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

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Manager
Joined: 29 May 2019
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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, 13:12
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 students 600= only F + Only G + Only E + (F+G) + (F+E) + (G+E) + (E+F+G) + None

Only F= 0 as given if F then also G
Only G= ?
Only E= 140
F+G = ?
F+E = 0 as F knows G as well
G+E = ?
E+F+G= 0 Given
None = ?

We are looking for (F+G) + (G+E)

(1) 120 members speak only German
We get the value of only G but do not know none.
Insufficient.

(2) 40 students do not speak any of the 3 languages
We have none but do not have only G.
Insufficient.

Together:
We can find out (F+G) + (G+E)

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, 13:55
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

Question stem analysis:
French - F
German - G
English - E
Neither - N
Total- T
T = F only + G only + E only + F and G but not E (x let)+ F and E but not G (y let) + E and G but not F (z let) + E and G and F + N
We are asked to find number of people who speak 2 out of 3 languages or x+y+z. If each who speak french also speak german then there are 0 students who speak french only. No member can speak all 3 so E and G and F = 0
or 600 = 0 + G only + 140 + x+y+z+0+N

statement 1 - 600 = 0+120+140+x+y+z+0+N - insufficient.
statement 2 - 600 = 0+G only + 140+x+y+z+0+40 - insufficient.
1 and 2 - 600 = 0+120+140+x+y+z+0+40
or x+y+z = 600-300 = 300 - sufficient. IMO 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, 14:06
1
Total = Germany only + French only + English only + G∩E only + G∩F only + F∩E only + G∩F∩E + Neither

translating the given:

Of the 600 students in a class --> Total = 600
each French speaker also speaks German --> French only = 0, and F∩E only = 0
140 of students only speak English --> English only = 140
no member can speak all 3 languages --> G∩F∩E = 0

formula after substituting known values:
600 = Germany only + 0 + 140 + G∩E only + G∩F only + 0 + 0 + Neither

question : what is the value of (G∩E only + G∩F only)

statement (1): Germany only = 120 --> insufficient because we don't know the Neither value
statement (2): Neither = 40 --> insufficient because we don't know the Germany Only value

Combining (1) and (2):
600 = 120 + 0 + 140 + G∩E only + G∩F only + 0 + 0 + 40
G∩E only + G∩F only = 420 --> sufficient

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, 15:01
1
Let students that can speak french= a
Let students that can speak only German= b
Let students that can speak only English= c
Let students that can speak both German and English=d
and students who can speak none = e

Given- a+b+c+d+e=600, and c=140
members that can speak 2 of the 3 languages= a+d
Hence if we have value of b and e, we can find out a+d

Statement 1
b=120. Still e is unknown
Insufficient

Statement 2
e= 40, b is unknown.
Insufficient

Combining both statements
We have value of b and e, hence we can find out a+d
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, 17:23
1
In this 3 overlapping sets problem, we are asked to find the number of members who speak 2 of the 3 languages.

We can use the below formula to calculate:
Total=E+G+F−(sum of 2−group overlaps)+(all three)+Neither
where E = students who speak English, F = Students who speak French and G = students who speak German

Question stem tells us Total = 600, F = G but not given the value, E = 140 and All three = 0

In order to use the above formula, we must know either F or G and how many speak neither of the languages.

Stmt 1: Gives G = 120, Hence F = 120, but don't know the value of Neither. Hence insufficient

Stmt 2: Tells us that Neither = 40. But still don't know G or F. Hence insufficient

Stmt 1 + 2. Sufficient to use the formula and get the number of students who speak any 2 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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10 Jul 2019, 18:32
1
Following are the regions:
a: only french
b: onlye german
c: only english
d: french and german
e: grench and english
f: german and english
g: all three
h: none of them

a+b+c+d+e+f+g+h=600
a=0; e=0; c=140
so, b+d+e+f+h=460
d+e+f is to be found

(1)b=120 still h is known. Insufficient.

(2)h=40, now b is unknown. Insufficient.

(1)+(2), b and h are known. value of d+e+f can be calculated. Sufficient.

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, 19:09
1
Given
each French speaker also speaks German
That means ONLY French =0,
Only ENGLISH=140
All three=0.
Total=600
Exactly TWO=?

Formula:
Total =EXACTLY ONE+EXACTLY TWO+All three +NONE.

Here, exactly one=only English + only french + only GERMAN.

We have all values (required to find out the value of exactly two)except the value of (a) ONLY GERMAN &(b) NONE.

Statement 1: value of ONLY GERMAN is given. But no info about NONE.
Insufficient.

Statement 2: value of NONE is given. But no info about ONLY GERMAN .
Insufficient.

Values of ONLY GERMAN (In statement 1) & NONE (in statement 2) are given.
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, 19:11
1
For (1) 120 members speak only German. So now we know 140 speak only English, 120 speak only German and there is nobody speak only French because each French speaker also speak German. And we know no member can speak all 3 languages, but we don't know if there is anyone speak none of the language, so (1) is insufficient.

For (2), now we know 40 students do not speak any of the 3 languages, so we can get the number 600-140-120-40=300, which equals to the number of members who can speak 2 of the 3 languages.

choose C
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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, 20:13
1
From the statement we have that:

Speak all 3:0
Only English:140
English and German:x
French and German:y
Only German:z
None of 3:t

So, 600 =140 + x + y + z + t, simplifying we get x + y + z + t = 460

So we need z and t values to get the number of members that speak 2 laguages.

From (1) 120 members speak only German, we only get the value of z, so clearly insufficient

From (2) 40 students do not speak any of the 3 languages, we only get the value of t, so insufficient

From (1) and (2) we get that x+ y = 300, so 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, 20:24
1
To answer this question, we need to find how many speak only German, and how many speak NONE. Then from Total we will substitute above variables and whatever is left that is our answer.

Statement one does not give us number of NONE, thus we can not determine exact value. We only know 140 (only english)+120(only german). So 600-140-120=340 is number of people who speak NONE and who speak 2 languages.

Statement two gives us value for NONE but no info for German only. Not sufficient.

Combining we get 600-140-120-40=300 speak only two languages. Sufficient. Answer 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, 20:37
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

The scenario will be as shown in the figure

Now given
we have to find f+x
as per statement 1
f+120+x+140+ y = 600
thus f+x+y = 340
we need y also
Hence not sufficient

As per statement 2

f+g+ x+ 140+40 = 600
again we have an extra g that we should know
Hence no suffciient
Combine 1 & 2

f+120+x+140+40 = 600
f+x = 300
this is what was the answer needed
Thus C is
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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, 21:15
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 students = 600

given each French speaker also speaks German ==> German = French/German + Only German
some thing like Fresh is a subset of German , a circle inside a big German circle.

English speaking students = 140
No student speaks all three = 0

Venn diagram will be like 2 big circles intersecting at 2 points with a comman area lets say E&G , the third circle is small circle inside German - lets say area of small circle = F&G

So Total member of students speaking only 2 languages = E&G +F&G
= TotalStudents - Only English-OnlyGerman-not any langues
= 600-140-(X-need) -(Y-need)

lets look our options

(1) 120 members speak only German -Insufficient
Ok We got our X , but don't know Y .

(2) 40 students do not speak any of the 3 languages-Insufficient
We got our Y but don't know X

Combined We know both X and Y , we get E&G+F&G -Students who speak 2 langues---Option C is our 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, 21:21
1
Attachment:

WhatsApp Image 2019-07-11 at 9.46.54 AM.jpeg [ 138.16 KiB | Viewed 168 times ]

The 2 formulas for 3 intersecting sets are,

1. TOTAL = A + B + C - (sum of 2 set overlaps) + (3 set overlap) + Neither
2. TOTAL = A + B + C - (sum of exactly 2 set overlaps) - 2 * (3 set overlap) + Neither

In our question,

Knowns are,

1. Total students in class = 600
2. Each French speaker also speaks German.
3. No members can speak all 3 languages.
=> 4. From 2 and 3 No French speaker also speaks English.

Unknowns are,

1. Number of students who speak both English and German.
2. Number of students who speak only German.
3. Number of students who speak both German and French.
4. Number of students who do not speak any of the languages.

What we need to find?

Number of students who speak 2 of the 3 languages.
=> Number of students who speak either
English and German OR
German and French OR
French and English

Now from our knowns we know,
French and English = 0

Options 1: 120 members speak only GERMAN.

As per all the above information, this is not enough as we still do not know the number of students who speak all the 3 languages.

Option 1 alone insufficient.

Option 2: 40 students do not speak any of the 3 languages.

As per all the above information, this is not enough as we still do not know how many students speak only GERMAN.

Option 2 alone insufficient.

However if we use the information available in both the options above together we get,

2 out of our 4 unknowns.
The other 2 unknowns are what we need to find out cumulatively, since we deduced that the number of students who speak only English and French is 0.

Hence, both statements 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, 21:37
1
Let the number of speakers of English, French, and German be E, F, and G respectively.

Data Given:
Total students: 600
Only F = 0
F n G = some value
Only E = 140
E n F n G = 0
E n F = 0
E u F u G = some value
So we need to find a definite value for (E n G) + (F n G)
We can find it by (E u F u G) – {140 + only G} -> [a]

(1) 120 members speak only German
Only G = 120
However, we are not sure about the value of E u F u G (Since it is not given that all 600 students speak at least one of the three languages).
Not Sufficient.

(2) 40 students do not speak any of the 3 languages
Now we know that the value of E u F u G is 600 – 40 = 560
But we do not know the value of ‘only G’ in [a]
Not Sufficient.

(1) + (2)
From [a] we now get the value of the students who speak 2 of these languages as
560 – (140 + 120) = 300
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, 21:42
Total students = 600 students
Students speaking French and German
Students speaking English and French
Students speaking English & German
Only French - Each French speaks german , so there are no only speaking students - 0
Only German
Only English = 140
Speaking all 3 = 0
Speaking none

Find no of FG, EF, EG

(1) 120 members speak only German
we are not given , how many speak none of these languages and how many speak only two lang French-German, English-German, and English-French. not sufficient.

(2) 40 students do not speak any of the 3 languages
we are not given how many speak only two lang French-German, English-German, and English-French. not sufficient.

combined stmts, don't tells us how many speak only two lang French-German, English-German, and English-French. not sufficient.

E
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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, 21:46
1
Since 140 speaks only english and each french speaks german.

So only french speaking and french & english speaking becomes zero. Also nobody speaks all three language.

so if french & german speaking is 'x' , english & german speaking is 'y' , only german is 'z' , and none of the above three language is 'a'.

x+y+Z+a+140=600

option1 :- z= 120 , x+y+a=340 (not sufficient to find x+y we need 'a' as well)

Option 2:- a= 40 x+y+z= 420 (not sufficient to find x+y we need 'z' as well)

combining both we x+y = 300 sufficient 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, 21:54
1
Answer is C as put together we can conclude correctly that 600- 140- 120- 40 speak both languages. Already said that noone speaks only French so all the people left have to speak at least 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, 22:15
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

Total = only F + only G + only E + (F and G) + (G and E) + (E and F) + (E and F and G) + None.
Now, (E and F and G) = 0
Only E = 140.
Only F= 0.
(E and F)=0

Statement 1 :
Only G = 120
Total = 120 + 140 + (F and G) + (G and E) + None.
Insuff.

Statement 2 :
None =40
Insuff.

Both 1 and 2
Total = 120 + 140 + (F and G) + (G and E) + 40.
600 = 120 + 140 + (F and G) + (G and E) + 40.
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, 23:00
1

2 categories = 0 + Y + Z = Y + Z

Formula: Total(T) = Neither(N) + 140 + 0 + C + (0 + Y + Z) + 0
--> 600 = N + 140 + C + (0 + Y + Z)
--> Y + Z = 460 - (N + C)

(1) 120 members speak only German
--> C = 120
--> Y + Z = 460 - (N + C)
--> Y + Z = 460 - (N + 120)
--> Y + Z = 340 - N

Insufficient

(2) 40 students do not speak any of the 3 languages
--> N = 40
--> Y + Z = 460 - (N + C)
--> Y + Z = 460 - (C + 40)
--> Y + Z = 420 - C

Insufficient

Combining (1) & (2)
C = 120 & N = 40
--> Y + Z = 460 - (N + C)
--> Y + Z = 460 - (120 + 40)
--> Y + Z = 300

Sufficient

IMO Option 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, 23:03
1
Total number of students (T) = 600
T = only English(E) + only French(F) + only German(G) + (EF + EG + FG) + EFG + not speaking any of these three languages (x)
Given: only English (E) = 140
only French (F) = 0, since every french speaks german
only German(G) = unknown
EFG = 0
Find: what is (EF+EG+FG) ?
600 = 140+0+only(G)+(EF+EG+FG)+x
(i) only(G) = 120, but we don't know x, not sufficient
(II) x = 40, but we don't know only(G)
(I) & (ii) --> we can find (EF+EG+FG) --> answer is C
Re: Of the 600 students in a class, each French speaker also speaks German   [#permalink] 10 Jul 2019, 23:03

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