Members who speak 2 of 3 languages

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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Tue May 31, 2011 6:40 pm

Of 200 members, each member who speaks German also speaks English,
and 70 of members only speak Spanish. If no member speaks all 3 languages, how
many of the members speak 2 of the 3 languages?
a. 60 members speak only English
b. 20 members do not speak any of the 3 languages

OA is C

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Source: Beat The GMAT — Data Sufficiency | Tue May 31, 2011 6:40 pm

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Tue May 31, 2011 7:05 pm

Very easy using a Venn diagram.
Use 3 overlapping circles.

Here I will represent it mathematically.
Let G be the group who speak only German.
E - Only English
S - Only Spanish
N - Speaks none of the three
GE - People speaking German and English
SE- Spanish and English and so on.
SGE - all three.

So our equation would simply be
S + G + E + SE + GE + SG + SGE + N = Total = 200.
From question we know that G = 0 since all german speaking people also speak english and fall into GE category.
Also S=70.
SGE = 0 (none speaks all three)
What we need is SE + GE + SG = 200 - 70 - N - E (G and SGE are anyway 0).

Stmt 1) E is given, but we dont have N.
Stmt 2) N is given but no E.
Combined N and E are available which gives us the required Sum

Hence C

Vineesh,
Just telling you what I know and think. I am not the expert.

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Tue May 31, 2011 11:19 pm

total 200
only spanish = s = 60
only english =e
only german = g = 0 (as who speaks german also speaks english)
all of the three = 0 (given)
none of the three = n
To find no. of members who speak 2 of 3 languages,x = total - (speak only 1 (can be any) + speak all 3 + speak none)
or x = 200-((60+e+0)+0+n)
x=140-(e+n)
a) provides only e, thus insufficient.
b) provides only n, insufficient.
a+b) e and n are given. can be solved for x.
Sufficient
IMO C

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