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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 ## Hotel California ##### This topic has 4 expert replies and 8 member replies ## Hotel California Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off? 1. 22(2/9)% 2. 16(2/3)% 3. 11(1/9)% 4. 10% 5. 5% Source : MGMAT OA later. Legendary Member Joined 21 Sep 2006 Posted: 1275 messages Followed by: 2 members Upvotes: 125 Test Date: April 2010 Target GMAT Score: 740 sumanr84 wrote: Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off? 1. 22(2/9)% 2. 16(2/3)% 3. 11(1/9)% 4. 10% 5. 5% Source : MGMAT OA later. Say hotel california has 1000 lights 800 are supposed to be on Now 80 of the 200 which are supposed to be off are on 80 of the lights that are supposed to be on are off 80 of the lights which are supposed to be off are on Total lights on =800 %of the lights which are supposed to be off are on = 80/800*100 =10% _________________ Always borrow money from a pessimist, he doesn't expect to be paid back. Master | Next Rank: 500 Posts Joined 27 Jan 2010 Posted: 241 messages Followed by: 2 members Upvotes: 23 Target GMAT Score: 760 GMAT Score: 690 please help! getting an incorrect answer: take x to be the total no. of lights ten percent of lights that are spsd to be switched on are switched off means that 90% of 80% are switched on forty percent of lights that are spsd to be off are on, which means than 40% of 20% are also switched on --> (0.8)(0.9)x + (0.2)(0.4)x are switched on --> 0.72x + 0.08x -> 0.8x are switched on Which means that 80% of lights are switched on and hence no change is required. So, my answer comes to 0% Newbie | Next Rank: 10 Posts Joined 10 Dec 2008 Posted: 7 messages Ajith, How did you get the " 800 are supposed to be on " part? The question says 80% ARE ON AT 8pm ONE PARTICULAR EVENING. Its not supposed to be like that. Am I missing something? I am getting 0% as well. Here is my approach: Let total number of lights = 100 Let total Supposed ON = x Then, Supposed OFF = 100-x Now, The number supposed to be ON = (ON Currently) - 40% of (100-x) + 10% x In other words, x = 80 - 40/100 (100-x) + 10x Solving for x, we get x = 80, which is of course the number on now. So no change is required.......... Newbie | Next Rank: 10 Posts Joined 02 Sep 2008 Posted: 9 messages Upvotes: 2 The question is asking what percent of lights that are switched on are supposed to be switched off? let total lights be = 100 so 80% or 80 are supposed to be switched on, and 40% of lights that are supposed to be switched off are on, hence 40% of remaining 20 which are supposed to be off are on. i.e. 8 lights which are supposed to be off are on. also 10% of lights that are supposed to be on are off, hence 10% of 80 lights that are supposed to be on are off, i.e 8 lights are off. consequently the total number of lights that are on is still 80. but the question is asking what percent of lights that are switched on are supposed to be switched off? therefore, 8/80*100 = 10% ( ANSWER 4) Legendary Member Joined 29 Aug 2009 Posted: 758 messages Followed by: 2 members Upvotes: 67 The correct answer is D. ( 10 % ) Thanks kunal & ajith for making it simple. Newbie | Next Rank: 10 Posts Joined 10 Dec 2008 Posted: 7 messages I am sorry, I still dont get it. I would really appreciate it if someone can explain where we are getting "80 are supposed to be ON"? It doesn't say so anywhere in the question. It says 80 lights are on. And that must be the wrong number because some lights that are supposed to be off are on and vica versa. In other words, 80 are not supposed to be ON but are ON by mistake. I must be missing something but just need to know where am I going wrong in my thought process. Legendary Member Joined 21 Sep 2006 Posted: 1275 messages Followed by: 2 members Upvotes: 125 Test Date: April 2010 Target GMAT Score: 740 vibhusethi wrote: I am sorry, I still dont get it. I would really appreciate it if someone can explain where we are getting "80 are supposed to be ON"? It doesn't say so anywhere in the question. It says 80 lights are on. And that must be the wrong number because some lights that are supposed to be off are on and vica versa. In other words, 80 are not supposed to be ON but are ON by mistake. I must be missing something but just need to know where am I going wrong in my thought process. Let's complicate things then! Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off? Let the total no of lights be, x now 0.8x are on one evening 0.2x lights are supposed to be off 40% of it is on = 0.08x of lights which are supposed to be off are on 0.8x lights are supposed to be on 10% lights are supposed to be on are off = 0.8*.1x = 0.08x The no of lights switched on which are supposed to be off = 0.08x the no of lights supposed to be on = .8x Now % = 0.08/0.8*100 =10% _________________ Always borrow money from a pessimist, he doesn't expect to be paid back. ### GMAT/MBA Expert GMAT Instructor Joined 21 Jan 2009 Posted: 3650 messages Followed by: 82 members Upvotes: 267 GMAT Score: 760 sumanr84 wrote: Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off? 1. 22(2/9)% 2. 16(2/3)% 3. 11(1/9)% 4. 10% 5. 5% Source : MGMAT OA later. There is another thread on the same question at the link below... better if you check it for solution. http://www.beatthegmat.com/lights-in-a-hotel-t34014.html#138417 I am yet to give it a shot, is that really required now? _________________ The mind is everything. What you think you become. â€“Lord Buddha Sanjeev K Saxena Quantitative Instructor The Princeton Review - Manya Abroad Lucknow-226001 www.manyagroup.com Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Senior | Next Rank: 100 Posts Joined 23 Oct 2007 Posted: 39 messages Upvotes: 1 Test Date: 03/22/2010 Target GMAT Score: 740 GMAT Score: 600 The crux of the problem lies in understanding the question line; "What percent of the lights that are switched on are supposed to be switched off?" But at the same time the question also provided, "forty percent of the lights that are supposed to be switched off are actually switched on" - We know it is 0.08x. I still didn't understood the question and those who understood it are lucky bunch. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 sumanr84 wrote: Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off? A. 22(2/9)% B. 16(2/3)% C. 11(1/9)% D. 10% E. 5% One option is to use the Double Matrix method. Here, we have a population of lightbulbs, and the two characteristics of each bulb are: - incandescent or fluorescent - on or off Since the questions asks us to find a certain PERCENT, let's say that there are 100 bulbs altogether. So, we can set up our matrix as follows: Eighty percent of ALL the bulbs are switched on at this moment So, 80 bulbs are turned ON. This also means that the remaining 20 bulbs are OFF. Add this to our diagram to get: Forty percent of the incandescent bulbs are switched on This one is tough, because we don't know how many incandescent bulbs there are. So, let's let x = the number of incandescent bulbs. This means the remaining 100-x bulbs are fluorescent Let's add this to our diagram first, and THEN tackle the given info: Okay, if x = the number of incandescent bulbs, and 40% of those bulbs are switched on, then the number of incandescent bulbs that are on = 40% of x = 0.4x Likewise, if 100-x = the number of fluorescent bulbs, and 90% of those bulbs are switched on, then the number of fluorescent bulbs that are on = 90% of 100-x = 0.9(100 - x) Add this to our diagram to get: When we examine the left-hand column, we can see that the sum of the boxes is 80. In other words: 0.4x + 0.9(100 - x) = 80 Expand: 0.4x + 90 - 0.9x = 80 Simplify: -0.5x = -10 Solve: x = 20 So, there are 20 incandescent bulbs, and 40% of them are on. 40% of 20 = 8, so 8 of the incandescent bulbs are on: We can see that, of the 80 bulbs that are on, 8 of them are incandescent. 8/80 = 1/10 = 10% Answer: D ------------------------ NOTE: 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/the-aam-aadmi-party-t272242.html - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html Medium Problem Solving questions - http://www.beatthegmat.com/probability-question-t273360.html - 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/ds-french-japanese-t222297.html - http://www.beatthegmat.com/prblem-solving-t279424.html Difficult Problem Solving questions - 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.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 - http://www.beatthegmat.com/double-set-matrix-question-t271423.html - 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 my video course along with Sign up for free Question of the Day emails And check out all of these 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! ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2527 messages Followed by: 352 members Upvotes: 1090 GMAT Score: 780 We have two groups of lights: lights that should be on, and lights that should be off. Overall, 80% of lights are on. Of lights that should be on, 90% are on (since 10% are off), and of lights that should be off, 40% are on. So we have a standard mixtures situation, which is always a weighted average situation; drawing these three 'averages' on a number line (I'm using a weighted average method here sometimes called 'alligation' that might not make much sense to anyone who has never seen it, but you can google that term to find a more detailed explanation) : ---40-----------------80---90---- the ratio of the distances to the middle must equal the ratio of the two groups. So the two types of lights are in a 40 to 10 ratio, or 4 to 1 ratio, and so 4/5 of them are supposed to be on (since 80 is closer to 90), and the rest, 1/5, are meant to be off. So if we have 100 lights in total, 20 should be off, but actually 40% of those, or 8 of them, are on. Overall 80 lights are on, so 8/80 = 10% of those should have been off. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 sumanr84 wrote: Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off? 1. 22(2/9)% 2. 16(2/3)% 3. 11(1/9)% 4. 10% 5. 5% Source : MGMAT OA later. We can let the total number of lights be 100 and let n = the number of lights supposed to be switched off. Thus, 100 - n = the number of lights supposed to be switched on. From the information given in the problem, we see that 0.4n of the supposed turn-off lights are on and 0.9(100 - n) of the supposed turn-on lights are on. Since the total number of lights that are currently turned on is 0.8 x 100 = 80, we can create the equation: 0.4n + 0.9(100 - n) = 80 0.4n + 90 - 0.9n = 80 -0.5n = -10 n = 20 Since there are 20 supposed turn-off lights, but 0.4 x 20 = 8 of them are turned on, the percent of turn-on lights that are supposed to be turned off is 8/80 = 0.1 = 10%. Answer: 4/D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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