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GMAT Instructor
Joined: 07 Jul 2003
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60 students take French 80 students take German 40 students [#permalink]
 11 Jul 2003, 23:14
60 students take French
80 students take German
40 students take Russian
60 students take exactly 2 of the 3 languages mentioned above.
4 students take all 3 of the languages mentioned above.
8 students take none of the 3 languages mentioned above.
Part 1: How many student do we have in total?
Part 2: In the above group of students, if 12 students take French only, and 25 students take both French and German but not Russian, how many students take Russian only?
P.S. It might interest you to know that I got a question very similar to part 1 on a real GMAT about 2 weeks ago.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993
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Manager
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Aha... I got the same one in my GMAT paper also,
Part 1 Ans = 60+80+40-60+4+8= 132.
Part 2.
Let students studying only French and Russian and not German be x.
and students studying only Russsian and German and not French be y.
and students studying only Russian be z.
Also, x+y+25=60 (Since, students studying only two subjects is 60)
Now, Again x+y+4+z=40 (Students studying Russian)
So, z = 1 = Students studying only Russian.
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GMAT Instructor
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evensflow wrote: Aha... I got the same one in my GMAT paper also,
Part 1 Ans = 60+80+40-60+4+8= 132.
Part 2.
Let students studying only French and Russian and not German be x.
and students studying only Russsian and German and not French be y.
and students studying only Russian be z.
Also, x+y+25=60 (Since, students studying only two subjects is 60)
Now, Again x+y+4+z=40 (Students studying Russian)
So, z = 1 = Students studying only Russian.
The 60, 80, 40 include those who are taking 2 and 3 languages (i didn't say there are 60 students taking French ONLY). YOu are double counting.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993
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(1) X-8=60+80+40-60-2*4
X=120
(2) It is given that 12 people learn only Frech, and 25 learn FG~R.
Total 60 people study F. Thus, 60=12+25+4+Y, where Y is the number of people who study FR~G. Y =19
We know that 60 people study exactly 2 languages; therefore, 60=25+19+Z, where Z -- people who study GR~F, Z=16
Finally 40 people study Russian, of which 4 learn additionally French and German, 19 study FR~G, 16 study RG~F, and R study Russian only.
40=4+19+16+R, where R=1
P.S. My notation FR~G means that a person studies French, Russian, but not German. GR~F means that a person studies german, Russian, but not French.
P.P.S. Having in mind all the above, how many people learn only German?
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GMAT Instructor
Joined: 07 Jul 2003
Posts: 773
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Correct on both counts. I found this to be a pretty challenging GMAT question (i.e., one that took over 2 minutes to ponder and solve).
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993
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Manager
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My bad. Means i go this wrong on my GMAT. 
Yes i do agree, i missed out on the word exactly 2 of the languages and not 2 or more languages.
So, going by that, ans will be 120 indeed.
Although, i guess i got the part 2 right...
Wish that should come on my GMAT 
but i like these problems, great show Akamai... please post more.... 
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Eternal Intern
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Can you post the real explanation, I can't make sense of evensflow and stolyar?
VT
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Eternal Intern
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60 + 80 + 40 - 60 + 4 = 124
is correct for the number of students taking a language and does not
include the 8 who are not taking a course.
Did you really get three groups at the time!
Tell me more what to really expect, does the test have a similar feel to old paper and pencil tests. The DS does according to many but not the PS?
VT
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GMAT Instructor
Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Curly05 wrote: 60 + 80 + 40 - 60 + 4 = 124
is correct for the number of students taking a language and does not
include the 8 who are not taking a course.
Did you really get three groups at the time!
Tell me more what to really expect, does the test have a similar feel to old paper and pencil tests. The DS does according to many but not the PS?
VT
Your answer and approach are NOT correct. You are double counting a few categories.
_________________
Best,
AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993
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Eternal Intern
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Math Teacher Said that Way Is Okay! [#permalink]
16 Jul 2003, 10:53
Any hints on what we are double counting by the way that was help from a math teacher. Jesus, your stuff is 200 times harder than ETS.
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GMAT Instructor
Joined: 07 Jul 2003
Posts: 773
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Re: Math Teacher Said that Way Is Okay! [#permalink]
16 Jul 2003, 11:00
Curly05 wrote: Any hints on what we are double counting by the way that was help from a math teacher. Jesus, your stuff is 200 times harder than ETS.
What did your math teacher get on the GMAT? Draw a venn diagram, then observe how many times each section is counted.
As I stated before, this problem WAS ON A REAL GMAT (taken 2 weeks ago) so its difficulty level is most certainly appropriate.
I design my problems to challenge students shooting for 750+. My very best students can solve them in less than 2 minutes (as well as the very best here) so they are all reasonable "challenge" problems. They usually involve some flash of insight and/or application of multiple principles rather than massive calculations. I also want my students to approach all problems with a open and creative mind. Most of my students appreciate the challenge and the prep books, IMO, do NOT adequately prepare the 90%+ student with challenging enough problems.
If you practice swinging a heavy bat, it will feel as light as a feather come "game time."
_________________
Best,
AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993
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Intern
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You are absolutely right. Thats why i am looking through all the posts !!!
Maybe I can explain .
Total = 60 (French) + 80(German) + 40(Russian) - 60 (taking two subjects) - [2x4] (students taking all 3 since we counted them 3 times) + 8 (poor souls who dont take any language) = 120
Part 2)
Looking at the French circle we have 4 areas. French only , French and German (no Russian), French and Russian (no German) and all three.
This all equals to 60. Now adding all segments of French circle.
60 = 12(french only) + 4(all 3) + 25 (both french and german) + FR
FR = 19 students taking French and Russian only.
No we know 60 students take 2 subjects only which are French-German, French-Russian and German-Russian. We know two of those and hence can get the 3rd.
60 = 25 + 19 + GR
GR = 16 taking only German and Russian
Now we make the segments for the Russian circle, RF , R only, all 3 and GR
40 = 19+4+16 + R only.
R = 1.
Seems long but its just simple addition and subtraction and one's brain works 100 times as fast as this. (maybe 10)
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