Many of the students at the International School speak

Question

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.

(1) Exactly 60 students speak French and German. 
(2) Exactly 75 students speak neither French nor German.

mikemcgarry · Accepted Answer

Dear monirjewel , I'm happy to help with this. :-)

First of all, here's an article about DS questions: https://magoosh.com/gmat/2013/gmat-data- ... ency-tips/ Let's say F = French only speakers G = German only speakers B = speak both N = speaker neither Four unknowns. F + G + B + N = the total population of students. Among the students who speak French, four times as many speak German as don't --> B = 4*F 1/6 of the students who don't speak German do speak French students who don't speak German = F + N 1/6 of those are F, so N = 5*F We have two equations from the prompt that we can use with either statement. Statement #1 : Exactly 60 students speak French and German. B = 60 Therefore, F = 15 Therefore, N = 75 We have no way of calculating the value of G, so this statement, alone and by itself, is insufficient . Statement #2 : Exactly 75 students speak neither French nor German. N = 75. Therefore, F = 15 Therefore, B = 60 Again, no way of calculating G. This statement, alone and by itself, is insufficient . Combined : Even when we combine this information, we will have no way to calculate G, so no way to answer the question. Everything together is still insufficient . Answer = (E) Does all this make sense? Mike :-)

282552 · Answer

Hi Mike
Can you please explain this line to me "Among the students who speak French, four times as many speak German as don't"

mikemcgarry · Answer

Dear 282552 , Yes, I am happy to help. We can divide all students who speak French into two groups Group A = those who speak French and who also speak German Group B = those who speak French but who do not speak German (Group A) + (Group B) = all students who speak French. The sentence says that (Group A) is four times bigger than (Group B). That's the meaning. While I wasn't intending this, this is actually a sophisticated SC structure, an instance of common words dropped in parallelism. For a discussion of this topic, see: https://magoosh.com/gmat/2013/dropping-c ... -the-gmat/ Here's the sentence again with the common word included: Among the students who speak French, four times as many speak German as don't speak German . That's the end of the sentence. The idiom at the beginning is also tricky --- " among , X is more/less/etc. than Y ." By beginning with " among ", we are saying that we are confining our statement only to members of that group. Among Democrats, women outnumber men . Among universities in California, Stanford has the best reputation . When the sentence begins, " among the students who speak French ," we are saying that we are going to consider all French-speaking students as a single group, and completely ignore all the students who don't speak French. Inside this category of all French-speaking students, we are comparing German-speakers to non-German-speakers. Does all this make sense? Mike :-)

282552 · Answer

Thanks Mike
Nicely explained.
It does make sense now!!

gauravsaggis1 · Answer

Hi  mikemcgarry 
Please explain the meaning of "four times as many speak German as don't".
The meaning I get from this in mathematical form using same variables as above -
 4* as many speak German (B)= who don't speak German (F).
please explain as I am totally confused.

mikemcgarry · Answer

Dear gauravsaggis1 , I'm happy to respond. :-)

My friend, I believe you understand this correctly. First of all, grammatically, this phrase omits words in the second branch of the parallelism. See this blog article: Dropping Common Words in Parallel on the GMAT This is always a particularly confusing issue for non-native speakers. Here's the phrase with all the common words retained ... four times as many students speak German as the students who don't speak German ... On the GMAT SC, you have to be able to read the green words and understand the presence of the other words. Now, the mathematics, which I believe you understand. As above, B = students who speak both French and German F = students who speak just French, and not German. The problem says: " Among the students who speak French, four times as many speak German as don't ." The phrase " Among the students who speak French " means, for the purposes of that sentence, we are going to consider only that group of people. We would paraphrase this in colloquial languages as " just looking at the students who speak French " or " considering only the students who speak French ." For example, I might say: Among US cities, New York City is the largest . Clearly, NYC is not the largest city on the planet, but that's not what this sentence is saying. We are merely making the comparison to other US cities. Much in the same way, this sentence from the problem is considering only the students who speak French: these students are divided into two groups, B and F. Among French speaking students, the students in B speak German and the students in F don't speak German. This entire sentence is merely saying that B = 4*F. Does all this make sense? Mike :-)

gauravsaggis1 · Answer

@mikemcgarry,Thanks for reply but, my question still remains the same. with which part will 4 be multiplied?
 I have multiplied it with B whereas you have multiplied it with F. This is the part where I am confused.

Thanks in Advance.

mikemcgarry · Answer

Dear gauravsaggis1 , I'm happy to respond. :-)

I'm going to recommend this blog Intro to GMAT Word Problems, Part 1: Translating from Word to Math The basic idea that is that the " to be " verb, " is " or " are ," is the mathematical equivalent of the equal sign. Thus X is four times Y means X = 4Y. Now what's tricky about this problem is that it uses a more sophisticated grammatical construction similar to an appositive phrase . This is another grammatical way to show that two things are the same: Julius Caesar, the great Roman general, conquered Gaul . Among other things, we are saying that Julius Caesar WAS a great Roman general. This is a grammatical way to show " is " without writing " is ." Thus, this is an alternate way to indicate the presence of the equal sign. If the problem says X is an important number, four times greater than Y, .... that's a true appositive phrase. Grammatically, we are saying X is an important number AND X IS four times greater than Y .... and this means mathematically that X = 4Y. Now, look at that sentence in the problem: Among the students who speak French, four times as many speak German as don't. This is an extremely compact and elegant phrasing, typically of the fine question craftsmanship of MGMAT. The construction is in some ways analogous to an appositive phrase. Let's write a much more sloppy expanded version of this same sentence. Looking at all the students who speak French, the French speakers who speak German are four time as many as those who don't speak German. Now, look where the " are " is in the sentence: that's the equal sign. Thus (French speakers who speak German) = 4*(French speakers who don't speak German) You always have to find the implicit " is " --- that's where the equal sign goes. Does all this make sense? Mike :-)

Dheerusha · Answer

Can you please explain this part: 1/6 of the students who don't speak German do speak French students who don't speak German = F + N 1/6 of those are F, so N = 5*F Thank you

KVKool · Answer

Can anyone share the Venn diagram format of this question?

Posted from my mobile device

frankgraves · Answer

Hi Mike, 
Thank you for your explanations.
I may have different interpretation of the question.

So, quoting your explanation :
"We can divide all students who speak French into two groups
Group A = those who speak French and who also speak German
Group B = those who speak French but who do not speak German
(Group A) + (Group B) = all students who speak French. The sentence says that (Group A) is four times bigger than (Group B). That's the meaning. "
I agree with Group A and Group B.
If we write this mathematically : French = A + B (i)

From the question, "Among the students who speak French, four times as many speak German as don't"
If we put this into equation : A = 4B (ii)
Combining (i) and (ii) : French = 4B + B = 5B
I think this equation differs with the one you have on your explanation.
Appreciate if you can provide guidance on this.

ChandlerBong · Answer

Hi Bunuel , Can you please share your approach to this? Thanks in advance

gmatophobia · Answer

We can use a 2 * 2 matrix to solve this question Among the students who speak French, four times as many speak German as don't Number of students who do speak French but not German = x Number of students who speak both German and French = 4x Therefore the number of students who speak French = 5x 2.jpg In addition, 1/6 of the students who don't speak German do speak French The 1/6th number of students who don't speak German but speak French is the same set of students, represented by x, in our table. Hence, the number of students who do not speak German is 6 times that number. Number of students who do not speak German = 6x. Number of students who do not speak French and German = 6x - x = 5x The filled table is shown below. 1.jpg Statement 1 (1) Exactly 60 students speak French and German. From the plotted data 4x = 60 x = 12 However, we do not have the required data to find the total number of students or to find the number of students speaking German. The statement alone is not sufficient. Statement 2 (2) Exactly 75 students speak neither French nor German. From the plotted data 5x = 75 x = 12 However, we do not have the required data to find the total number of students or to find the number of students speaking German. The statement alone is not sufficient. Combined Statement 2 and Statement 1 provide us with the same information. Hence, the statements together are not sufficient as well. Option E

sayan640 · Answer

gmatophobia  should be x=15 ; kindly check.

Rebaz · Answer

mikemcgarry

What does  Among the students who speak French, four times as many speak German as don't.  even mean?

What does as don't mean in this context? Is that even good english?

Thanks in Advance!

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Many of the students at the International School speak

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