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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, b, x & y are positive integers. If ay=bx, is 7 a fact tagged by: vinni.k ##### This topic has 1 expert reply and 2 member replies ## a, b, x & y are positive integers. If ay=bx, is 7 a fact ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult a, b, x & y are positive integers. If ay=bx, is 7 a factor of x? (1) 35 is a factor of a (2) b when prime factorized will be of the form (5)^s OA is C ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10023 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi vinni.k, We're told that A, B, X and Y are positive INTEGERS and that (A)(Y) = (B)(X). We're asked if 7 a factor of X. This is a YES/NO questions. While this prompt might look 'scary', it's built around a Prime Factorization 'shortcut' that you can use to avoid doing lots of math. 1) 35 is a factor of A. Fact 1 tells us that A must be a multiple of 35. Thus (A)(Y) will have at least one 5 and at least one 7 among its prime factors. By extension (B)(X) must ALSO have at least one 5 and at least one 7 among its prime factors. IF.... there's just one 7 and it's "in" the B, then the answer to the question is NO. there's just one 7 and it's "in" the X, then the answer to the question is YES. Fact 1 is INSUFFICIENT 2) B when prime-factorized will be of the form (5)^S. Fact 2 tells us that the ONLY prime factors that COULD be in B are 5s, but this tells us nothing about the value of X. Fact 2 is INSUFFICIENT Combined, we know... 35 is a factor of A. The ONLY prime factors that COULD be in B are 5s (A)(Y) will have at least one 5 and at least one 7 among its prime factors and (B)(X) must ALSO have at least one 5 and at least one 7 among its prime factors. We know that there can NOT be any 7s 'in' B though, so that one 7 MUST be "in" X. Thus, X will ALWAYS be a multiple of 7 and the answer to the question is ALWAYS YES. Combined, SUFFICIENT Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 420 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 Rich, Thank you for the explanation. It is a very good explanation and easily understandable. Regards Vinni ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 786 messages Followed by: 1 members ay = bx Question ; Is 7 a factor of x? Statement 1 ; 35 is a factor of a That is, a must be a multiple of 35. That is, it must have at least a 5 and 7 among it's prime factors to mate 35, here we have only 7 and it's in the right hand side with x. Hence, Statement 1 is INSUFFICIENT. $$Statement 2;\ b,\ when\ prime\ factorized\ will\ be\ of\ the\ form\ of\ \left(5\right)^5$$ $$That\ is,\ the\ only\ prime\ factors\ that\ could\ be\ in\ b\ are\ \left(5\right)^5.$$ This does not give enough information about the value of x. Hence, Statement 2 is INSUFFICIENT. Combining statement 1 and 2 together, ay will have at least one 5 and one 7 among it's prime factors and bx must also have at least one 5 and one 7 among it's prime factors, there cannot be any 7 in b. So therefore, 7 must be in x and x will always be multiple of 7, hence both statement combined together is SUFFICIENT. Option C is CORRECT. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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