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Faster way : Venn diagrams

Expert replies
Source: — Data Sufficiency |

by ed09 » Sun Jul 06, 2008 4:04 pm
Hi wilderness,

My opinion is that Venn Diagrams is, probably, the simplest and the most comprehensive visual solution for this problem. It doesn't take much time, helps in understanding of concept without bogging down in math, and aids in error avoidance.
There is the way of solving this problem exploiting formulae for sets; yet, in my assessment, it is not worthy, particularly, for data sufficiency problems.

Best!
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by ildude02 » Mon Jul 07, 2008 1:29 pm
I'm curious to see how you guys solved it. I assumed German people to be X, so E+G= 60-x; Also, 60 -x is the ONLY common people since we are given of ONLY Spanish speaking and the final equation I came up with is,

200 = x + 60 + 70 - (60 -x ) + 20;

Is this right or I missed something ?
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by wilderness » Mon Jul 07, 2008 1:39 pm
I did not understand how you made this equation. Can you please explain a little bit more ? What about the people who speak Spanish AND English ?
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by ildude02 » Mon Jul 07, 2008 3:59 pm
Since the question gave us the number for Spanish ONLY speaking people, there is no intersection of spanish speaking people with other language speaking people. At least, that's how I went about solving it. If I can't assume so, I would appreciate any responses as to how to solve it.
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by lion147 » Mon Jul 07, 2008 4:27 pm
I setup this equation:

200 =
Only Spanish (70) +
Spanish and English (?) +
Only English (?) +
English and German (?) +
None (?)

So:

1) 200 =
Only Spanish (70) +
Spanish and English (?) +
Only English (60) +
English and German (?) +
None (?)
Insufficient

2) 200 =
Only Spanish (70) +
Spanish and English (?) +
Only English (?) +
English and German (?) +
None (20)
Insufficient

1&2) 200 =
Only Spanish (70) +
Spanish and English (?) +
Only English (60) +
English and German (?) +
None (20)

People speaking two languages (Spanish and English OR English and German) = 200 - 70 - 60 - 20 = 50

Sufficient.

EDIT: I did this in my head, but normally I draw the venn diagram just to make sure.
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by lunarpower » Fri Jul 11, 2008 3:09 am
this is just my empirical observation, but i have found that EVERY SINGLE ONE of the official gmat problems involving three sets are specifically written in such a way as to make them extremely venn-friendly.

in particular, a randomly written problem would be, in all likelihood, extremely ugly from the standpoint of a venn diagram. for instance, an innocent-sounding statement such as "40 members speak english" would actually span FOUR regions of the venn diagram (eng only, eng/span, eng/germ, all 3). throw together a couple of statements like that, and you've got a disaster just waiting to happen.
however, the gmat writers apparently take pains to ensure that this sort of thing won't happen on their 3-set problems. note all the convenient restrictions in this problem:
* the 60 and the 20 in the statements both go into single well-defined regions of the venn diagram (english only for (1), outside the circles for (2))
* 0 for german only
* 0 for spanish and german (this takes some thought)
* 70 for spanish only
* 0 for all three
notably, there is not a single figure given in the problem statement that spans two or more regions of the venn diagram. compared to random venn problems in math textbooks, which go out of their way to make you create ugly simultaneous equations, this is a nice treat.

lesson: use a venn diagram for 3-set problems. the problem is going to roll out the proverbial red carpet with its restrictions.
Ron has been teaching various standardized tests for 20 years.

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by cubicle_bound_misfit » Fri Jul 11, 2008 9:09 am
I have a doubt regarding the stmt
"each member who speaks Grman also speaks english"

does that mean German-speakers are a subset of English Speakers ???

Please Help.

regards,
Cubicle Bound Misfit
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by lunarpower » Fri Jul 11, 2008 11:19 am
cubicle_bound_misfit wrote:I have a doubt regarding the stmt
"each member who speaks Grman also speaks english"

does that mean German-speakers are a subset of English Speakers ???

Please Help.

regards,
correct.

for the purposes of a traditional venn diagram, though, you should think of it as "speakers of english AND german" instead of just german speakers.

if you want, i could attach a hand-drawn pitcture of the following 2 possibilities: (1) the traditional venn diagram for this problem, (2) a modified venn diagram that shows the german-speaking circle inside the english-speaking circle.
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron
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by cubicle_bound_misfit » Fri Jul 11, 2008 12:04 pm
I got it Ron.
Danke Schon.
Cubicle Bound Misfit
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by cubicle_bound_misfit » Fri Jul 11, 2008 12:37 pm
then is the OA is A?

because basically we are finding people speaking spanish and english + people speaking germany and english and stmt 1 tells us the only value for English.

Please let me know OA.

regards,
Cubicle Bound Misfit
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by beeparoo » Wed Jul 16, 2008 9:38 am
cubicle_bound_misfit wrote:then is the OA is A?

because basically we are finding people speaking spanish and english + people speaking germany and english and stmt 1 tells us the only value for English.

Please let me know OA.

regards,
As stated by wilderness in the original post, the OA is C.

Statement 1 reports the number of people who only speak ONE language - English.
This is not the same as "people who CAN speak English", which would then include people who speak English plus a second language.
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by aslan » Sun Nov 28, 2010 9:04 am
Hi,

Can we apply the formula here of

TOTAL = G1 + G2 + G3 - (Double overlap) -2* (Triple overlap) + Neither

?
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by aslan » Sun Nov 28, 2010 9:20 am
I did it with a little bit of tweaking of the formula

Total = G1 + G2 + G3 - (Both) + -2*(all three overlap)+Neither

Stm1:-

Total=200
G1=Spanish=70
G2=English=?
Both (here is assumed that since German speak both Both English and German so basically its asking for German=Both)
Three overlap=0

200= 60 + 70 -Both + Nei
70= - Both +Nei----->not solvable

stm 2:

200=G1 + 70 - Both + 20
110=G1-Both------Not solvable

Combining 1 & 2

200= 60 + 70 - Both + 20
70-20 = Both

Both = 50 (i.e German and English speaking)

It looks a risky solution compared to Venn but maybe shaves off some time.
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