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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, 23:17
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?

Three Overlapping set
Total = only French + Only german + only english + Sum of only 2 + sum of only 3 + none

From Question Stem
Total = 600
Only English = 140
Only French = 0
Sum of only 3 = 0

A 120 members speak only German
Only German = 120
Not Sufficient

B 40 students do not speak any of the 3 languages
None = 40
Not Sufficient

With A and B
Total = only French + Only german + only english + Sum of only 2 + sum of only 3 + none
600 = 0 + 120 + 140 + Sum of only 2 + 0 + 40
600-120-140-40 =300 = Sum of only 2

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

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11 Jul 2019, 01:07
1
As shown in the image,

(a+b+c) + (p+q+r) + s = 600 is given.
c=140 is given
Each French speaker also speaks German = a & q both are zero.
This I think is the most important inference.

Now, we need to find (p+r) and we have (p+r) + (b+s) = 460
So, we need to find values of b & s.

(1) 120 members speak only German

b=120 but we still don't know s. Insufficient.

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

s = 40 but we don't know b. Insufficient.

If we combine two, we get an answer. So, Ans should be (C)
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Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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11 Jul 2019, 01:43
1
IMO-C

a-FG, b-FGE=0, c-GE, 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

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

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11 Jul 2019, 01:49
1
(1) 120 members speak only German

Here, information about the students not speaking any language is missing. Without that we can not answer the question.
'1' can not answer the question independently.

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

Here, given information is very less to answer the question. Because remaining 420 (600-140-40) can be arranged in many ways.
'2' can not answer the question independently.

Combining 1&2, We can find the sum of students speaking french (they will speak German too) & students speaking German and English. That will be our answer to the asked question. (Note: We can not find number of students separately for both cases, but that is not required to answer the question.)

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

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11 Jul 2019, 02:03
1
----each French speaker also speaks German (given)
----students only speak English = 140 (given)
combining statement (1)&(2) we get 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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11 Jul 2019, 02:03
1
we need to use this formula here
T=E only + F only (0, because overlaps with G) + G only + 2 languages spoken + 3 languages spoken + none
Statement 1 gives number of students who speak G only but we still do not know how many speak None. Not sufficient
Statement 2 gives number of students that speak none but we don't know how many speak only G. Not sufficient.
Combined, we have
600=140 (E only) +120 (G only)+2 languages spoken (need to find)+0 (3 lang) +40 (none). Since we can find number of those who speak two languages, C is 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, 07:02
1
given

total -neither= only f + only g + only e +only (fg +ge + ef) + fge
600 - neither = 0 + 140 + only g + x ( x is what we have to find out out of which fge is 0)

so 3 variables needed

condition 1 gives one variable ie 120 members speak only German so not sufficient
condition 2 gives one variable ie 40 students do not speak any of the 3 languages so not sufficient

together its bingo, we can find x , so sufficient

Originally posted by ccheryn on 11 Jul 2019, 02:14.
Last edited by ccheryn on 11 Jul 2019, 07:02, 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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11 Jul 2019, 03:15
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?

The condition gives us:
All = 600
Eng = 140
Fr = 0
FrEn = 0
FrEnGe = 0
Ge = ?
NotSpeak = ?

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

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

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11 Jul 2019, 03:18
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

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

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11 Jul 2019, 03:20
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?

Given:
Total=600
Only F=0
Only E=140
All 3 =0

Exactly 2?

We can use this formula:
Total = Exactly 1 + Exactly 2 + Exactly 3 + Neither
What we need to solve this equation is info about Only German and Neither

(1) 120 members speak only German
Not sufficient. Explained above.
(2) 40 students do not speak any of the 3 languages
Not sufficient. Explained above.

Both statement together is 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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11 Jul 2019, 03:32
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?

Given:
f = French speakers
g = German speakers
e = English speakers

140 of students only speak English => e - eg=140 ---(i)
Total=600 = (population can speak atleast one of the 3 languages) + (population can 's speak any of the 3 languages) = fUgUe + (fUgUe)' = (gUe) + (gUe)', because f is subset of g (fUg = g --(ii)& fg =f --(iii))
600 = g + e -ge + (gUe)'
=> g + 140 + (gUe)' = 600, from (i)
=> g+ (gUe)' = 460 --(iv)
how many of the members speak 2 of the 3 languages? ==> fg+ge = f + ge = ?

(1) 120 members speak only German --> g - fg -ge = 120 ==> g-f-ge --(v) --> can't determine f + ge =?
(2) 40 students do not speak any of the 3 languages --> 40 = (fUgUe)' = (gUe)' --(vi) --> can't determine f + ge =?

combine (1) & (2)
replace the (vi) in (iv) => g = 460-40 = 420 -- (vii)
replace (vii) in (v) =>420 -f-ge = 120 => f+ge= 300

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

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11 Jul 2019, 04:15
Essentially E is the answer as both the statements even together does not tell the size of population asked. In other words the size of the asked population can't be estimated just by the given data. We at most can know that at max. the French speakers are 140 in no.
Quote:
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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11 Jul 2019, 04:28
1
IMO C. [Both statements are required]

Total= 600.
Since, each french person also speaks german, the number of students only speaking french=0 and number of students who speak both french and english=0.

Statement 1: 140 students speak only German. This statement doesn't give us the total number of students speaking either one of the languages. Hence, this statement alone is insufficient.

Statement 2: 40 students do not speak any of the 3 languages. This tells us that our universal set has come from 600->560 but we do not know the number of students only speaking german. Hence, this statement alone is insufficient.

When we combine them, we get that the total number of students who can speak any of the 2 languages is 270.
Hence, both the 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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11 Jul 2019, 04:45
1
Through Venn Diagram :-
Data Provided-
1) Only French=0
2)Only English=140
3)All Three=0

We need to find Speakers with 2 language at least.

Required -

1) No language known (Option 2)
2)Only Speak German (Option 1)

Either will not Conclude for Ans, But Combining Both will Support for Sure.

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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11 Jul 2019, 05:21
1
Simple one. Drawing a Venn diagram will be much helpful while solving this Q.

Quickly looking at the information provided in the question stem, each French speaker also speaks German means People who ONLY speak French = 0, and 140 of students only speak English means People who ONLY speak English = 140

Given that a + b + c + d + e + f + g + n = 600; where a = ONLY French, b = ONLY German, c = ONLY English, d = BOTH French and German, e = BOTH German and English, f = BOTH English and French, g = ALL THREE, n = NONE OF THE THREE

We already have a = 0, c = 140, g = 0, and we need to find d + e + f

Looking at Statement (1):

We have b = 120

Putting in the values, we have 0 + 120 + 140 + d + e + f + 0 + n = 600

d + e + f + n = 600 - (120 + 140)

d + e + f + n = 340, since we don't know the value of n we can't compute the value of d + e + f

STATEMENT (1), hence, is NOT SUFFICIENT

Looking at Statement (2):

We have n = 40

Since here, we don't know the value of b, we again have insufficient information in this Statement, and hence, STATEMENT (2) is NOT SUFFICIENT

Combining both (1) and (2), we now have values of both n and b, putting in which we get 0 + 120 + 140 + d + e + f + 0 + 40 = 600

d + e + f = 300

And hence, (C) is the correct answer here
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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11 Jul 2019, 05:39
1
According to math book, we have formula to count those who speak two out three languages.
Total=None+only one language+all three+only two out of three. From this formula, we have been already given by the problem, total - 600, only one language (we have only German and only English spoken, French is not counted because those who speak French, speak German too. So we have those who speak English only 140 We need to find those who speak German only)+all three-0+only two out of three+none. If we find bold faced variables, we can solve question.
Now, none of the two statements provide both variables in itself, but they do so when we combine them. This means answer is C for this problem

(1) Not sufficient since it does not tell us how many dont speak any language
(2) Not sufficient since we cannot conclude from this how many speak just one language (we know about english but not spanich)

(1) + (2) Sufficient

Total = 200
Speak none = 20
Speak exactly 1 = 60 (E) + 70 (S) + 0 (G, as all who speak german also speak english)
Speak all three = 0
Hence exactly two = 50

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

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11 Jul 2019, 05:59
600
-140
-120
--------
340
-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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11 Jul 2019, 06:15
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?

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

Stmt 1: As French and German speaker are equal, we need to know anyone. it satisfies the need. so sufficient.

Stmt 2: As 40 students do no speak anyone, 540 students speak at least one of the languages. it is also given no student can speak all languages. so, sufficient.

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

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11 Jul 2019, 06:21
out of the 600 people is 120 speak only German we cannot find the number of people who speak both German and English. there is no person who speaks both french and English as that would violate the condition of 3 languages.
By combining this option with the second one that there are 40 people who speak none of the languages we are left with
600-(140+40+120)=300
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Re: Of the 600 students in a class, each French speaker also speaks German  [#permalink]

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11 Jul 2019, 06:42
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:

We need to find the number of numbers who can speak 2 of the 3 languages.

Total number of unique members = No of members who only speak french + number of members who only speak german + no. of members who only speak english + No of members who only speak 2 launguages + No of people who speak all 3 languages + No of people who speak neither language.

600 = Only F + Only G + only E + B(2 languages) + 0 + N(neither)

Statement one analysis

Statement one gives us the value of G i.e 120 and F. If each of french speakers speaks German,then there is no member who can only speak french hence F=0 but we still don't have the value of N Hence insufficient.

Statement two analysis

This statement straight away gives us the value of N, but we don't have the value of G hence insufficient.

Both together:

From combining these 2, we get 600 = 0 +120+ 140 +B + 0 + 40

Therefore, B= 200.
Hence sufficient

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Re: Of the 600 students in a class, each French speaker also speaks German   [#permalink] 11 Jul 2019, 06:42

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