Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58438

A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
14 Sep 2015, 07:50
Question Stats:
82% (01:04) correct 18% (01:13) wrong based on 1295 sessions
HideShow timer Statistics
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) 5,000 – z (B) 5,000 – x – y (C) 5,000 – x + z (D) 5,000 – x – y – z (E) 5,000 – x – y + z og2016
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Intern
Joined: 17 Aug 2015
Posts: 6

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
14 Sep 2015, 16:46
Easier formula to remember is Group1+ Group2 Both +Neither = Total (Source: Kaplan) So, solution is x + y  z + Neither = 5000 Neither = 5000  x  y + z ..Choice E!




Manager
Joined: 17 Aug 2015
Posts: 96
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Information Technology (Investment Banking)

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
14 Sep 2015, 08:02
ske 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) 5,000 – z (B) 5,000 – x – y (C) 5,000 – x + z (D) 5,000 – x – y – z (E) 5,000 – x – y + z
og2016 I believe the wording of the question is incorrect (for the options given)  when you say "take music", that means take either music or music and art. In that case here's the answer: Music U Art = Music + Art  Music n Art = (xz) + (yz)  z = x+y3z Total = 5000 So, people not taking any of these is: 5000  (x+y3z). Now, from the options, I understand that the question asked has the assumption that "take music" means "music only". In that case, the calculation becomes: 5000  (x+yz) = 5000  x  y + z So, (E) is the answer.
_________________
If you like this post, be kind and help me with Kudos!
Cheers!



Intern
Joined: 04 Sep 2015
Posts: 2

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
16 Sep 2015, 07:36
HardWorkBeatsAll wrote: I believe the wording of the question is incorrect (for the options given)  when you say "take music", that means take either music or music and art. In that case here's the answer: Music U Art = Music + Art  Music n Art = (xz) + (yz)  z = x+y3z
Total = 5000 So, people not taking any of these is: 5000  (x+y3z)
Thanks for submitting an explanation. It is correct to say that: Music U Art = Music + Art  Music n Art. However, your logic falls apart when you attribute Music = xz and Art = yz. This is wrong because (xz) and (yz) refers to the number of students who ONLY take music or who ONLY take art. So in your equation, you've subtracted the number of students who take both music and art three times over. It should be: x + y  z. That represents the number of students who took music OR art. Then, 5,000  (x + y  z) would give you the number of students who took neither. And you would have answer choice (E). Alternatively, if you want to follow your methodology of accounting for the students who took music ONLY and Art ONLY, use the following equation (which would still arrive at the same original equation for union of two sets): (x  z) + (y  z) + z = x + y  z.



Intern
Joined: 24 Dec 2014
Posts: 1

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
07 Oct 2015, 09:51
pdxyj wrote: HardWorkBeatsAll wrote: I believe the wording of the question is incorrect (for the options given)  when you say "take music", that means take either music or music and art. In that case here's the answer: Music U Art = Music + Art  Music n Art = (xz) + (yz)  z = x+y3z
Total = 5000 So, people not taking any of these is: 5000  (x+y3z)
Thanks for submitting an explanation. It is correct to say that: Music U Art = Music + Art  Music n Art. However, your logic falls apart when you attribute Music = xz and Art = yz. This is wrong because (xz) and (yz) refers to the number of students who ONLY take music or who ONLY take art. So in your equation, you've subtracted the number of students who take both music and art three times over. It should be: x + y  z. That represents the number of students who took music OR art. Then, 5,000  (x + y  z) would give you the number of students who took neither. And you would have answer choice (E). Alternatively, if you want to follow your methodology of accounting for the students who took music ONLY and Art ONLY, use the following equation (which would still arrive at the same original equation for union of two sets): (x  z) + (y  z) + z = x + y  z. from the options, I understand that the question asked has the assumption that "take music" means "music only". In that case, the calculation becomes: 5000  (x+yz) = 5000  x  y + z So, (E) is the answer.



SVP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1686
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Real Estate)

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
20 Oct 2015, 04:29
Bunuel 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) 5,000 − z (B) 5,000 − x − y (C) 5,000 − x + z (D) 5,000 − x − y − z (E) 5,000 − x − y + z
Kudos for a correct solution. My Solution:
Total = 5000
Total = X + Y Z+Neither
Neither = Total  X Y +Z
Neither = 5000XY+Z Option E Answer
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Retired Moderator
Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
20 Oct 2015, 09:46
Bunuel 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) 5,000 − z (B) 5,000 − x − y (C) 5,000 − x + z (D) 5,000 − x − y − z (E) 5,000 − x − y + z
Kudos for a correct solution. The simple formula for overlapping sets is as follows: Total = Group A + Group B  Both + NeitherIn this case we have 5,000 = x + y  z + n Solving for N equals 5,000 − x − y + z Answer E
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
20 Oct 2015, 09:55
Bunuel 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) 5,000 − z (B) 5,000 − x − y (C) 5,000 − x + z (D) 5,000 − x − y − z (E) 5,000 − x − y + z
Kudos for a correct solution. Students taking Music and art both = z Students taking Music only = x  z Students taking Art only = y  z Students taking Music and/or art = (xz) + (yz) + z = x + y  z Students without Music and Art = 5000  (x + y  z) Students without Music and Art = 5000  x  y + z Answer: option E
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15315
Location: United States (CA)

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
21 Oct 2015, 11:07
Hi All, While this question can be solved Algebraically, it can also be solved by TESTing VALUES and taking some basic notes: We're given a series of facts to work with: 1) A certain high school has 5,000 students. 2) Of these students: X are taking music, Y are taking art, and Z are taking BOTH music and art. We're asked how many students are taking NEITHER music nor art? Let's TEST X = 2 Y = 2 Z = 1 So, we have 2 students taking music, 2 taking art and 1 taking BOTH music and art. That 1 person has been counted TWICE though (once in the music 'group' and once in the art 'group'), so what we really have is... 1 student taking JUST music 1 student taking JUST art 1 student taking BOTH music and art Total = 3 students We're asked for the total number of students who are taking NEITHER Course. That is 5000  3 = 4997. So that's the answer that we're looking for when X=2, Y=2 and Z=1. There's only one answer that matches... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8029
GPA: 3.82

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
22 Oct 2015, 02:00
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. 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) 5,000 − z (B) 5,000 − x − y (C) 5,000 − x + z (D) 5,000 − x − y − z (E) 5,000 − x − y + z The number of students who take music or art is X+YZ( Z students take also art among the students who take music and the same Z students are included in the students who take art, so the number of students who take music or art is X+YZ). The number of students who take neither music nor art is 5000(X+YZ) = 5000XY+Z. The answer is (E)
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Current Student
Joined: 31 Jan 2016
Posts: 19

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
08 Aug 2016, 16:12
Can someone show me how to solve this using the Matrix Method?
For some reason I cannot find E, I find D as the answer.



Intern
Joined: 29 Jun 2016
Posts: 41

A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
11 Aug 2016, 11:51
g3lo18 wrote: Can someone show me how to solve this using the Matrix Method?
For some reason I cannot find E, I find D as the answer. Hope this is helpful. 5000=x+yz+n As z is counted twice both in x and also in y, we should subtract once to get the actual count. Let n be the number of students taking neither music nor art so n=5000xy+z answer option (E)
Attachments
venn.jpg [ 22.93 KiB  Viewed 16004 times ]



Manager
Status: On a 600long battle
Joined: 22 Apr 2016
Posts: 136
Location: Hungary
Concentration: Accounting, Leadership
GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23

A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
25 Apr 2017, 21:42
The items in the yellow boxes are the ones given to us (the 'y' is also given) and the green one is what we're looking for: 5000x(yz) 5000xy+zOA
_________________
"When the going gets tough, the tough gets going!"
Welcoming tips/suggestions/advices (you name it) to help me achieve a 600



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
29 Apr 2017, 09:05
ske 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) 5,000 – z (B) 5,000 – x – y (C) 5,000 – x + z (D) 5,000 – x – y – z (E) 5,000 – 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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



CrackVerbal Quant Expert
Joined: 12 Apr 2019
Posts: 268

Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
Show Tags
03 Sep 2019, 23:34
This is a very simple question on overlapping sets where we need to draw a twoset Venn diagram and fill out the regions to obtain the answer. It’s as simple as that. Here's how the Venn diagram should look: Attachment:
04th Sept 2019  Reply 2.JPG [ 18.09 KiB  Viewed 1204 times ]
From the Venn diagram, we can say that the sum of all the regions should be equal to 5000. So, xz + y – z + z + n = 5000. Here, n represents the number of people who have taken up neither music nor art. Therefore, n = 5000 – x – y +z. The correct answer option is E. Hope this helps!
_________________




Re: A certain high school has 5,000 students. Of these students, x are
[#permalink]
03 Sep 2019, 23:34






