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Overlapping sets (GMAT PREP)

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Overlapping sets (GMAT PREP)

by Stockmoose16 » Tue Nov 04, 2008 6:26 pm
Of the 200 members of certain association, each member who speaks german also speaks english. and 70 members speak only spanish. no member speaks all 3 languages. how many of the members speaks 2 of 3 languages ?
1. 60 members speaks only english
2. 20 members do not speak any of the three languages

I picked A, but OA is C


Here's my logic:

If you have 200 members, and 70 speak only Spanish (from stem), nobody speaks all 3 (from stem), nobody speaks only German (from stem), and 60 people speak only English, then, out of the 200 people, 130 are accounted for. Since nobody speaks only German, the remaining 70 speak two languages. Where am I going wrong here? I don't understand why we need Stmt #2.
Last edited by Stockmoose16 on Tue Nov 04, 2008 6:46 pm, edited 1 time in total.
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by cramya » Tue Nov 04, 2008 6:41 pm
Please check OA. Is it [spoiler]C)[/spoiler] & not [spoiler]E)[/spoiler]
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by Stockmoose16 » Tue Nov 04, 2008 6:47 pm
cramya wrote:Please check OA. Is it [spoiler]C)[/spoiler] & not [spoiler]E)[/spoiler]
Yes, you are correct. I've changed my post to reflect this information.

I still don't understand why we need STMT #2, though.
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by cramya » Tue Nov 04, 2008 6:55 pm
This is my solution. Critique welcome!

Lets take grp1 as Spanish, grp 2 as Eng and grp 3 as German
For 3 sets

Total = Grp1 + Grp2 + Grp3 +Neither - (grp 1 & 2) - (grp 2 &3) - (grp 3 and 1) -2(grp 1&2&3)

From question stem given:
total=200
grp1 exclusive = 70
(grp 1&2&3) = 0
grp3 exclusive = 0

To find (grp 1 & 2) + (grp 2 &3) + (grp 3 and 1)

Stmt I)
grp2 exclusive = 60
Still dont know what Neither is INSUFF

Stmt II)
neither = 20
grp2 exclusive missing

INSUFF

Stmt I and II together:

Rearranging

Total = Grp1 + Grp2 + Grp3 +Neither - (grp 1 & 2) - (grp 2 &3) - (grp 3 and 1) -2(grp 1&2&3)

to

(Since grp1 = group1exclusive + (grp 1&2)+ (grp 1&3) + grp(1&2&3) Simlarly grp 2 and grp 3 can be replaced accordingly)


Total =

Grp1exclusive +(grp 1 & 2) + (grp1 & 3) + grp(1&2&3) +

Grp2exclusive +(grp 2 & 1) + (grp2 & 3) + grp(1&2&3) +

Grp3exclusive +(grp 3 & 1) + (grp 3& 2) + grp(1&2&3) +

+Neither - (grp 1 & 2) - (grp 2 &3) - (grp 3 and 1) -2(grp 1&2&3)


(one set of grp 1,2 (grp2 & 3) +(grp 3 &1) cancel and grp 1 & 2 & 3 is 0 )


Total = Grp1exclusive +Grp2exclusive+Grp3 exclsuive +(grp 1 & 2) + (grp2 & 3) +(grp 3 &1) + Neither




Total - Grp1exclusive -Grp2exclusive-Grp3 exclsuive-Neither = (grp 1 & 2) + (grp2 & 3) +(grp 3 &1)


All info for this we have from I and II and question stem hence C)
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Re: Overlapping sets (GMAT PREP)

by logitech » Tue Nov 04, 2008 6:56 pm
Stockmoose16 wrote:

Here's my logic:

If you have 200 members, and 70 speak only Spanish (from stem), nobody speaks all 3 (from stem), nobody speaks only German (from stem), and 60 people speak only English, then, out of the 200 people, 130 are accounted for. Since nobody speaks only German, the remaining 70 speak two languages. Where am I going wrong here? I don't understand why we need Stmt #2.
70 = # Who speaks 2 languages + # Who does not speak any of the languages.

This is why you need ST 2, and this why the answer to this question is 50 but not 70.
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by bluementor » Wed Nov 05, 2008 5:36 am
This can be viewed as a problem of 2 overlapping sets (English and Spanish) for the following reasons:
- no one speaks all three languages
- German is a subset of English because all german-speaking people speak english.
- The German subset does not overlap with the Spanish subset because no one speaks all three languages.

Therefore, the English set consists of:
a) z people who speak only English
b) x people who speak English + German
c) y people who speak English + Spanish

And the Spanish set consists of:
a) 70 people who speak only Spanish
b) y people who speak Spanish + English


So you have:

Total = English + Spanish – Both +Neither
200 = (x + y + z) + (70 + y) – y + Neither
130 = x + y + z + Neither

The question is asking for the number of people who speak 2 languages: x + y

From statement 1:
Z = 60, but we still don’t know the number of people who speak neither of these languages, so insufficient.

From statement 2:
Neither = 20. But we still don’t know z, so insufficient.

Combining both statements:
You have info for z and Neither, sufficient to evaluate x+y, hence C.
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