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

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A certain high school offers two foreign languages, Spanish and French  [#permalink]

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New post 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  [#permalink]

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New post 27 Jan 2017, 04:16
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Hi Ziyuenlau,

For overlapping sets, Venn – Diagram is the best way to solve the question:

From the Venn-diagram 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  [#permalink]

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New post 27 Jan 2017, 01:18
1
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  [#permalink]

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New post 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


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Re: A certain high school offers two foreign languages, Spanish and French  [#permalink]

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New post 27 Jan 2017, 06:21
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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  [#permalink]

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New post 27 Jan 2017, 07:10
1
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 100-10-70=20% study both and this is given as 50..
20% of Total =50... Total= 50*100/20=250..

Only Spanish = total-french+both=90-50+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  [#permalink]

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New post 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 100-10-70=20% study both and this is given as 50..
20% of Total =50... Total= 50*100/20=250..

Only Spanish = total-french+both=90-50+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  [#permalink]

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New post 21 Feb 2017, 05:28
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  [#permalink]

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New post 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  [#permalink]

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New post 21 Feb 2017, 09:25
1
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 (100-70-10), 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  [#permalink]

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New post 23 Feb 2017, 10:37
4
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  [#permalink]

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New post 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 100-10-70=20% study both and this is given as 50..
20% of Total =50... Total= 50*100/20=250..

Only Spanish = total-french+both=90-50+20=60%
60% of Total= 60/100 * 250=150..
B


Dear chetan2u, How do you able to get the total equal to 90?


ziyuen

chetan2u 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  [#permalink]

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New post 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  [#permalink]

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New post 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

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Re: A certain high school offers two foreign languages, Spanish and French  [#permalink]

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New post 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 + Both

x - \(\frac{x}{10}\) = \(\frac{7x}{10}\) + 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  [#permalink]

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New post 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 (125-50)

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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Re: A certain high school offers two foreign languages, Spanish and French  [#permalink]

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