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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 ## A group of candidates for two analyst positions consists... tagged by: swerve ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A group of candidates for two analyst positions consists... A group of candidates for two analyst positions consists of six people. If one-third of the candidates are disqualified and three new candidates are recruited to replace them, the number of ways in which the two job offers can be allocated will: A. Drop by 40% B. Remain unchanged C. Increase by 20% D. Increase by 40% E. Increase by 60% The OA is D. Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks. ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 10 members Upvotes: 86 GMAT Score: 770 We originally have 6 people, of which we are trying to choose two - in other words, we have a 6 choose 2 combination: $$\frac{6!}{\left(6-2\right)!2!}=\frac{6!}{4!2!}=\frac{6\cdot5\cdot4!}{4!\cdot2\cdot1}=\frac{6\cdot5}{2\cdot1}=15$$ So we originally have 15 ways in which the two offers can be allocated. Then 1/3 of the candidates are disqualified. 1/3 of 6 is 2, so 2 candidates are disqualified and 4 remain. Then, 3 candidates replace them. Now there are 7 candidates to choose from to fill the two job offers. So we now have a 7 choose 2 combination: $$\frac{7!}{\left(7-2\right)!2!}=\frac{7!}{5!2!}=\frac{7\cdot6\cdot5!}{5!\cdot2\cdot1}=\frac{7\cdot6}{2\cdot1}=21$$ So we now have 21 ways in which the two offers can be allocated. The answers take the form of percent change, so we'll want to use the percent change equation: $$\frac{new\ -\ old}{old}\cdot100=\frac{21-15}{15}\cdot100=\frac{6}{15}\cdot100=\frac{2}{5}\cdot100=\frac{200}{5}=40$$ So the number of ways in which the two offers can be allocated increased by 40%, or answer choice D. _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 17 members Upvotes: 39 swerve wrote: A group of candidates for two analyst positions consists of six people. If one-third of the candidates are disqualified and three new candidates are recruited to replace them, the number of ways in which the two job offers can be allocated will: A. Drop by 40% B. Remain unchanged C. Increase by 20% D. Increase by 40% E. Increase by 60% The number of ways to choose 2 candidates from 6 is 6C2 = 6![2!(6-2)!] = 6!/(2! 4!) = (6 x 5)/2! = 30/2 = 15. After 2 of the 6 candidates leave and 3 new candidates are recruited, there will be 7 candidates, and the number of ways to choose 2 candidates from 7 is 7C2 = 7!/[2!(7-2)!] = 7!/(2!5!) = (7 x 6)/2! = 42/2 = 21. Thus, the number of ways to choose 2 candidates is increased by (21 - 15)/15 x 100% = 6/15 x 100% = 2/5 x 100% = 40% Answer: D _________________ Jeffrey Miller Head of GMAT Instruction • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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