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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 ## Algebra tagged by: BTGmoderatorRO ##### This topic has 1 expert reply and 0 member replies ## Algebra If 4 is divided into the positive integer x, it leaves a remainder of 3. If 9 is divided into x, it leaves a remainder of 4. If y is a positive integer such that x + y is divisible by 36, what is the smallest possible value of y? (A) 4 (B) 5 (C) 7 (D) 33 (E) 36 OA is B pls, How could B be right? I need a profound explanation from an Expert ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: If 4 is divided into the positive integer x, it leaves a remainder of 3. If 9 is divided into x, it leaves a remainder of 4. If y is a positive integer such that x + y is divisible by 36, what is the smallest possible value of y? (A) 4 (B) 5 (C) 7 (D) 33 (E) 36 OA is B pls, How could B be right? I need a profound explanation from an Expert Hi Roland2rule, Let's take a look at your question. If 4 is divided into the positive integer x, it leaves a remainder of 3. If p represents the quotient, then, $$4p+3=x...(i)$$ If 9 is divided into x, it leaves a remainder of 4. If q represents the quotient, then, $$9q+4=x...(ii)$$ Using equation(i) and (ii), $$4p+3=9q+4$$ $$4p=9q+4-3$$ $$4p=9q+1$$ $$p=\frac{9}{4}q+\frac{1}{4}$$ On test and trial basis, we can find the value of p. Since p and q are the quotients so these are integers, lets put q = 1 to find if the value of P comes out to be an integer. $$p=\frac{9}{4}\left(1\right)+\frac{1}{4}=\frac{9}{4}+\frac{1}{4}=\frac{10}{4}=\frac{5}{2}$$ Which is not an integer, so q can not be equal to 1. Let's try q = 2, $$p=\frac{9}{4}\left(2\right)+\frac{1}{4}=\frac{18}{4}+\frac{1}{4}=\frac{19}{4}$$ Which is also not an integer, hence q can not be 2. Let's try q = 3, $$p=\frac{9}{4}\left(3\right)+\frac{1}{4}=\frac{27}{4}+\frac{1}{4}=\frac{28}{4}=7$$ Which is an integer, hence, $$q=3,\ p=7$$ We can now find x using eq(i), $$4p+3=x$$ $$4(7)+3=x$$ $$28+3=x$$ $$x=31$$ The question states, " If y is a positive integer such that x + y is divisible by 36, what is the smallest possible value of y". since x = 31, therefore, we need to find 31+y is divisible by 36. The smallest possible value of y should be 5, so it will be divisible by 36. therefore, Option B is correct. Hope it helps. I am available if you'd like any follow up. _________________ 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. • Award-winning private GMAT tutoring Register now and save up to$200

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