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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 ## Each bead in an urn is marked with... tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Each bead in an urn is marked with... Each bead in an urn is marked with a distinct positive integer and colored according to that integerâ€™s remainder after division by 5, as shown in the following table: Remainder Color 0 ----------- Red 1 ----------- Blue 2 ----------- Green 3 ----------- Yellow 4 ----------- Orange 15 blue beads, 18 green beads, 13 yellow beads, and 3 orange bead are withdrawn. If the product of the numbers on these beads is displayed on another bead, according to the rules above, then the color of that bead isâ€¦ (A) red (B) blue (C) green (D) yellow (E) orange The OA is D. I need help to solve this PS question. Can any expert explain it for me please? Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello LUANDATO. I hope you're well. This is a tough question, but let's take a look at it. We only have to take care about the remainders. * It has been removed 15 numbers whose remainder when divided by 5 is 1. The product of these 15 numbers could be write as $$R_1=\left(5n_1+1\right)\cdot\cdot\cdot\left(5n_{15}+1\right).$$ * It has been removed 18 numbers whose remainder when divided by 5 is 2. The product of these 18 numbers could be write as $$R_2=\left(5m_1+2\right)\cdot\cdot\cdot\left(5m_{18}+2\right).$$ * It has been removed 13 numbers whose remainder when divided by 5 is 3. The product of these 13 numbers could be write as $$R_3=\left(5j_1+3\right)\cdot\cdot\cdot\left(5j_{13}+3\right).$$ * It has been removed 3 numbers whose remainder when divided by 5 is 4. The product of these 3 numbers could be write as $$R_4=\left(5h_1+4\right)\left(5h_2+4\right)\left(5h_3+4\right).$$ Now, we can see that $$\left(5t_1+r\right)\cdot\cdot\cdot\left(5t_P+r\right)=5W+r^P.$$ So, $$R_1=5W_1+1^{15}=5W_1+1.$$ $$R_2=5W_2+2^{18}=5W_2+262144=5W_2+262140+4$$ $$=5W_2+5\cdot52428+4=5\left(W_2+52428\right)+4.$$ $$R_3=5W_3+3^{13}=5W_3+1594323=5W_3+1594320+3$$ $$=5W_3+5\cdot318864+3=5\left(W_3+318864\right)+3.$$ $$R_4=5W_4+4^3=5W_4+64=5W_4+60+4$$ $$=5W_4+5\cdot12+4=5\left(W_4+12\right)+4.$$ Finally, the product of ALL numbers is $$T=R_1\cdot R_2\cdot R_3\cdot R_4=5H+1\cdot4\cdot3\cdot4=5H+48=5H+45+3$$ $$=5H+5\cdot9+3=5\left(H+9\right)+3.$$ It implies that the remainder when T is divided by 5 is equal to 3. So, the color of the bead should be YELLOW. So, the correct answer is D. I really hope this can help you. As I said, we are only interested in the remainders. Feel free to ask me any doubt you could have. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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