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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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26 Jan 2017, 22:23
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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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27 Jan 2017, 03:16
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Top Contributor
1
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

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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27 Jan 2017, 00:18
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

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

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27 Jan 2017, 01:35
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

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  [#permalink]

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27 Jan 2017, 05:21
1
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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27 Jan 2017, 06:10
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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15 Feb 2017, 22:23
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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21 Feb 2017, 04:28
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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21 Feb 2017, 05:06
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

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

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21 Feb 2017, 08:25
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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23 Feb 2017, 09:37
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

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

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30 Apr 2017, 09:44
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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06 May 2017, 16:29
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.

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

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12 Jun 2017, 20:58
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  [#permalink]

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12 Jun 2017, 22:14
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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20 Jul 2017, 18:10
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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05 Dec 2018, 18:43
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

$$? = S = a + 50$$

$$\left\{ \matrix{ a + b = 7T\,\,\,\left( {{\rm{given}}} \right) \hfill \cr a + \underbrace {b + 50}_{5T} = 9T \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,2T = 50 \hfill \cr \,a = 4T = 100 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 150$$

This solution follows the notations and rationale taught in the GMATH method.

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

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06 Dec 2018, 08:53
Top Contributor
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

Let's use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- taking Spanish or not taking Spanish
- taking French or not taking French

Let x = the TOTAL number of students.
We get the following diagram:

10% of students do not take a foreign language class
In other words, 10% of x (aka 0.1x) are taking NEITHER language.

70% of students take exactly one foreign language class.
The highlighted boxes below represent students who are taking exactly one foreign language class.
We know that these two boxes add to 0.7x:

Since all 4 boxes must add to x students, we can conclude that there are 0.2x students in the unaccounted for box in the top-left corner:

Half of all students are in a French class
In other words, 50% of x (aka 0.5x) are taking French.
So, the two left-hand boxes must add to 0.5x

Since the two left-hand boxex must add to 0.5x, the bottom-left box must contain 0.3x students

Also, since all 4 boxes must add to x students, we can conclude that there are 0.4x students in the remaining box in the top-right corner:

When we add the boxes in the top row, we see that 0.6x students are in Spanish.

50 students take classes in both languages
Diagram tells us that 0.2x students take classes in both languages
So, we can write: 0.2x = 50, which means x = 250

How many students are in a Spanish class?
There are 0.6x students in Spanish.
x = 250, so the number of students in Spanish = 0.6(250) = 150

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

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Re: A certain high school offers two foreign languages, Spanish and French &nbs [#permalink] 06 Dec 2018, 08:53
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