Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

26 Jan 2017, 22:23

2

18

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

54% (02:14) correct 46% (02:51) wrong based on 383 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?

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

Show Tags

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
_________________

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

Show Tags

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?
_________________

"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."

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

Show Tags

21 Feb 2017, 04:28

1

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
_________________

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

Show Tags

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

Answer: option B

Attachments

File comment: www.GMATinsight.com

1234.jpg [ 145.25 KiB | Viewed 4762 times ]

_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

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

Show Tags

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.

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

Show Tags

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

Answer: B
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

Show Tags

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?

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

Show Tags

06 May 2017, 16:29

1

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 Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

Show Tags

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

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

Show Tags

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 \(\frac{7x}{10}\)

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

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

Show Tags

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?

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

Show Tags

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. Add this to our diagram:

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 Add this to our diagram:

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

Answer: B

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

To learn more about the Double Matrix Method, watch this video:

_________________

Test confidently with gmatprepnow.com

gmatclubot

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