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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 ## When the positive integer x is divided by 11 tagged by: VJesus12 ##### This topic has 3 expert replies and 2 member replies ## When the positive integer x is divided by 11 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19? A. 0 B. 1 C. 2 D. 3 E. 4 The OA is the option A. I am struggling to solve this PS question. Could someone give me a clarification here? Please. Legendary Member Joined 07 Sep 2017 Posted: 808 messages Followed by: 3 members Upvotes: 6 Top Reply Hello Vjesus12. Let's take a look at your question. When the positive integer x is divided by 11, the quotient is y and the remainder 3, this implies that $$x=11\cdot y+3.$$ When x is divided by 19, the remainder is also 3 $$x=19\cdot k+3.$$ Using these two equations we get $$11\cdot y+3=19\cdot k+3\ \ \Rightarrow\ \ 11y=19k$$ $$\Rightarrow\ \ y=\frac{19k}{11}$$ Now, since y is an integer and 19 is not divisible by 11, then we have that k must be divisible by 11 (in order to get an integer value in the right side). So, $$\Rightarrow\ \ y=19\cdot\frac{k}{11}=19\left(integer\right)$$ This implies that y is multiple of 19. In conclusion, y is divisible by 19 and therefore the remainder when y is divided by 19 is 0. This is why the correct answer is the option A. I hope it helps. Senior | Next Rank: 100 Posts Joined 02 Jul 2018 Posted: 32 messages Followed by: 1 members Since the number x gives remainder 3 for both 11 and 19, we can say that x-3 is multiple of 11 and 19 both. So, y which we get when we divide x by 11 is same when we divide x-3 by 11 => y is a multiple of 19, hence remainder will be 0 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12735 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 VJesus12 wrote: When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19? A. 0 B. 1 C. 2 D. 3 E. 4 A fast approach is to find a value of x that meets the given conditions. When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3.... Notice that x = 3 meets the above conditions. 3 divided by 11 = 0 with remainder 3. In this case, y = 0 Likewise, 3 divided by 11 also leaves a remainder of 3 What is the remainder when y is divided by 19? In the above example, y = 0 So, when we divide 0 by 19, the remainder is 0 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! ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 18 members Upvotes: 39 VJesus12 wrote: When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19? A. 0 B. 1 C. 2 D. 3 E. 4 We can create the following expressions: x = 11y + 3 and x = 19Q + 3 Thus: 11y + 3 = 19Q + 3 11y = 19Q 11y/19 = Q Since Q is an integer and 11 is not divisible by 19, then y must be divisible by 19, and hence the remainder when y is divided by 19 is zero. Answer: A _________________ Jeffrey Miller Head of GMAT Instruction ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10106 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi VJesus12, We're told that... X/11 = Y remainder 3 X/19 = something remainder 3 With the first piece of information, we know that X is 3 greater than a multiple of 11; with the second piece of information, we know that X is 3 greater than a multiple of 19. To have a remainder of 3 when you divide X by BOTH 11 and 19, X must be a number that is 3 greater than a MULTIPLE of BOTH 11 and 19. We're asked what the remainder would be when Y is divided by 19. At this point, you might recognize that you could choose Y=19 and solve from there. If you don't recognize why that that relationship exists, then here's a more step-heavy way to get to the correct answer: X = (11)(19) + 3 = 209 + 3 = 212 212/11 = Y remainder 3 212 = 11Y + 3 209 = 11Y 209/11 = Y 19 = Y We're ultimately asked what the remainder would be when 19 is divided by 19. The remainder is 0. Final Answer: A GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • FREE GMAT Exam Know how you'd score today for$0

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