  Sir Can You Post Official Explanation to the question.

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chetan2u · Answer

I would agree the question is not worded in the best possible way.

But if this question is in GMAT, I will answer B for two reasons
1) Almost all questions on GMAT will not have an option that states ‘cannot be determined.’
2) There is nothing in the question that states that there is some more information than what is given.

Of course, as I said there is a bit of confusion in the wordings.

NitishJain · Answer

I agree with your point 1 sir. Since this question has option E as "Cannot be determined", it leaves little room for assumption. I can still agree with other values as 0, but how did you arrive at Badminton and Soccer=2?

chetan2u · Answer

There are 5 like to play B and S. Now this 5 will consist of 
1) only B+S
2) B+S+V, which is given as 3.

So only B+S=5-3=2

gvij2017 · Answer

Its really strange how did you assume something as there may be other possibility. 
I read you explanation, sir! But I didn't get how assumption is applicable in quant section. 
In my opinion, what if only B is 2 and Only S is 1, then I would get 2 as answer. Or B and S can have 1 and 2 respectively. 
Q asks number of people who don't like to play any of the 3 games. Means number of students completely outside of shown circles.
 
Please explain.

gurmukh · Answer

It's a pretty straight forward sum in which there is nothing to assume and there is no problem in the wording of the sum. Answer is cannot be determined. You can assume anything in Quant section.

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gurmukh · Answer

Sorry I wanted to write you cannot assume anything in Quant.

chetan2u · Answer

Hi

Yes, we are not supposed to assume anything, and nothing has been assumed. If you say there is something more than what is given, then you are assuming.

The details you are looking at is important for DS question. Because traps lie in these kind of lines. They give you that there are 2 red balls and 2 white balls and we are looking at the probability of picking red. Of course we would require to know the total balls or that no other colour is present.

But if in a PS question, I give you that there are 2 red balls and 2 white balls, and you have to find the same probability. Will you say that it cannot be determined because there can be other colours too. No, you cannot as you have to work on data given.

Same is the case here. If some data is given, why should I take that the data is inadequate if there is nothing in the question stem that tells me that there have to be some playing soccer alone ?

But if it were DS and I had this data , I would mark E the same way as I would do it for red and white balls example.

Finally, as I have written, you will not find such wordings in GMAT.

gurmukh · Answer

Sir, going by your logic suppose it is given in the sum that there are 14 balls in the bag and there are 5 red balls in the bag, find the probability of taking out yellow balls, will you assume that all rest of the balls in the bag are yellow and also when one of the option is cannot be determined. Also if you are talking about that there is no such option in GMAT then you are also assuming that they can't give such option because nowhere GMAC mentions that there cannot be a option like this.

Posted from my mobile device

chetan2u · Answer

Hi Gurmukh,
The case you have taken is not the similar to one we are looking at. You are asking for a probability of a thing that is not even given. 
The example of finding probability of picking a blue out of a bag and it is given that the bag contains 4 blue and 5 black will stand. You are not given any other colour so take it that you have only 2 colours in PS. Why should we read more than what is given in PS? And as I said, this question does not reflect the wording of actual questions.

chacinluis · Answer

"Yes, because that is what the data suggests" !?

C'mon dude are you serious? You are suppose to be the GMAT expert. 
Number 1 rule in the GMAT:  NEVER ASSUME ANYTHING

chetan2u · Answer

Dude, thanks for reminding me that I am a math expert. I wouldn't have known otherwise.

Your number 1 rule, for which you have taken considerable pain in writing in bold and capital, has already been discussed above.

Number 1 advice in the forums - Go through the entire thread, you will avoid asking unnecessary questions. If you still don't follow the thread, you can ask or leave it.
As I wrote - In PS, you are supposed to get a value as an answer so the values given would be the only thing required for an answer. 
If there are red cones and blue squares, and nothing else specified in PS, you can take that no red squares exist.
OR
If a PS says that there are 75 students out of which 45 play cricket, and 50 play football. How many play both games?
You can take it that all play at least one game. Although the official questions would almost every time mention that clearly.

draftpunk · Answer

Why do you assume that Only B and Only S are zero? In my opinion, this question should be discarded because of its ambiguity.

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Out of the 14 people in a group, 3 like to play Badminton, Soccer and

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