• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Most awarded test prep in the world Now free for 30 days 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 • 5 Day FREE Trial Study Smarter, Not Harder 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 ## A certain high school has 5,000 (OG2016) This topic has 3 expert replies and 2 member replies boomgoesthegmat Senior | Next Rank: 100 Posts Joined 25 Apr 2016 Posted: 93 messages Upvotes: 1 #### A certain high school has 5,000 (OG2016) Fri May 06, 2016 12:30 pm A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art? A) 5000 - z B) 5000 - x - y C) 5000 - x + z D) 5000 - x - y - z E) 5000 - x - y + z OA: E ### GMAT/MBA Expert Scott@TargetTestPrep GMAT Instructor Joined 25 Apr 2015 Posted: 781 messages Followed by: 3 members Upvotes: 43 Thu Dec 14, 2017 6:00 am boomgoesthegmat wrote: A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art? A) 5000 - z B) 5000 - x - y C) 5000 - x + z D) 5000 - x - y - z E) 5000 - x - y + z We can use the following formula: Total students = # taking music + # taking art - # taking both + # taking neither 5,000 = x + y - z + neither 5,000 - x - y + z = neither Answer: E _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2640 messages Followed by: 113 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Wed May 11, 2016 11:47 pm You could also just pick numbers. Suppose x = 100, y = 50, and z = 10. Since z is counted in both x and y, we have 90 taking just music, 40 taking just art, and 10 taking both. 5000 - 90 - 40 - 10 = 4860 = E. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! OptimusPrep Master | Next Rank: 500 Posts Joined 13 Mar 2015 Posted: 410 messages Followed by: 7 members Upvotes: 120 GMAT Score: 770 Sat May 07, 2016 7:50 pm boomgoesthegmat wrote: A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art? A) 5000 - z B) 5000 - x - y C) 5000 - x + z D) 5000 - x - y - z E) 5000 - x - y + z OA: E Music = x, Art = y Both Music and Art = z Therefore people who take atleast one = x + y - z People who have taken none = 5000 - (x + y - z) = 5000 - x - y + z Correct Option: E _________________ Ankur 99th Percentile GMAT Tutor | Optimus Prepâ„¢ Optimus Prepâ„¢ GMAT Courses: www.Optimus-Prep.com/GMAT Free Online Trial Hour: http://www.optimus-prep.com/request-free-online-trial-hour/ Free GMAT Study Plan: http://www.optimus-prep.com/ebook/ Optimus Prepâ„¢ Rates: GMAT Private Tutoring Online:$80-100/hr.*
GMAT Private Tutoring In-Person: $130-150/hr.* GMAT On Demand Course:$299 (Use Discount Code BEATTHEGMAT111)*

*All GMAT Courses Have A 50 Points Score Improvement Or Full Refund Guarantee

### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
Joined
09 Apr 2015
Posted:
753 messages
Followed by:
11 members
39
Mon May 09, 2016 10:46 am
boomgoesthegmat wrote:
A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art?

A) 5000 - z
B) 5000 - x - y
C) 5000 - x + z
D) 5000 - x - y - z
E) 5000 - x - y + z

OA: E
Solution:

We are given an overlapping set with 2 categories: music and art. In any two-category set problem we can use the following formula:

Total number of members = # in category A + # in category B - # in both categories + # in neither category

Using the formula for the current problem we have:

5,000 = x + y - z + neither

5,000 - x - y + z = neither

_________________
Jeffrey Miller Head of GMAT Instruction

800_or_bust Master | Next Rank: 500 Posts
Joined
26 Apr 2014
Posted:
199 messages
Followed by:
4 members
16
Test Date:
7/9/2016
GMAT Score:
780
Mon May 09, 2016 11:31 am
boomgoesthegmat wrote:
A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art?

A) 5000 - z
B) 5000 - x - y
C) 5000 - x + z
D) 5000 - x - y - z
E) 5000 - x - y + z

OA: E
In lieu of solving, I'll just post a reminder that you have to add the members of the combined set to avoid double counting. With that said, the answer should be fairly intuitive.

_________________
800 or bust!

### Best Conversation Starters

1 lheiannie07 108 topics
2 ardz24 67 topics
3 Roland2rule 63 topics
4 LUANDATO 50 topics
5 swerve 43 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

152 posts
2 Jeff@TargetTestPrep

Target Test Prep

106 posts
3 Rich.C@EMPOWERgma...

EMPOWERgmat

103 posts
4 Scott@TargetTestPrep

Target Test Prep

96 posts
5 Max@Math Revolution

Math Revolution

86 posts
See More Top Beat The GMAT Experts