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 GRE 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:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
A certain high school offers two foreign languages, Spanish and French
[#permalink]
06 May 2021, 05:33
Expert Reply
5
Bookmarks
00:00
Question Stats:
71% (02:59) correct
28% (02:35) wrong based on 28 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]
06 May 2021, 05:40
Carcass 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?
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
To learn more about the Double Matrix Method, watch this video:
Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
07 May 2021, 10:59
Let the total students = 100 unit 10% did not take any foreign language class= 10 unit
Students who took the class = 90 unit Students in exactly one class = 70% = 70unit Students who took both class = (Total - no class - only one class) = 100 -10 -70 = 20 units. ATQ, 20 units = 50 students. 1 unit = 2.5 students, Total students = 2.5*100 = 250
Students in French class = half to total = 250/2 = 125 Students in only French = 125 - 500 = 75 Students who took class = 90% of 250 = 225 Students who took Spanish = Students who took class - only French = 225 - 75 = 150
Re: A certain high school offers two foreign languages, Spanish and French
[#permalink]
06 Aug 2024, 22:22
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep 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.
gmatclubot
Re: A certain high school offers two foreign languages, Spanish and French [#permalink]