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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 ## Flor is choosing three of five colors of paint to use for he ##### This topic has 4 expert replies and 0 member replies ### Top Member ## Flor is choosing three of five colors of paint to use for he ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project? A. 7 B. 9 C. 10 D. 13 E. 17 OA A Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1295 messages Followed by: 29 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project? A. 7 B. 9 C. 10 D. 13 E. 17 Source: Princeton Review RENAME colors to "unblock your brain": A, B, C, D and E. Restriction: A and B cannot be BOTH chosen. ? = Number of choices of 3 colors among the 5 given, restriction obeyed. First Scenario: neither A nor B is chosen. There is just one possibility : CDE Second Scenario: A is chosen (hence B is not) There is just three possibilities: ACD, ACE, ADE. Third Scenario: B is chosen (hence A is not) This is similar to the previous scenario, hence additional 3 cases. All cases mentioned above are MUTUALLY EXCLUSIVE, therefore they may be added: 7 possibilities. All 7 cases are EXHAUSTIVE, hence we are sure the answer is (at least seven and) not greater than 7. This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2012 messages Followed by: 15 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project? A. 7 B. 9 C. 10 D. 13 E. 17 There are three cases: 1) green is one of the five colors chosen, but yellow isn’t, 2) yellow is one of the five colors chosen, but green isn’t, and 3) neither green nor yellow is chosen. Let’s analyze each case. Case 1: Green is one of the five colors chosen, but yellow isn’t. If green is chosen but yellow isn’t, then we have to choose 2 more colors from the 3 remaining colors. The number of ways to do that is 3C2 = 3. Case 2: Yellow is one of the five colors chosen, but green isn’t. This is analogous to case 1, so there are 3 ways for this case. Case 3: Neither green nor yellow is chosen. If neither color is chosen, then we have to choose 3 colors from the 3 remaining colors. The number of ways to do that is 3C3 = 1. Thus, the total number of ways Flor can choose the colors for her project is 3 + 3 + 1 = 7. Alternate Solution: We can use the formula: Number of ways where yellow and green are not both included = total number of ways to pick 3 colors - number of ways where yellow and green are both included Since we are choosing 3 colors from 5 available colors, there are 5C3 = (5 x 4)/2 = 10 ways of doing this when there are no restrictions. The number of ways in which yellow and green are both included can be found easily by observing that yellow and green occupy two of the three slots; any one of the remaining three colors can occupy the final slot. So, there are 3 ways to choose colors where yellow and green are both included. Thus, the number of ways to pick colors where yellow and green are not included together is 10 - 3 = 7. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1770 messages Followed by: 28 members Upvotes: 470 BTGmoderatorDC wrote: Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project? A. 7 B. 9 C. 10 D. 13 E. 17 OA A Source: Princeton Review The number of ways, three out of five colors can be chosen, without any restriction = 5C3 = 5C2 = (5.4)/(1.2) = 10 ways Out of these 10 ways, there are ways that have both Green and Yellow colors; we must exclude them. Say, Flor chose Green and Yellow, thus, now only one color out of the three remaining colors are to be chosen. The number of ways to choose one color out of three = 3C1 = 3 ways Thus, the number of ways Flor can choose the colors for her project = 10 - 3 = 7 ways. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GRE Prep Locations: GRE Classes Raleigh NC | GRE Prep Course Singapore | GRE Prep Philadelphia | SAT Prep Classes Toronto | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12663 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project? A. 7 B. 9 C. 10 D. 13 E. 17 Jay's approach is the approach that I'd typically use. However, it's important to note that, when the answer choices are so small (as they are here), we should also consider the straightforward strategy of listing and counting Let R, B, P, G and Y represent the colors Red, Blue, Purple, Green and Yellow respectively. Now let's list the possible outcomes that meet all of the given conditions: - RBP - RBG - RBY - RPG - RPY - BPG - BPY Done!! So, there are 7 possible outcomes Answer: A Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder 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 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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