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The members of a club were asked whether they speak

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The members of a club were asked whether they speak [#permalink] New post 05 Aug 2007, 03:32
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E

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The members of a club were asked whether they speak Cantonese, Mandarin and Japanese. 100 said that they spoke Cantonese, 150 said that they spoke Mandarin and 200 said that they spoke Japanese. 120 said that they spoke exactly two of the three languages. How many members does the club have?

(1) There are twice as many members who speak none of the languages as there are who speak all three languages.
(2) Half of the members who speak Japanese and Cantonese also speak Mandarin.
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Re: DS: Polyglots [#permalink] New post 05 Aug 2007, 07:12
kevincan wrote:
The members of a club were asked whether they speak Cantonese, Mandarin and Japanese. 100 said that they spoke Cantonese, 150 said that they spoke Mandarin and 200 said that they spoke Japanese. 120 said that they spoke exactly two of the three languages. How many members does the club have?

(1) There are twice as many members who speak none of the languages as there are who speak all three languages.
(2) Half of the members who speak Japanese and Cantonese also speak Mandarin.


A for me.
Set x = number of people who speak all three languages.
(1) (100+150+200) - 120 - 2x + Neither = Total
Neither = 2x
We can cancel out the 2x in the equation; thus, find the total.
SUFFICIENT.

(2) Don't know anything about "Neither" information. INSUFFICIENT.
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Re: DS: Polyglots [#permalink] New post 05 Aug 2007, 07:34
kevincan wrote:
The members of a club were asked whether they speak Cantonese, Mandarin and Japanese. 100 said that they spoke Cantonese, 150 said that they spoke Mandarin and 200 said that they spoke Japanese. 120 said that they spoke exactly two of the three languages. How many members does the club have?

(1) There are twice as many members who speak none of the languages as there are who speak all three languages.
(2) Half of the members who speak Japanese and Cantonese also speak Mandarin.


I take A here

Given that

Cantonese = 100
Mandarin = 150
Japanese = 200

Let x,y and z represent the ONLY 2 lanuages sections in the Venn diagram and "t " represent all three

So

Only Cantonsese = 100 - (x+y+t)
Only Mandarin = 150 - (x+z+t)
Only Japanese = 200 - (z+y+t)

Formula now goes as

Total = Only A + Only B + Only C + Only AB+ Only BC+ Only CA + ABC + None

From 1 we have
None = 2*t

Substitute the rest in above eq.

100 - (x+y+t) + 150 - (x+z+t) + 200 - (z+y+t) + 120 + t + 2*t

= 330


From(2) I dont think we can decipher anything..
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Re: DS: Polyglots [#permalink] New post 06 Aug 2007, 12:46
dahcrap wrote:
bkk145 wrote:
kevincan wrote:
The members of a club were asked whether they speak Cantonese, Mandarin and Japanese. 100 said that they spoke Cantonese, 150 said that they spoke Mandarin and 200 said that they spoke Japanese. 120 said that they spoke exactly two of the three languages. How many members does the club have?

(1) There are twice as many members who speak none of the languages as there are who speak all three languages.
(2) Half of the members who speak Japanese and Cantonese also speak Mandarin.


A for me.
Set x = number of people who speak all three languages.
(1) (100+150+200) - 120 - 2x + Neither = Total
Neither = 2x
[b]
I think the highlighted sign shud be + and not -[/b]
We can cancel out the 2x in the equation; thus, find the total.
SUFFICIENT.

(2) Don't know anything about "Neither" information. INSUFFICIENT.


The answer has to be E


I am quite sure it is negative there...if you have sum of all the numbers, you have to subtract all the "repeats", then add neither to equal to total.
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 [#permalink] New post 06 Aug 2007, 13:30
dont we add the singles, minus the doubles and add the triples????

kevincan wrote:
OA=A
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 [#permalink] New post 06 Aug 2007, 14:38
fresinha12 wrote:
dont we add the singles, minus the doubles and add the triples????

kevincan wrote:
OA=A


If you can explain why you should add the triple, I'll see if I can say something...
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 [#permalink] New post 06 Aug 2007, 16:32
Here is why i say we add the triple..

see when we calculate the doubles..it already takes into account the triple...i.e we have already minused the triple to get the doubles... so we cant deduct triple again cause we have already taken em into account..



bkk145 wrote:
fresinha12 wrote:
dont we add the singles, minus the doubles and add the triples????

kevincan wrote:
OA=A


If you can explain why you should add the triple, I'll see if I can say something...
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Re: DS: Polyglots [#permalink] New post 06 Aug 2007, 16:58
trivikram wrote:
kevincan wrote:
The members of a club were asked whether they speak Cantonese, Mandarin and Japanese. 100 said that they spoke Cantonese, 150 said that they spoke Mandarin and 200 said that they spoke Japanese. 120 said that they spoke exactly two of the three languages. How many members does the club have?

(1) There are twice as many members who speak none of the languages as there are who speak all three languages.
(2) Half of the members who speak Japanese and Cantonese also speak Mandarin.


I take A here

Given that

Cantonese = 100
Mandarin = 150
Japanese = 200

Let x,y and z represent the ONLY 2 lanuages sections in the Venn diagram and "t " represent all three

So

Only Cantonsese = 100 - (x+y+t)
Only Mandarin = 150 - (x+z+t)
Only Japanese = 200 - (z+y+t)

Formula now goes as

Total = Only A + Only B + Only C + Only AB+ Only BC+ Only CA + ABC + None

From 1 we have
None = 2*t

Substitute the rest in above eq.

100 - (x+y+t) + 150 - (x+z+t) + 200 - (z+y+t) + 120 + t + 2*t

= 330


From(2) I dont think we can decipher anything..







gottacha here. :twisted:
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 [#permalink] New post 06 Aug 2007, 17:12
fresinha12 wrote:
Here is why i say we add the triple..

see when we calculate the doubles..it already takes into account the triple...i.e we have already minused the triple to get the doubles... so we cant deduct triple again cause we have already taken em into account..



bkk145 wrote:
fresinha12 wrote:
dont we add the singles, minus the doubles and add the triples????

kevincan wrote:
OA=A


If you can explain why you should add the triple, I'll see if I can say something...


No, double doesn't take triple into account. They are different. If the question say something like "two or more languages", then it would take triple into account. But this problem said specifically that exactly two languages.
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 [#permalink] New post 07 Aug 2007, 08:26
OK let me understand...

in a 3 set venn diagram...say C for chinese, M for Mandarian and J for Japense

120 speak exactly 2 languages...is equal to the sum of intersect of C n J, C n M and J n M...?? right if thats the case then 120 has already minused the number of people who speak C+J+M, correct?

bkk145 wrote:
fresinha12 wrote:
Here is why i say we add the triple..

see when we calculate the doubles..it already takes into account the triple...i.e we have already minused the triple to get the doubles... so we cant deduct triple again cause we have already taken em into account..



bkk145 wrote:
fresinha12 wrote:
dont we add the singles, minus the doubles and add the triples????

kevincan wrote:
OA=A


If you can explain why you should add the triple, I'll see if I can say something...


No, double doesn't take triple into account. They are different. If the question say something like "two or more languages", then it would take triple into account. But this problem said specifically that exactly two languages.
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 [#permalink] New post 07 Aug 2007, 12:10
fresinha12 wrote:
OK let me understand...

in a 3 set venn diagram...say C for chinese, M for Mandarian and J for Japense

120 speak exactly 2 languages...is equal to the sum of intersect of C n J, C n M and J n M...?? right if thats the case then 120 has already minused the number of people who speak C+J+M, correct?

bkk145 wrote:
fresinha12 wrote:
Here is why i say we add the triple..

see when we calculate the doubles..it already takes into account the triple...i.e we have already minused the triple to get the doubles... so we cant deduct triple again cause we have already taken em into account..



bkk145 wrote:
fresinha12 wrote:
dont we add the singles, minus the doubles and add the triples????

kevincan wrote:
OA=A


If you can explain why you should add the triple, I'll see if I can say something...


No, double doesn't take triple into account. They are different. If the question say something like "two or more languages", then it would take triple into account. But this problem said specifically that exactly two languages.


That's right. Let's look at something more simple and neglect "neither" at this point.
1) Say 2 people speak Chinese, 2 people speaker Mandarin, and 2 people speak Japanese. Say 3 speak "exactly two languages". Let x = people who speaker all three languages, we have:
2+2+2-3-2x = people who speak one language

2) If 3 people speak "two languages or more", then 2+2+2-3-x = people who speak only one language.

Notice the "2" factor is missing in the second one. The idea here is that if you speak two languages, then it overlap one time. If you speak all, then it overlap two times.

I hope I didn't confuse you even more. I think my reasoning is right, but feel free to correct if anyone disagree.
  [#permalink] 07 Aug 2007, 12:10
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