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

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

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10 Jul 2019, 08:00
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Question Stats:

70% (01:51) correct 30% (02:02) wrong based on 287 sessions

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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

 This question was provided by Crack Verbal for the Game of Timers Competition

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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, 08:21
4
all = only E + only F + only G + group of 2 ( ef + eg + fg) + group of 3 + none

From questions stem,

600= 140 + 0 + only G + group of 2 ( 0 + eg + fg) + 0 + none

from 1 & question stem,

600= 140 + 0 + 120 + group of 2 ( 0 + eg + fg) + 0 + none
insufficient

from 2 & question stem

600= 140 + 0 + only G + group of 2 ( 0 + eg + fg) + 0 + 40
insufficient

1&2,

600= 140 + 0 + 120 + group of 2 ( 0 + eg + fg) + 0 + 40
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, 08:34
2
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

Please see attached file for solution.

IMO C
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Solution GMATClub.jpg [ 790.57 KiB | Viewed 1769 times ]

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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, 04:57
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
(2) 40 students do not speak any of the 3 languages

Total no = 600
no member can speak all 3 languages => members speaking 2/3 languages = (no speaking F and G) + (no speaking G and E)
no speaking only E = 140.
no speaking F and G = Total no speaking F

Total no = (no speaking F and G) + (no speaking G and E) + (no speaking G) + (no speaking E) + (speaking none)
600 = (No speaking 2/3) + G + 140 + None
No speaking 2/3 = 460 - (G + none)

Statement 1: Gives no speaking G alone as 120.
But we do not know the no of members speaking none of the languages.
Not sufficient.

Statement 2: Similarly this statement gives no speaking none but not G.
Not sufficient

Combining both together,

we get,
No speaking 2/3 = 460 - (120 + 40)

Hence, both statements together are sufficient.

Option C.

Originally posted by prashanths on 10 Jul 2019, 08:09.
Last edited by prashanths on 11 Jul 2019, 04:57, edited 3 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, 08:10
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
(2) 40 students do not speak any of the 3 languages

if all the students who speaks french also speak german and no member speaks all three languages. Means overlap of french and english is 0.

Option 1: 120 members speak only german. But we dont know the number of members speaking none of 3 languages. Hence remaining members do not speak any of three languages or speak 2 languages. - Insufficient
Option 2: 40 members speak none of three languages. But we dont number of members speaking only german. - Insufficient

Combing 1 + 2 - we get members speaking none of three languages. Speaking only English and only german. Remaining members out of 600 are members who speak 2 languages. - Sufficient
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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, 04:28
1
while we can certainly solve this question using vienn diagram, a more logical approach is available. We are told that there are 600 students in total, and 140 of them speak only English. So maximum number of students speaking two languages is 600-140=460. In this 460 we are including those students who speaking only German, NONE, and those who speak 2 languages are included (note that we have no students speaking 3 languages and no student speaking only French). So, we can conclude from stem that we need to find BOTH students who speak none and those who speak only German.
St 1 gives us just one piece of information, thus not sufficient.
St 2, similarly gives us another piece of missing information.
Combined, they both provide us with missing information using which we can find number of students who speak 2 languages out of 3. (C), imo

Originally posted by mira93 on 10 Jul 2019, 08:20.
Last edited by mira93 on 11 Jul 2019, 04:28, edited 1 time 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, 08:23
1
C

600 students include everyone including those who speak none of the languages, so in order to find the union, we need st 2. So, f U G U E = 600 - 40 = 560
Now, we are looking for FG + GE + EF
So, F U G U E = F + G + E - FG - GE - EF + FGE. Now, using st 1 and info in the question, we have F, G, E and FGE = 0. So, FG + GE + EF can be easily calculated.
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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, 08:24
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?

Total = Only French +Only German+Only English+Only Two+All+Not any
600=0+G+140+B+0+N ; 600=140+G+B+N

(1) 120 members speak only German - Insufficient, No information on "Not any"
(2) 40 students do not speak any of the 3 languages Insufficient, No information on "only German"
(3) Combined - 600=140+120+B+40; B=300 Sufficient

IMO 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, 08:25
1
Total=600
E=English,F=French,G=German,E'=No English,F'=No ,G'=No German
E=140
F=FG
EFG=0
EF=0 as All F can speak German and no one can speak all 3 lang
E=140

600= E+F+G-EF-FG+GE-2EFG-E'F'G' (Since only E and only G are given, so adding those who can speak both E and G)
As EFG=0 and EF=0
600= E+F+G-0-F+GE-2*0-E'F'G'
600=140+G+GE-E'F'G'

a. G=120
600=140+120+GE-E'F'G'
So Insufficient

b. E'F'G'=40
600=140+G+GE-40
So Insufficient

Combining, 600=140+120+GE-40
GE=380

Hence 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, 08:27
1
We have 3 languages E, F, G (Eng, Fr, Grmn)

Only E =140
Only F = 0
Only G = g
E+F+G =0
E+F =x
F+G =y
G+E =z
No language= a

Also, 140+x+y+z+g+a= 600.....Eqn 1
Question asks the value of x+y+z

St1 - g=120
Definitely not sufficient

ST 2- a=40
Definitely not sufficient

St1 + St 2

From.eqn 1 we get x+y+z=300
Sufficient

Imo 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, 08:36
1
Statement 1 is not sufficient since there is no information about the number who don’t speak any language.

Statement 2 is also insufficient since no information is available about the number who speak only German.

1+2 however provides sufficient information to get the number who speak only two languages as follows:

600-140-120-40=300

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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, 08:41
1
1 & 2 Independently insufficient, but 1+2 gives the required answer

Attachment:

Capture.PNG [ 298.28 KiB | Viewed 1470 times ]

Originally posted by LeoN88 on 10 Jul 2019, 08:39.
Last edited by LeoN88 on 10 Jul 2019, 08:41, edited 1 time 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, 08:40
1
Quote:
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

Find both:
600=F+G+E-both-2mid+neither
600=F+G+E-both+neither
(1) 600=(140+eg)+(120+fg)+(fg)-both+neither; inusf.
(2) 600=(140+eg)+(G+fg)+(fg)-both+neither; inusf.
(C) 600=(140+eg)+(120+fg)+(fg)-both+40
-300=2eg+2fg-both
-300=2eg+2fg-(eg+fg)
300=(eg+fg)=both
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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, 08:43
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
(2) 40 students do not speak any of the 3 languages

3 different sets, union of sets Total = n(F) + n(G) + n(E) – n(F and G) – n(F and E) – n(G and E) + n(F and G and E) + n(No Set).
now, n(F and G and E) = 0 here; we have to figure out n(F and G) + n(F and E) + n(G and E)

i, e - Total - {n(F) + n(G) + n(E)} - n(No Set) = n(F and G) + n(E and G) + n(F and E) .... eq 1

From the information ; n(E) - n(E and G) - n(E and F) = 140;

each French speaker also speaks German , i.e n(F) = n(F and G)+n(E and F)

coming from statement 2:

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

n(No Set) = 40;

from eq 1
n(F and G) + n(E and G) + n(F and E) = Total - {n(F) + n(G) + n(E)} - 40 = 600-40 -{n(F) + n(G) + n(E)}
=560 - {n(F) + n(G) + n(E)}

not sufficient;

coming from statement 1:

120 members speak only German

n(G) - n(G and F) - n(E and G) = 120;

n(F and G) + n(E and G) + n(F and E) = Total - {n(F) + n(G) + n(E)} - n(No Set)

we dont have n(No Set) value; hence insufficient;

combining both statements together -

560 - {n(F) + n(G) + n(E)} = n(F and G) + n(E and G) + n(F and E)

560 - 120 - n(G and F) - n(E and G) - n(F and G) - 140 - n(E and G) - n(E and F) - n(E and F) = n(F and G) + n(E and G) + n(F and E);

we can obtain 300 as answer from here;
hence option C is correct
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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, 08:44
1
From (1) we don't know the number of students who speak none of the three languages

Insufficient

From (2) we don't know the number of students who speak German only

Insufficient

(1)+(2)

We know that the number of students speaking French only is 0

We have the number of students who speak German only and the number of students who speak none and so we can calculate the total number of students speaking any 2 of the three

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, 08:50
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
(2) 40 students do not speak any of the 3 languages.

All three - ZERO.
Only French - ZERO.
FRENCH & GERMAN - x
GERMAN & ENGLISH - y
ENGLISH & FRENCH -z.
Only English - 140.

We need to find out = x+y+z = ?.

To find out this. We need to know Only German & None of 3 Languages.

Statament 1 - Gives detail only for German. Not sufficient.
Statement 2 gives details of None of 3 Languages. Not sufficient.

Both Statement Together - We get the details that we need.
Only German = 120
None of 3 Languages = 40

x+y+z = 600- 140-120-40 = 300

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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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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] 10 Jul 2019, 09:20

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