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A certain high school offers two foreign languages, Spanish and French
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26 Jan 2017, 23:23
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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
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Re: A certain high school offers two foreign languages, Spanish and French
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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.
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Re: A certain high school offers two foreign languages, Spanish and French
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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



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Re: A certain high school offers two foreign languages, Spanish and French
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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
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Re: A certain high school offers two foreign languages, Spanish and French
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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.
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Re: A certain high school offers two foreign languages, Spanish and French
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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
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Re: A certain high school offers two foreign languages, Spanish and French
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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?
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Re: A certain high school offers two foreign languages, Spanish and French
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21 Feb 2017, 05:28



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Re: A certain high school offers two foreign languages, Spanish and French
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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
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Re: A certain high school offers two foreign languages, Spanish and French
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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.



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Re: A certain high school offers two foreign languages, Spanish and French
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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
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Re: A certain high school offers two foreign languages, Spanish and French
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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).



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Re: A certain high school offers two foreign languages, Spanish and French
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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
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Re: A certain high school offers two foreign languages, Spanish and French
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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



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Re: A certain high school offers two foreign languages, Spanish and French
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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)
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Re: A certain high school offers two foreign languages, Spanish and French
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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



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