Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 May 2019
Posts: 122

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 13:12
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. Answer: C
_________________
Pick yourself up, dust yourself off, and start again.
Success is the sum of all small efforts.
MAKE IT HAPPEN



Manager
Joined: 21 Nov 2018
Posts: 78
Location: India
GMAT 1: 680 Q48 V35 GMAT 2: 640 Q48 V29

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 13:55
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 = 600300 = 300  sufficient. IMO Ans  C
_________________
Beautiful is the one who continues to try despite failure.



Director
Status: Manager
Joined: 27 Oct 2018
Posts: 746
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 14:06
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



VP
Joined: 19 Oct 2018
Posts: 1152
Location: India

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 15:01
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
Attachments
r.png [ 12.36 KiB  Viewed 268 times ]
r.png [ 12.36 KiB  Viewed 267 times ]



Manager
Joined: 12 Mar 2018
Posts: 83
Location: United States

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 17:23
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.
Correct answer: C



Manager
Joined: 28 Feb 2014
Posts: 202
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE: Engineering (Education)

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 18:32
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.



Manager
Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 19:09
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.
Posted from my mobile device



Intern
Joined: 17 Apr 2019
Posts: 17

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 19:11
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 60014012040=300, which equals to the number of members who can speak 2 of the 3 languages.
choose C



Manager
Joined: 28 Jan 2019
Posts: 127
Location: Peru

Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 20:13
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.
(C) is the answer.



Intern
Joined: 08 Jul 2019
Posts: 37

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 20:24
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 600140120=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 60014012040=300 speak only two languages. Sufficient. Answer C.



Director
Joined: 28 Jul 2016
Posts: 670
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 20:37
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
Attachments
File comment: Diagram
VennDiagram.png [ 12.97 KiB  Viewed 212 times ]



Senior Manager
Joined: 18 Jan 2018
Posts: 304
Location: India
Concentration: General Management, Healthcare
GPA: 3.87
WE: Design (Manufacturing)

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 21:15
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 EnglishOnlyGermannot any langues = 600140(Xneed) (Yneed)
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 languagesInsufficient 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 languesOption C is our answer



Manager
Joined: 18 Jun 2013
Posts: 139
Location: India
Concentration: Technology, General Management
GPA: 3.2
WE: Information Technology (Consulting)

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 21:21
Attachment:
WhatsApp Image 20190711 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. Answer: C



Manager
Joined: 08 Jan 2018
Posts: 129

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 21:37
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
Answer C



Manager
Joined: 17 Jul 2014
Posts: 177

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
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 FrenchGerman, EnglishGerman, and EnglishFrench. not sufficient.
(2) 40 students do not speak any of the 3 languages we are not given how many speak only two lang FrenchGerman, EnglishGerman, and EnglishFrench. not sufficient.
combined stmts, don't tells us how many speak only two lang FrenchGerman, EnglishGerman, and EnglishFrench. not sufficient.
E



Intern
Joined: 28 Feb 2018
Posts: 17

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 21:46
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



Intern
Joined: 19 Mar 2012
Posts: 33

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 21:54
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.



Manager
Joined: 21 Jan 2019
Posts: 100

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 22:15
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.



VP
Joined: 20 Jul 2017
Posts: 1139
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 23:00
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 InsufficientCombining (1) & (2) C = 120 & N = 40 > Y + Z = 460  (N + C) > Y + Z = 460  (120 + 40) > Y + Z = 300 SufficientIMO Option C Pls Hit Kudos if you like the solution
Attachments
2.png [ 14.77 KiB  Viewed 139 times ]



Manager
Joined: 24 Sep 2014
Posts: 51
Concentration: General Management, Technology

Re: Of the 600 students in a class, each French speaker also speaks German
[#permalink]
Show Tags
10 Jul 2019, 23:03
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



Go to page
Previous
1 2 3 4
Next
[ 80 posts ]



