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# Of the 600 students in a class, each French speaker also speaks German

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 08:54
IMO E:

total = F+G+E-(exactly 2) -(2*all theree) + neither
600 = F+G+140-2x-0+neither
from 1: we know G = 120, as neither is not known, not suff
from 2: neither = 40, we do not know G value, or F value, so noot suff

1+2

600 = F+G+E-2x+40

we do not know the total number of F,G and E. so not suff. I guess E
600= F+G+
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Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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Updated on: 11 Jul 2019, 07:19
1
From the stem itself we know that the overall number of students is $$600$$. Since $$140$$ students speak only English, the max possible number of students who speak $$2$$ languages is $$600-140=460$$. If each French speaker also speaks German, then no student speaks only French. French speakers for sure speak two languages. However, German speakers may speak only German. We know nothing about them from the stem. Additionally, no one can speak all three languages.

ST1. $$120$$ members speak only German. Now the max possible number of students who speak $$2$$ languages is $$460-120=340.$$ However, we still don’t know about all students. There may be those who don’t speak all languages. In such problems we usually have such groups and thus should be alert. In overlapping sets problems it would be wise to take a look at both ST1 and ST2 before we make conclusion.

ST2. $$40$$ students do not speak any of the 3 languages. Bingo! That was something we were curious about while reading ST1. But ST2 itself is not enough too.

ST1+ST2. Finally we have all what we need: $$340-40=300$$.

Hence C
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Originally posted by JonShukhrat on 10 Jul 2019, 09:01.
Last edited by JonShukhrat on 11 Jul 2019, 07:19, edited 2 times in total.
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:02
We need to calculate E n G ( no of people speaking both English and German) and total no of French people (since all French people speak German language)

(1) 120 members speak only German

Since every German does not speak French, so we can't calculate no of French people. and we do not know the English speaking person.

So (1) is insufficient

(2) 40 students do not speak any of the 3 languages

This means 560 people speak at least one of the languages. Since we not know the value of E n G.

Hence, (2) is insufficient.

(1)+(2) We can't calculate the No of French people speaking German. Hence, Insufficient.

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Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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Updated on: 10 Jul 2019, 17:42
1
Total = 600
English only = 140
French only = 0 (every French speaker also speaks German)
German only = G

English+French+German = 0 (no member can speak all 3 languages)
English+French = 0 (every French speaker also speaks German and no member can speak all 3 languages)
English+German = y
French+German = x
No language = z

QUESTION: How many of the members speak 2 of the 3 languages? --> x + y ?

(1) 120 members speak only German
G = 120 --> 600 = (140+0+120) + (x+y+0+0) + z --> 340 = (x+y)+z
(1) is NOT SUFFICIENT, because z is not known.

(2) 40 students do not speak any of the 3 languages
z = 40 --> 600 = (140+0+G) + (x+y+0+0) + 40 --> 420 = (x+y)+G
(2) is NOT SUFFICIENT, because G is not known.

Using both: G=120, z=40
600 = (140+0+120) + (x+y+0+0) + 40
300 = (x+y)
Combination of (1) and (2) is SUFFICIENT

Originally posted by chondro48 on 10 Jul 2019, 09:08.
Last edited by chondro48 on 10 Jul 2019, 17:42, edited 2 times in total.
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:13
1
from the A option we can not know how many do not speak any of the the three languages, and B does not gives us any details about the Count of people speaking German, A,D and B goes out of option.
When combined we can find the value which will be :
Total no of students- those who speak only 1 language
=600 - 120 -140=340
So S.
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:20
1
Since the question said each French speaker also speaks German
and English only = 140

Statement 1: Only German = 120
There is no value for French speakers and no value for 2 out 3 language speakers, therefore, NOT SUFFICIENT - BCE

Statement 2: 40 speak None of the language and no any other
information. NOT SUFFCIENT - CE

Combining statement 1 and 2: English only = 140
German only = 120
None speakers = 40
also since nobody speaks all three and no French only

therefore, 2 language out of 3 = 600 - 140 - 120 - 40

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:22
1
IMO-C

Refer attached image for visualization-
Denote: (F-French, E-English,G-German)
a-F+G
b-F+G+E=0
c-G+E
d-E =140
e-G
n-None

A/C question, b=0, d=140
Required to find: FG+FE+GE= FG+GE= a+c.........[FE=0 as all F=G so FE=FGE=b=0]

Now, a+b+c+d+e+n=600
=> (a+c)+e+n=600-140=460

Statement 1- (1) 120 members speak only German => e=120
Still n in equation unknown, (a+c)+e+n=460
Not Sufficient

Statement 2- 40 students do not speak any of the 3 languages => n=40
Still e in equation unknown, (a+c)+e+n=460
Not Sufficient

Together, Both e & n known
therefore a+c= 460-(e+n) known

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:31
1
IMO C

(1) 120 members speak only German - from this statement we don't know how many students speak neither of the 3 languages
Insufficient

(2) 40 students do not speak any of the 3 languages - from this statement we don't know how many of the students speak German or French
Insufficient

(1)+(2) => Together we can get the number of students who speak any 2 languages

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:36
1
We need to find the French speakers.
1) Insufficient
German=120; English=140; Total=600 no member?
600=140+120+x+No member
2) Insufficient
German=120; English=140; Total=600 None: 40
600=140+120+x +40

1&2 is sufficient. we clearly have all the information
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:41
Total=600
Only English=140
All 3=0
We need to find the members who speak 2 of the 3 languages
Formula: Total=English+German+French-(sum of 2 group overlaps)+all 3 +Neither
600=140+G+F-(sum of 2 group overlaps)+0+Neither
We need the value of G, F, and Neither to find the sum of 2 group overlaps.

St. 1: Only German=120. Still 2 unknowns. Not Sufficient.
St.2 : Neither=40. Still 2 unknowns. Not Sufficient.
St. 1 & 2 together: 600=140+120+F-(sum of 2 group overlaps)+0+40. Still 2 unknowns. Not sufficient

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 09:44
1
Of the 600 students in a class, each French speaker also speaks German, and 140 of students only speak English. If no member can speak all 3 languages, how many of the members speak 2 of the 3 languages?

We know the following:
Only German (G) + Only English (E) + Only French (F) + G&E (GE) + G&F (GF) + E&F (EF) + None (N) + All 3 (GEF) = 600

Simplified form:
G + E + F + GE + GF + EF + N + GEF = 600

F=0... because every F also speaks G, there is noone who speaks only F

E=140... because 150 speak only eng

GEF=0... because none speaks all 3

EF = 0.... because, all F speak G, so no F can speak E (F cannot speak 3 languages)

Substituting these 3 values in above:

G + 140 + 0 +GE + GF + 0 + N + 0 = 600

G + GE + GF + N = 460

We want to find GE+GF... (no EF because we already established that EF=0)

(1) 120 members speak only German

So 120 + GE + GF + N = 460...... We need N to get GE+GF

(1) is NOT SUFFICIENT

(2) 40 students do not speak any of the 3 languages

So G + GE + GF + 40 = 460 ...... We need G to get GE+GF

(2) is NOT SUFFICIENT

(1)&(2) both:
120 + GE + GF + 40 = 460.... This is Sufficient

GE+GF = 300

Answer: C - BOTH together are sufficient
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 10:03
1
Of the 600 students in a class, each French speaker also speaks German, and 140 of students only speak English. If no member can speak all 3 languages, how many of the members speak 2 of the 3 languages?

Before moving to the statements, analyze the question first.

The question is on overlapping set. Total = Group 1+ Group 2+ Group 3 -2*(2 Out of the three languages) + Neither
We are given that 140 Speak English.

(1) 120 members speak only German
This statement is insufficient as we are not given the number of students who don't speak any of the languages.

(2) 40 students do not speak any of the 3 languages
This statement is insufficient as we are not given the number of people speaking German or French.

Combining the two statements is sufficient as French will fall under the combined section So the answer is 600-140-120-40= 300

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 10:24
Total number of students =600

Students only speaking french =0

Students only speaking German=140=g

Speaking all three =0

Speaking both French and German =m.

Speaking both English and German =b

Speaking English =e

Statement one gives us value of e=120
Then we need value of b+m

We have

m+g+b+e=600

We have e any g thus we can find b+m

Then second statement says that we have 40 not learning any language

This is for no use we still don't have value of only german on equation

A wins clearly

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 10:53
1
Statement 1: There can be some students who do not speak any of the above 3 languages. So, Statement 1 alone is not sufficient.
Statement 2: This statement alone does not give the number of German-speaking students.

Statement 1 & 2: Number of students who 2 of the 3 languages = 600-140-120-40. So, C is the answer.
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 11:06
Of the 600 students in a class, each French speaker also speaks German, and 140 of students only speak English. If no member can speak all 3 languages, how many of the members speak 2 of the 3 languages?

(1) 120 members speak only German
(2) 40 students do not speak any of the 3 languages

Given

600=E + F +G -2(two members) +all three

F=G , E=140 all three=0
600=140+ 2G-2(two members)+none

a) G=120

600=140 + 2(120) -2(two languages)

Sufficient

B) clearly insufficient as we have 3 unknown variables
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 11:43
1
Of the 600 students in a class, each French speaker also speaks German, and 140 of students only speak English. If no member can speak all 3 languages, how many of the members speak 2 of the 3 languages?

(1) 120 members speak only German----> Insufficient. It doesn't tell about the students who don't know any of the languages.
(2) 40 students do not speak any of the 3 languages----> Insufficient. As we don't know the number of students who don't speak English or French but German.

Both statements together are sufficient

IMO. the correct answer is (c)
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 11:44
From question we need to know how many students speak german + french to know how many speak 2 languages.
As 140 speak only english : so 600-140 = 460 .
460 is no. of students who speak german + french. : As all french speakers , speak german, we just need to exclude from this Only german speakers which will give us speakers of 2 languages.

Statement 1 exactly tells us that. : No of german speakers. : Hence sufficient
Statement 2 : Does not gives this information: hence insufficient
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 12:06
1
No. of Students Speaking English Alone= E
No. of Students Speaking German Alone=G
No. of Students Speaking French Alone=F
No. of Students Speaking none of the 3 languages=N

Number of students speaking two languages= 600-N-(E+G+F) =600-N-(140+G+0)

(1) 120 members speak only German---->N is unknown, Not sufficient.

(2) 40 students do not speak any of the 3 languages-----> N is unknown, Not Sufficient

(1)+(2), both N and G are known, Sufficient.

Ans:C

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 12:25
1
The question if how many people speak French (because each of them also speaks German)
We can figure out the number of French - speakers if we will now how many people don't speak and language and how many people speak only German.

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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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10 Jul 2019, 12:29
1
According to the stem, we can make an equation
all students=only English+Only German+both English and german+Both French and German+neither

I. "Both english and German" does not overlap "both French and German" because noone speaks 3 languages;
II. we want to find "both English and german+Both French and German"

We have got:
All the students = 600
Only English =140

We have to find:
Only German
neither

1 stm --> gives "only German". We dont know "neither". Insuff
2 stm --> gives "neither". We dont know "only German". Insuff

Both statements together give sufficient data to find the number of people who speak 2 languages

IMO
Ans: C
Re: Of the 600 students in a class, each French speaker also speaks German   [#permalink] 10 Jul 2019, 12:29

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