• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A certain high school offers two foreign languages, Spanish tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 1 member reply ### Top Member ## A certain high school offers two foreign languages, Spanish ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Veritas Prep 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 The OA is B. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1000 messages Followed by: 27 members Upvotes: 59 BTGmoderatorLU wrote: Source: Veritas Prep 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 Excellent opportunity for the Venn diagram (aka overlapping sets)! $$? = S = a + 50$$ $$\left\{ \matrix{ a + b = 7T\,\,\,\left( {{\rm{given}}} \right) \hfill \cr a + \underbrace {b + 50}_{5T} = 9T \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,2T = 50 \hfill \cr \,a = 4T = 100 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 150$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12442 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU 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 Another approach is to 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: http://www.gmatprepnow.com/module/gmat-word-problems?id=919 Once youâ€™re familiar with this technique, you can attempt these additional practice questions: Easy Problem Solving questions - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html Medium Problem Solving questions - http://www.gmatprepnow.com/module/gmat-word-problems/video/920 - http://www.beatthegmat.com/posted-speed-limit-t272374.html - http://www.beatthegmat.com/motel-t271938.html - http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html - http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html - http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-school-study-japanes-t274669.html - http://www.beatthegmat.com/prblem-solving-t279424.html Difficult Problem Solving questions - http://www.gmatprepnow.com/module/gmat-word-problems/video/946 - http://www.beatthegmat.com/ratio-problem-t268339.html - http://www.beatthegmat.com/overlapping-sets-question-t265223.html - http://www.beatthegmat.com/fractions-t264254.html - http://www.beatthegmat.com/overlapping-sets-t264092.html - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2 Easy Data Sufficiency questions - http://www.gmatprepnow.com/module/gmat-word-problems/video/943 - http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html - http://www.beatthegmat.com/ds-quest-t187706.html Medium Data Sufficiency questions - http://www.beatthegmat.com/sets-matrix-ds-t271914.html - http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html - http://www.beatthegmat.com/a-manufacturer-t270331.html - http://www.beatthegmat.com/in-costume-for-halloween-t269355.html - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1 Difficult Data Sufficiency questions - https://youtu.be/dsCeqF9Kbk8 - http://www.beatthegmat.com/double-set-matrix-question-t271423.html - https://youtu.be/dOZ9KM1m5Hs - http://www.beatthegmat.com/sets-t269449.html - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3 Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 684 messages Followed by: 4 members 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 Hence, the correct answer is B. • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### Top First Responders*

1 fskilnik@GMATH 62 first replies
2 Brent@GMATPrepNow 62 first replies
3 Jay@ManhattanReview 50 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 25 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

126 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 Max@Math Revolution

Math Revolution

90 posts
4 Jay@ManhattanReview

Manhattan Review

84 posts
5 Rich.C@EMPOWERgma...

EMPOWERgmat

63 posts
See More Top Beat The GMAT Experts