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French or German

by LalaB » Sun Oct 23, 2011 9:20 am
Many of the students at the International School speak French or German or both. Among the students who
speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak
German do speak French. What fraction of the students speak German?
(1) Exactly 60 students speak French and German.
(2) Exactly 75 students speak neither French nor German.
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by sl750 » Mon Oct 24, 2011 9:57 am
LalaB wrote:Many of the students at the International School speak French or German or both. Among the students who
speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak
German do speak French. What fraction of the students speak German?
(1) Exactly 60 students speak French and German.
(2) Exactly 75 students speak neither French nor German.
Can you please fix the error
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by saketk » Mon Oct 24, 2011 12:31 pm
LalaB wrote:Many of the students at the International School speak French or German or both. Among the students who
speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak
German do speak French. What fraction of the students speak German?
(1) Exactly 60 students speak French and German.
(2) Exactly 75 students speak neither French nor German.
Things which are given to us.

Let X= People who speak only French i.e. they do not speak German
Y = People who speak only German i.e. they do not speak French
Z = People who speak both
N = People who do not speak any language. [remember the question says 'Many of the students'

Also, we know that Z = 4X
And, we also know that 1/6th People who do not speak German do speak French(this includes X and N)
This means X = 1/6 (X+N) or 5x = N or X = N/5

Statement 1 -- From this statement we can only find the number of student who speak both languages. Nothing can be deduced about the people who don't speak any of the two. Also, we cannot deduce anything about the student who speak only 1 language.

Insufficient

Statement 2-- From this statement we know N= 75
From this we can find X, which is 1/5 of N i.e. 15. We also know that Z = 4X or = 4*15 = 60
Again, we cannot deduce anything about people who speak ONLY GERMAN from this statement


Combine the two statement

we know the value of X, Z, N but still nothing about Y can be deduced.

IMO E
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by SaraLotfy » Tue Oct 08, 2013 4:38 am
Can someone please provide OE and OA??
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by theCodeToGMAT » Tue Oct 08, 2013 4:57 am
SaraLotfy wrote:Can someone please provide OE and OA??
According to me, the Answer is [spoiler]{E}[/spoiler]... What's your answer??

To find: G/Number of Students
Statement 1:
4A = 60 --> A = 15
NG = 6(A) = 90
We cannot find "G"; INSUFFICIENT

Statement 2:
NG - NG/6 = 75
NG = 75 * 6/5 = 90
We cannot find "G" ; INSUFFICIENT

Combining...
We cannot find "G"
INSUFFICIENT
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by SaraLotfy » Tue Oct 08, 2013 5:47 am
Yes I got E using the double matrix method.
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by Brent@GMATPrepNow » Tue Oct 08, 2013 6:29 am
If anyone out there is wondering about the "double matrix method" that SaraLotfy mentioned (and theCodeToGMAT demonstrated), it's a technique can be used for most questions involving a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- speak German, or don't speak German
- speak French, or don't speak French

To learn more about this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/sets-t269449.html#692540
- https://www.beatthegmat.com/in-costume-f ... tml#692116

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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