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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # All of the students of Music High School are in the band  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 07 Feb 2010 Posts: 129 All of the students of Music High School are in the band [#permalink] ### Show Tags Updated on: 11 Nov 2012, 04:57 4 35 00:00 Difficulty: 45% (medium) Question Stats: 72% (03:03) correct 28% (02:55) wrong based on 648 sessions ### HideShow timer Statistics All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only? A. 30 B. 51 C. 60 D. 85 E. 11 Originally posted by anilnandyala on 27 Nov 2010, 06:12. Last edited by Bunuel on 11 Nov 2012, 04:57, edited 1 time in total. Renamed the topic and edited the question. ##### Most Helpful Expert Reply Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8678 Location: Pune, India Re: music high school [#permalink] ### Show Tags 27 Nov 2010, 12:55 33 9 Look at the diagram below: If total 80% students are in one group, and 50% are in band only then 30% must be in orchestra only. Remaining 20% must be in both. Total 70% students are in band and this number is equal to 119. Attachment: Ques2.jpg [ 13.21 KiB | Viewed 12063 times ] 70% of total students = 119 so total students = 170 No of students in orchestra only = 30% of 170 = 51 _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > ##### General Discussion Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: music high school [#permalink] ### Show Tags 27 Nov 2010, 07:28 11 6 anilnandyala wrote: All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only? 30 51 60 85 11 {total} = {band only} + {orchestra only} + {both}; As {band only} + {orchestra only} = 80% and {band only} = 50% then {orchestra only} = 30%. So, {band}= 100% - {orchestra only} = 70% --> 70% of {total} = 119 --> {total} = 170 --> {orchestra only} = 30% of {total} = 51. Answer: B. _________________ Retired Moderator Joined: 20 Dec 2010 Posts: 1820 Re: Sets [#permalink] ### Show Tags 14 Mar 2011, 00:48 AnkitK wrote: All of the students of music high school are in the band ,the orchestra or both.80 percent of students are in one group.There are 119 students in the bands.If the 50 percent of the students are in the band only,how many students are in the orchestra? A.30 B.51 C.60 D.85 E.119 If 50% of the students are in the band only; then the group that contains 80% of the students must be the band group. However, if I try to find 0.8x = 119; x is coming as a decimal, which is not possible. Wonder, what am I doing wrong!!! _________________ Retired Moderator Joined: 16 Nov 2010 Posts: 1425 Location: United States (IN) Concentration: Strategy, Technology Re: Sets [#permalink] ### Show Tags 14 Mar 2011, 01:18 I also tried it like this, but getting a fraction : Let a be the total # of students only in orchestra, b be the total # of students only in Band and Let x be the common # of students in Band and Orchestra b +x = 119 b = 1/2(a + b +x) 2b = a + b + 119 - b => 2b = 119 + a x = 30/100(a + b + x) => 119 - b = 3/10( a + 119) 119 - (119 + a)/2 = 3/10(a + 119) 119/2 - a/2 = 3a/10 + 119 * 3/10 119 ( 1/2 - 3/10) = a(1/2 + 3/10) 119 * 2/10 = a ( 8)/10) => a = 119 * 2/8 _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Manager Joined: 02 Apr 2010 Posts: 100 Re: music high school [#permalink] ### Show Tags 14 Mar 2011, 03:28 My solution: Let's define variables as follows: w = # students in orchestra only x = # students in band only y = # students in both band & orchestra z = # students who are neither in band nor orchestra t = total # students From question we know the following All of the students of Music High School are in the band, the orchestra, or both => (i) z = 0 80 percent of the students are in only one group => (ii) 0.8*t = w + x There are 119 students in the band => (iii) x + y = 119 If 50 percent of the students are in the band only => (iv) x = 0.5*t From (i) and (iv) follows (v) w = 0.3*t Given that (iv) x = 0.5*t and (v) w=0.3*t => y = 0.2*t Since (iii) x + y = 119 => t = 170 Hence, w = 0.3*170 = 51 Retired Moderator Joined: 16 Nov 2010 Posts: 1425 Location: United States (IN) Concentration: Strategy, Technology Re: music high school [#permalink] ### Show Tags 14 Mar 2011, 23:21 Ok, here is my retake, I couldn't figure this line earlier : Let x be the total # of students. B + C - B&C = x Given that -> B - B&C = 0.5x => C = 0.5x NOw, given that 80 percent of the students are in only one group => B - B&c + C - B&C = 0.8x => B&C = 0.2x and C - B&C = 0.3x Also given that B = 119, so B + B&C = 0.7x = 119 => x = 170 and 0.3x = 51, so the answer is B. _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Director Status: No dream is too large, no dreamer is too small Joined: 14 Jul 2010 Posts: 520 Re: music high school [#permalink] ### Show Tags 15 Mar 2011, 04:51 VeritasPrepKarishma wrote: Look at the diagram below: If total 80% students are in one group, and 50% are in band only then 30% must be in orchestra only. Remaining 20% must be in both. Total 70% students are in band and this number is equal to 119. Attachment: Ques2.jpg 70% of total students = 119 so total students = 170 No of students in orchestra only = 30% of 170 = 51 How can i reason that "total 80% students are in one group" 30 percent for orchestra and 50%band. Why not 50 percent for band and 30% for both? _________________ Collections:- PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8678 Location: Pune, India Re: music high school [#permalink] ### Show Tags 15 Mar 2011, 08:01 2 Baten80 wrote: VeritasPrepKarishma wrote: Look at the diagram below: If total 80% students are in one group, and 50% are in band only then 30% must be in orchestra only. Remaining 20% must be in both. Total 70% students are in band and this number is equal to 119. Attachment: Ques2.jpg 70% of total students = 119 so total students = 170 No of students in orchestra only = 30% of 170 = 51 How can i reason that "total 80% students are in one group" 30 percent for orchestra and 50%band. Why not 50 percent for band and 30% for both? Look at the question again: All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only? It says 80% students are in 1 group only (either orchestra only or band only but not both). The leftover 20% must be in both the groups, orchestra as well as band. (since every student is in at least one group) Say, out of 100 students, 80 are in only one group. 50% students are in band only. So we now know how the 80% of 'one group only' is split: 50% in band only and 30% in orchestra only. Look at the diagram in my previous post for more clarity. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 09 Feb 2013 Posts: 7 Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 19 May 2013, 05:26 1 2 The official solution is below. This is an overlapping sets problem concerning two groups (students in either band or orchestra) and the overlap between them (students in both band and orchestra). If the problem gave information about the students only in terms of percents, then a smart number to use for the total number of students would be 100. However, this problem gives an actual number of students (“there are 119 students in the band”) in addition to the percentages given. Therefore, we cannot assume that the total number of students is 100. Instead, first do the problem in terms of percents. There are three types of students: those in band, those in orchestra, and those in both. 80% of the students are in only one group. Thus, 20% of the students are in both groups. 50% of the students are in the band only. We can use those two figures to determine the percentage of students left over: 100% - 20% - 50% = 30% of the students are in the orchestra only. Great - so 30% of the students are in the orchestra only. But although 30 is an answer choice, watch out! The question doesn't ask for the percentage of students in the orchestra only, it asks for the number of students in the orchestra only. We must figure out how many students are in Music High School altogether. The question tells us that 119 students are in the band. We know that 70% of the students are in the band: 50% in band only, plus 20% in both band and orchestra. If we let x be the total number of students, then 119 students are 70% of x, or 119 = .7x. Therefore, x = 119 / .7 = 170 students total. The number of students in the orchestra only is 30% of 170, or .3 × 170 = 51. The correct answer is B. I'm in confusion in the below sentence. Can someone please elaborate? "We know that 70% of the students are in the band: 50% in band only, plus 20% in both band and orchestra" Intern Joined: 05 Mar 2013 Posts: 44 Location: India Concentration: Entrepreneurship, Marketing GMAT Date: 06-05-2013 GPA: 3.2 Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 19 May 2013, 05:49 2 connexion wrote: All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only? A)30 B)51 C)60 D)85 E)119 Attachment: Untitled4.jpg [ 16.74 KiB | Viewed 10259 times ] Let the total number of students be x 119 = only band + both 0.8x = only band + only orchestra which also implies 0.2x students are in both(x-0.8x) 0.5x = only band which implies only orchestra = 0.3x So number of students in band = 0.5x + 0.2x = 0.7x = 119 which gives x as 170 So the number of students in orchestra only is 0.3*170 = 51 Answer B _________________ "Kudos" will help me a lot!!!!!!Please donate some!!! Completed Official Quant Review OG - Quant In Progress Official Verbal Review OG 13th ed MGMAT IR AWA Structure Yet to do 100 700+ SC questions MR Verbal MR Quant Verbal is a ghost. Cant find head and tail of it. Senior Manager Joined: 28 Apr 2012 Posts: 281 Location: India Concentration: Finance, Technology GMAT 1: 650 Q48 V31 GMAT 2: 770 Q50 V47 WE: Information Technology (Computer Software) Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 19 May 2013, 07:23 connexion wrote: All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only? A)30 B)51 C)60 D)85 E)119 80% Students are only in one group. => 20% are in both group 50% students are in band only => i. 50% (Band Only)+ 20%(both Band and Orchetsra) = 70% are in the band = 119 Students(given) ii. 80% (Either only in Band or Only in Orchestra) - 50%(only in Band) = 30% are in only Orchestra If $$70% = 119 => 30% = 119*(30/70) = 51$$(Ans = B) _________________ "Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well." ― Voltaire Press Kudos, if I have helped. Thanks! Manager Joined: 25 Oct 2013 Posts: 152 Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 25 Jan 2014, 02:26 Initially it was difficult for me to understand the question. But solved in 3 mins. Let t be total number of students. 80% is in only one group => 0.8t 50% is in only band => 0.5t so 0.8t-0.5t = 0.3t is in Only Orchestra. Now, Orchestra Only + both + Band Only = t 0.3t + x + 0.5t = t It is given that 119 are in band means 0.5t+x = 119 So, 0.3t+119 = t t = 119/0.7 = 170 Orchestra Only = 0.3t = 0.3*170 = 51 ---B is the answer. _________________ Click on Kudos if you liked the post! Practice makes Perfect. Manager Joined: 21 May 2015 Posts: 232 Concentration: Operations, Strategy GMAT 1: 750 Q50 V41 Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 01 Jun 2015, 22:23 B St. in both band + both = 50+(100-80) = 70% of total = 119 Total st. = 119/0.7 St. in orchestra only = (80-50) % of total students = 0.3 * 119/0.7 = 51 _________________ Apoorv I realize that i cannot change the world....But i can play a part e-GMAT Representative Joined: 04 Jan 2015 Posts: 2313 Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 01 Jun 2015, 23:09 1 1 Presenting the matrix approach to the solution Let's assume the total number of students to be x. We are given that 50% of the students are in band only. Number of students in band only =0.5x. Also, we are given that there are 80% students in one group only = 0.8x Students in one group only = students in band only + students in orchestra only 0.8x = 0.5x +students in orchestra only i.e. students in orchestra only = 0.3x As there are no students who are in neither band nor orchestra, number of students who are not in orchestra = 0.5x. Therefore, number of students who are in orchestra = x - 0.5x = 0.5x. Students in orchestra = students in orchestra only + students in both band and orchestra 0.5x = 0.3x + students in both band and orchestra students in both band and orchestra = 0.2x We are told that there are 119 students in band. Students in band = students in band only + students in both band and orchestra 119 = 0.5x + 0.2x i.e. x = 170. We are asked to find the number of people in orchestra only = 0.3x = 0.3 * 170 = 51 Hope this helps Regards Harsh _________________ Register for free sessions Number Properties | Algebra |Quant Workshop Success Stories Guillermo's Success Story | Carrie's Success Story Ace GMAT quant Articles and Question to reach Q51 | Question of the week Must Read Articles Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2 Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2 Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry Algebra- Wavy line | Inequalities Practice Questions Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com Intern Joined: 17 Feb 2013 Posts: 10 All of the students of Music High School are in the band [#permalink] ### Show Tags 06 Nov 2015, 14:25 1 anilnandyala wrote: All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only? A. 30 B. 51 C. 60 D. 85 E. 11 not the best use of double-set matrix but a sure-thing. There are more time-efficient ways but good enough as a framework. Can be slow if not fast at long division. Attachments IMG_20151106_222021~01.jpg [ 452.51 KiB | Viewed 6099 times ] Intern Status: preparing Joined: 30 Dec 2013 Posts: 40 Location: United Arab Emirates Concentration: Technology, Entrepreneurship GMAT 1: 660 Q45 V35 GMAT 2: 640 Q49 V28 GMAT 3: 640 Q49 V28 GMAT 4: 640 Q49 V28 GMAT 5: 640 Q49 V28 GPA: 2.84 WE: General Management (Consumer Products) Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 13 Aug 2017, 10:18 Let T be total number of students. 80% are in only one group. so in both = b & o = (100-80)% of total= 20%T b & o = 119 - T/2 ( since band has 119 people and 50% of T are in band only) 20% T= 119 -T/2 T=170 80 % are in only one group and 50% are in band only. so 30% T are in orchestra only. 30% 170 =51 ANS = 51 KUDOS PLEASE EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13087 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: All of the students of Music High School are in the band [#permalink] ### Show Tags 21 Feb 2018, 20:33 Hi All, This prompt is one big 'logic' problem with a little bit of arithmetic thrown in. We're given a number of facts to work with: 1) ALL students are in the band, the orchestra or BOTH. 2) 80% of students are ONLY in 1 group. 3) There are 119 students in the band. 4) 50% of the students are in the band ONLY. We're asked how many students are in the orchestra ONLY. From facts 2 and 4, we can break the students down into groups (by percent): 80% are in ONLY 1 group and 50% are in the band ONLY. This means that 100% - 80% = 20% are in BOTH groups. This also means that 80% - 50% = 30% are in the orchestra ONLY. From fact 3, we know that 119 students are in the band (which includes the students in band ONLY and the students in BOTH) Band only = 50% Both = 20% 50% + 20% = 70% = 119 students .7(Total) = 119 Total = 119/.7 Total = 170 Finally, we're asked for the number of students in the orchestra: 30% of 170 = 51 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 23 Jan 2018
Posts: 15
Re: All of the students of Music High School are in the band  [#permalink]

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22 Mar 2018, 15:15
I feel stupid, I left out the part where the number of people in neither is 0, I over complicated it and was trying to figure out how i could get to the right answer
Manager
Joined: 07 Jun 2018
Posts: 110
All of the students of Music High School are in the band  [#permalink]

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20 Aug 2018, 04:24
Can somebody tell me how this statement:
"80% of the students are in ONLY one group"
Implies that:
"80% of the students are in both the Orchestra and the Band"?

It says ONLY ONE group! Can someone clarify this please?
Thanks!
All of the students of Music High School are in the band &nbs [#permalink] 20 Aug 2018, 04:24

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