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Many of the students at the International School speak [#permalink]

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12 Nov 2013, 07:41

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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.

Helpful Geometry formula sheet: http://gmatclub.com/forum/best-geometry-93676.html I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

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.

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
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Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: Many of the students at the International School speak [#permalink]

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25 Mar 2014, 19:03

mikemcgarry wrote:

monirjewel 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.

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

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"
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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"

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: http://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'tspeak German. That's the end of the sentence.

The idiom at the beginning is also tricky --- "among [group], X is more/less/etc. than Y." By beginning with "among [group]", 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
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: Many of the students at the International School speak [#permalink]

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26 Mar 2014, 17:58

mikemcgarry wrote:

282552 wrote:

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"

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: http://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'tspeak German. That's the end of the sentence.

The idiom at the beginning is also tricky --- "among [group], X is more/less/etc. than Y." By beginning with "among [group]", 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

Thanks Mike Nicely explained. It does make sense now!!
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Re: Many of the students at the International School speak [#permalink]

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11 Aug 2016, 03:22

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.

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.

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 manystudentsspeak German asthe students whodon'tspeak 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
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Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: Many of the students at the International School speak [#permalink]

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12 Aug 2016, 02:16

@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.

@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.

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 XISfour 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 Germanarefour 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
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Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: Many of the students at the International School speak [#permalink]

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10 Nov 2017, 21:47

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