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Register now and save up to $200 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 ## A certain high school has 5,000 (OG2016) This topic has 2 expert replies and 2 member replies boomgoesthegmat Senior | Next Rank: 100 Posts Joined 25 Apr 2016 Posted: 93 messages Thanked: 1 times #### A certain high school has 5,000 (OG2016) Fri May 06, 2016 12:30 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 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 Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! OptimusPrep Master | Next Rank: 500 Posts Joined 13 Mar 2015 Posted: 410 messages Followed by: 7 members Thanked: 120 times 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.*
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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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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

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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.

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Matt@VeritasPrep GMAT Instructor
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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.

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