Author 
Message 
TAGS:

Hide Tags

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262
Location: Madrid

The members of a club were asked whether they speak [#permalink]
Show Tags
05 Aug 2007, 04:32
6
This post was BOOKMARKED
Question Stats:
37% (02:28) correct
63% (02:18) wrong based on 145 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.



VP
Joined: 10 Jun 2007
Posts: 1438

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
05 Aug 2007, 08:12
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.



VP
Joined: 28 Mar 2006
Posts: 1369

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
05 Aug 2007, 08:34
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..



VP
Joined: 10 Jun 2007
Posts: 1438

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
06 Aug 2007, 13:46
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.



Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
06 Aug 2007, 17:32
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...



VP
Joined: 10 Jun 2007
Posts: 1438

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
06 Aug 2007, 18:12
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.



Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
07 Aug 2007, 09:26
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.



VP
Joined: 10 Jun 2007
Posts: 1438

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
07 Aug 2007, 13:10
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+232x = people who speak one language
2) If 3 people speak "two languages or more", then 2+2+23x = 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.



VP
Joined: 22 Nov 2007
Posts: 1079

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
27 Nov 2007, 10:52
1
This post received KUDOS
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 2 of the 3 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 3 languages.
2. half of the members who speak Japanese and Cantonese also speak Mandarin.
I don't have the answer...in my opinion that's E....does smbd thinks differently?



CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
27 Nov 2007, 11:04
marcodonzelli 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 2 of the 3 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 3 languages.
2. half of the members who speak Japanese and Cantonese also speak Mandarin.
I don't have the answer...in my opinion that's E....does smbd thinks differently?
x = 100 + 150 +200  120  [all three languages *2] + neither
1. tell us relative info on the 2 variables
insuff
2. irrelvant as we already know 120 consists of all the overlap of 2 languagespeaking ppl
insuff
E
thoughts?



Manager
Joined: 20 Jun 2007
Posts: 156

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
03 Dec 2007, 09:50
I think it's C, the two statements together are sufficient.
The total number of members has to be:
100 Cantonese
+150 Mandarin
+200 Japanese
less 120 (speak exactly 2)
less (speak all 3)*2
less speak none
So we need to know how many speak all three languages and how many speak none.
Does 1 answer this for us? Obviously not. But it does give us interesting information  twice as many speak none as speak all three.
2 tells us that half of those who speak Japanese (100) and half of those who speak Cantonese (50) also speak Mandarin. Since only 120 speak exactly 2 languages, 30 must speak all three. But still we don't know how many speak none.
If we combine 2 with 1 we get the answer.



Intern
Joined: 10 Nov 2007
Posts: 13

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
03 Dec 2007, 10:10
Raffie wrote: I think it's C, the two statements together are sufficient.
The total number of members has to be:
100 Cantonese +150 Mandarin +200 Japanese less 120 (speak exactly 2) less (speak all 3)*2 less speak none
So we need to know how many speak all three languages and how many speak none.
Does 1 answer this for us? Obviously not. But it does give us interesting information  twice as many speak none as speak all three.
2 tells us that half of those who speak Japanese (100) and half of those who speak Cantonese (50) also speak Mandarin. Since only 120 speak exactly 2 languages, 30 must speak all three. But still we don't know how many speak none.
If we combine 2 with 1 we get the answer.
We are trying to find ALL members.
Why are you using for all of them MINUS non languages???
But U right, we can find answer because "exactly 2 languages" gives us necessary info.
Last edited by Blad on 03 Dec 2007, 10:11, edited 1 time in total.



Senior Manager
Joined: 09 Oct 2007
Posts: 466

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
03 Dec 2007, 10:11
If you fill it up this way, it doesn't add up. 120 people who speak both Japanese and Cantonese + 30 who speak all three = 150. But only 100 speak Cantonese.
Without more information on how all the people who speak 2 languages we can't solve. At least I can't. Love to hear to OE.
Raffie wrote: I think it's C, the two statements together are sufficient.
The total number of members has to be:
100 Cantonese +150 Mandarin +200 Japanese less 120 (speak exactly 2) less (speak all 3)*2 less speak none
So we need to know how many speak all three languages and how many speak none.
Does 1 answer this for us? Obviously not. But it does give us interesting information  twice as many speak none as speak all three.
2 tells us that half of those who speak Japanese (100) and half of those who speak Cantonese (50) also speak Mandarin. Since only 120 speak exactly 2 languages, 30 must speak all three. But still we don't know how many speak none.
If we combine 2 with 1 we get the answer.



Intern
Joined: 28 Aug 2007
Posts: 19
Location: London, United Kingdom

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
04 Dec 2007, 07:37
1
This post received KUDOS
Let those that speak C&M (but not J) = x, C&J (but not M) = y and M&J (but not C) = z
From the stimulus, we know that x + y + z = 120
Let those that speak C&M&J = w
Total members = (C  x  y  w) + (M  x  z  w) + (J  y  z  w) + x + y + z + w + None
Total members = C + M + J (x + y + z)  2w + None
Total members = 330  2w + None (as mentioned in previous post)
From Statement1: we know that: None = 2w
Total members = 330  2w + 2w = 330. Therefore answer is A or D
From Statement2: we know that: y + w (all those that speak Japanese & Canotense) = 2w (all those that speak Japanese, Cantonese & Mandarin). Therefore y = w
Total members = 300  2y + None...still have two unknown variables, therefore INSUFFICIENT!
Answer is A.



Intern
Joined: 13 Jun 2007
Posts: 48

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
04 Dec 2007, 07:46
>2. half of the members who speak Japanese and Cantonese also speak Mandarin.
To me this implies
0.5 of the members how speak both Japanese and Cantonese (info we don't have)
and NOT
0.5 of the members how speak either Japanese or Cantonese (info we do have)
so i think the answer is E



Director
Joined: 09 Aug 2006
Posts: 755

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
04 Dec 2007, 23:04
2
This post received KUDOS
marcodonzelli 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 2 of the 3 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 3 languages.
2. half of the members who speak Japanese and Cantonese also speak Mandarin.
I don't have the answer...in my opinion that's E....does smbd thinks differently?
Getting A
Total = C + M + J  (2 of 3)  2(all 3) + Niether
Total = 330  2(all 3) + Niether
Stat 1:
If x = all 3, then 2x = Niether
Total = 330  2x + 2x = 330. Sufficient
Stat 2:
Tells us that all 3 = 150 but doesn't say anything about niether. Insuff.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15941

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
22 Nov 2014, 03:57
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Current Student
Joined: 04 Jul 2014
Posts: 289
Location: India
GMAT 1: 640 Q47 V31 GMAT 2: 640 Q44 V34 GMAT 3: 710 Q49 V37
GPA: 3.58
WE: Analyst (Accounting)

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
22 Nov 2014, 04:15
1
This post received KUDOS
mantymooney wrote: Total members = 330  2w + None (as mentioned in previous post) How are we getting 330 here? For those who didn't understand how 330 is arrived at, here it is. Great work mantymooney! Total members = (C  x  y  w) + (M  x  z  w) + (J  y  z  w) + x + y + z + w + None Total members = C  x  y  w + M  x  z w + J  y  z  w + x + y + z + w + None Total members = C + M + J (x + y + z)  2w + None OR Total members = 100 + 150 + 200 (120)  2w + None OR Total members = 330  2w + None
_________________
Cheers!!
JA If you like my post, let me know. Give me a kudos!



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15941

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
25 Nov 2015, 17:53
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 31 May 2016
Posts: 4

Re: The members of a club were asked whether they speak [#permalink]
Show Tags
13 Aug 2016, 06:45
Total  neither = C + M + J  ( (C&M) + (M&J) + ( C&J))  2 ( C&J&M)
Given C = 100 , M =150 , J =200 C&M) + (M&J) + ( C&J) = 120
a) A says Neither = 2 * ( C &J&M) When we equate this is above 3 overlapping set equation , then neither and all 3 cancelled out we left with Total = C + M + J  120
A is sufficient to answer




Re: The members of a club were asked whether they speak
[#permalink]
13 Aug 2016, 06:45







