Author 
Message 
TAGS:

Hide Tags

Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia

A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
26 Jan 2017, 23:23
Question Stats:
54% (02:21) correct 46% (02:54) wrong based on 288 sessions
HideShow timer Statistics
A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class? (A) 100 (B) 150 (C) 200 (D) 240 (E) 250
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!
Advanced Search : https://gmatclub.com/forum/advancedsearch/




Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 520
Location: India

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
27 Jan 2017, 04:16
Hi Ziyuenlau, For overlapping sets, Venn – Diagram is the best way to solve the question: From the Venndiagram we can see that, a+b+50+neither = total …….(1) Given that, a+b that is exactly one foreign language is 70% and neither is 10% Then, 70%+ 50+10% = 100% So 50 is equal to 20 percent of total 20% * total = 50 Then total = 250 We know that, According to the Venn diagram, we have to find “b+50”, Since french is half of the total, we can write, a+50 = 125 So a = 75, Substitute in the equation 1, 75+b+50+25 = 250 b+50 = 150 So the answer is B. Hope this is clear.
Attachments
venn diagram.png [ 13.02 KiB  Viewed 4463 times ]
_________________
For more info on GMAT and MBA, follow us on @AskCrackVerbal




SC Moderator
Joined: 13 Apr 2015
Posts: 1710
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
27 Jan 2017, 01:18
Neither French nor Spanish = 10% Only French or only Spanish = 70% Both Spanish and French = 100  10  70 = 20%
Given: Both Spanish and French = 50 = 20% > 100% = 250 = Total number of students
French = 0.5 * 250 = 125 > Only French = 125  50 = 75 Neither = 0.1 * 250 = 25 Spanish = 250  25  75 = 150
Answer: B



Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
27 Jan 2017, 02:35
Vyshak wrote: Neither French nor Spanish = 10% Only French or only Spanish = 70% Both Spanish and French = 100  10  70 = 20%
Given: Both Spanish and French = 50 = 20% > 100% = 250 = Total number of students
French = 0.5 * 250 = 125 > Only French = 125  50 = 75 Neither = 0.1 * 250 = 25 Spanish = 250  25  75 = 150
Answer: B Why my solution is not workable? Sent from my iPhone using GMAT Club Forum mobile app
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!
Advanced Search : https://gmatclub.com/forum/advancedsearch/



SC Moderator
Joined: 13 Apr 2015
Posts: 1710
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
27 Jan 2017, 06:21
Hi ziyuenlau, Your solution is not correct as you have incorrectly assumed the number of students opting for spanish as "0.5x". Refer the corrected solution in the figure.
Attachments
IMG_20170127_184342.jpg [ 777.87 KiB  Viewed 4432 times ]



Math Expert
Joined: 02 Aug 2009
Posts: 6561

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
27 Jan 2017, 07:10
ziyuenlau wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A)100 B)150 C)200 D)240 E)250 Hi if you use logic, we will not require Venn diagram.. 10% study nothing and 70% study exactly ONE.. SO 1001070=20% study both and this is given as 50.. 20% of Total =50... Total= 50*100/20=250.. Only Spanish = totalfrench+both=9050+20=60% 60% of Total= 60/100 * 250=150.. B
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
15 Feb 2017, 23:23
chetan2u wrote: ziyuenlau wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A)100 B)150 C)200 D)240 E)250 Hi if you use logic, we will not require Venn diagram.. 10% study nothing and 70% study exactly ONE.. SO 1001070=20% study both and this is given as 50.. 20% of Total =50... Total= 50*100/20=250.. Only Spanish = totalfrench+both= 9050+20=60% 60% of Total= 60/100 * 250=150.. B Dear chetan2u, How do you able to get the total equal to 90?
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!
Advanced Search : https://gmatclub.com/forum/advancedsearch/



Math Expert
Joined: 02 Sep 2009
Posts: 48110

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
21 Feb 2017, 05:28



SVP
Joined: 08 Jul 2010
Posts: 2139
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
21 Feb 2017, 06:06
Bunuel wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A. 100 B. 150 C. 200 D. 240 E. 250 Make a grid and solve as mentione dbelow... Follow the sequence of steps as per color coding Answer: option B
Attachments
File comment: www.GMATinsight.com
1234.jpg [ 145.25 KiB  Viewed 3524 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Intern
Joined: 08 Oct 2016
Posts: 22
Location: Nepal
Concentration: Finance, Marketing
WE: Account Management (Accounting)

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
21 Feb 2017, 09:25
GMATinsight wrote: Bunuel wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A. 100 B. 150 C. 200 D. 240 E. 250 we are given 70% students take only one language which means 20% take both (1007010), 10 for none. further we are given 50 students take both classes therefore if 20% make up 50 then 250 will make up 100% (50/20 * 100). so we get total students 250. now apply formula: [[total none = french + spanish  both]] , we get: 250 25= 125 + spanish  50 which is equal to 150. so ans is B.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2781

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
23 Feb 2017, 10:37
Bunuel wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A. 100 B. 150 C. 200 D. 240 E. 250 To solve this problem, there are two useful formulas we can use: 1) Total = French Only + Spanish Only + Both + Neither 2) Total = French + Spanish  Both + Neither In terms of percentage of students, we will use the first formula. We are given that the “Neither” group is 10%. Even though we don’t know “French Only” and “Spanish Only” individually, we know the total of these two groups is 70%; thus we have: 100% = 70% + Both + 10% Both = 20% We are also given that 50 students take classes in both languages. If we let t = total number of students, we have: 0.2t = 50 t = 250 Since half of all students take French and 10% take neither, we have 125 students who take French and 25 who take neither. Therefore, in terms number of students, we will use the aforementioned second formula: 250 = 125 + Spanish  50 + 25 250 = 100 + Spanish Spanish = 150 Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 05 Mar 2015
Posts: 984

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
30 Apr 2017, 10:44
ziyuen wrote: chetan2u wrote: ziyuenlau wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A)100 B)150 C)200 D)240 E)250 Hi if you use logic, we will not require Venn diagram.. 10% study nothing and 70% study exactly ONE.. SO 1001070=20% study both and this is given as 50.. 20% of Total =50... Total= 50*100/20=250.. Only Spanish = totalfrench+both= 9050+20=60% 60% of Total= 60/100 * 250=150.. B Dear chetan2u, How do you able to get the total equal to 90? ziyuenchetan2u is talking of 90% which he takes in account after deducting 10% (which is neither case).



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3197
Location: United States (CA)

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
06 May 2017, 17:29
ziyuen wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A)100 B)150 C)200 D)240 E)250 We can create the following equation: Total number of students = # who take Spanish + # who take French  # who take both + # who take neither We can let n = the total number of students Since 10% of students do not take a foreign language class, 0.1n = # number who take neither class We are also given that 50 students take both classes. Thus: n = S + F  50 + 0.1n 50 + 0.9n = S + F The number of students who take only Spanish is S  50. Similarly, the number of students who take only French is F  50. Thus, the number of students who take only one class is S  50 + F  50 = S + F  100. We are given that this makes up 70% of the class; thus S + F  100 = 0.7n, or equivalently, S + F = 0.7n + 100. Recall that S + F = 50 + 0.9n; thus, we have: 50 + 0.9n = 0.7n + 100 0.2n = 50 n = 250 Thus, the total number of students is 250. We know that half of all students take French; thus, F = 125. Since S + F = 0.7n + 100, we have S + 125 = 0.7(250) + 100 = 275; thus S = 150. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 12 Nov 2016
Posts: 771
Location: United States
GPA: 2.66

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
12 Jun 2017, 21:58
hazelnut wrote: A certain high school offers two foreign languages, Spanish and French. 10% of students do not take a foreign language class, and 70% of students take exactly one foreign language class. If half of all students are in a French class and 50 students take classes in both languages, how many students are in a Spanish class?
A)100 B)150 C)200 D)240 E)250 If .10 of students take neither and .70 students are in exactly one set then P(A ∩ B)= .20 50= x(.20) 50/.20 =250 250/2 = 125 250(.10) = 25 students neither Now apply set theory formula 250 = x + 125 25 x= 150 B



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3059
Location: India
GPA: 3.12

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
12 Jun 2017, 23:14
Let the total students be x Given data: \(\frac{x}{10}\) is the number of students studying neither language Number of students, learning both languages are 50 Number of students, studying exactly one language is \(\frac{7x}{10}\) We know that Total  Neither = Only one + Bothx  \(\frac{x}{10}\) = \(\frac{7x}{10}\) + 50 \(\frac{9x}{10}\)  \(\frac{7x}{10}\) = 50 x=250 If x=250, students studying Only one is \(\frac{7x}{10}\) = 175 Since students studying French are half of the total(125) and the students studying both are 50, students studying Only French = 75 Students studying Only Spanish = Only one  Only French = 175  75 = 100 Hence, students studying Spanish = Only Spanish + Both = 100 + 50 = 150(Option B)
_________________
You've got what it takes, but it will take everything you've got



Manager
Joined: 31 Dec 2016
Posts: 84

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
20 Jul 2017, 19:10
Venn Diagram is the way to go. A= Only Spanish B= Only French C= Both D= Neither
A+B+C+D=1 D=0.1 (stated) Therefore A+B+C=0.9 A+B =0.7 (70% take only one language class)
A+B+C=0.9 A+B =0.7 Therefore C =0.2
C= 50 so therefore there are 250 students 50/0.2 (as C = 0.2 if C is 20% of the pie and is 50 then 100% of the pie is 250)
B+C=0.5 (stated, half the students take French) Therefore B+C = 125 (250*0.5) C=50 therefore B = 75 (12550)
A+B =0.7 Therefore A+B =175 (250*0.7) B=75 therefore A=100, B =75, C =50 and D=25
Now the question asks how many in Spanish??
Here is a little trick at the end. Only Spanish is 100 =A However C also takes Spanish so it is 100+50 for a total of 150.
How many take French? It is 75+50 = 125?
How many take Spanish or French it is 75+50+100 or 225.
So ensure you don't get tricked at the end. Had they said, how many only take Spanish then the answer is 100



NonHuman User
Joined: 09 Sep 2013
Posts: 7780

Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
Show Tags
03 Aug 2018, 23:02
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A certain high school offers two foreign languages, Spanish and French &nbs
[#permalink]
03 Aug 2018, 23:02






