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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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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

 

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

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

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

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New post 10 Jul 2019, 08:19
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


From the information we have, we can conclude that the total number of students is 600 and none of the students can speak three languages. We have several groups of students:
1) those who speak English only - 140 students
2) those who speak German only
3) those who speak German and French
4) those who speak English and German
5) those who speak English and French.
Notice that there are no students who speak only French as each French speaker also speaks German.

If we subtract students who speak only English from the total number of students, we will be left with 600 - 140 = 460 students, who are spread across the left 4 categories. Now let us analyze each statement separately.

Statement 1.
If there are 120 students who speak only German, it means that there are 460 - 120 = 340 students left in the remaining 3 categories. We can note that all of the remaining categories consist of students who speak two languages and this is the task of the example. Thus, the statement 1 is sufficient to give an answer.

Statement 1 is sufficient.

Statement 2.
If there are 40 students who do not speak any language, it means that there are still 4 categories remaining, and one of these categories is students who speak only German. For this reason, we cannot predict precisely how many students are there speaking 2 languages.

Statement 2 is insufficient.

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

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New post Updated on: 11 Jul 2019, 09:24
total = 600
F+G and E=140
all three = 0
both we need to find
so #1
120 german = french
so 600=120+120+140-2(both)-all three-neither
neither not given
insufficient
#2
40 students do not speak any of the 3 languages
neither given but F and G values not given ; insufficient
IMO C

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

Originally posted by Archit3110 on 10 Jul 2019, 08:19.
Last edited by Archit3110 on 11 Jul 2019, 09:24, edited 1 time in total.
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Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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New post 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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New post 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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New post 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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New post 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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New post 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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New post 10 Jul 2019, 08:28
If we make a van diagram of the information provided we will get French students are a subset of only German speaking students. We have only English speaking students as even with the diagram we can find English speaking German students. We have no information to find french and German students therefore both the sentences are insufficient to answer the question.

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

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New post 10 Jul 2019, 08:36
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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

The answer therefore is C

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

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New post Updated on: 10 Jul 2019, 08:41
1
We need the shaded part.
1 & 2 Independently insufficient, but 1+2 gives the required answer

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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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New post 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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New post 10 Jul 2019, 08:43
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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

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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New post 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

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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New post 10 Jul 2019, 08:48
IMO : E

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

Sol:
total=A+B+C -(sum of 2 group overlaps) +(all three)+ Neither

600=140+B+C -(to be found) +0 +neither


1: 600=140+120 +C -(to be found) +neither

not sufficient

2 : 600=140+B+C -(to be found) +40

not sufficient


C

600=140+120+40 +C -(to be found)

300=c+(to be found)

we dont know how many peole speak french alone, also we dont know how many speak german and english.

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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New post 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

Answer C.
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Re: Of the 600 students in a class, each French speaker also speaks German   [#permalink] 10 Jul 2019, 08:50

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