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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 ## If y is the smallest positive integer such that 3,150 tagged by: VJesus12 ##### This topic has 2 expert replies and 1 member reply ## If y is the smallest positive integer such that 3,150 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be A. 2 B. 5 C. 6 D. 7 E. 14 OA=E Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Top Reply VJesus12 wrote: If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be A. 2 B. 5 C. 6 D. 7 E. 14 OA=E Source: Official Guide This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number. Letâ€™s start by prime factorizing 3,150. 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2^1 x 3^2 x 5^2 x 7^1 Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square. However, we are given that the product of 3,150 and y is a perfect square. Thus, we can write this as: 2^1 x 3^2 x 5^2 x 7^1 x y = square of an integer According to our rule, we need all unique prime factors' exponents to be even numbers. Remember also that y is the smallest positive integer that makes 3150y a perfect square. Thus, we need one more 2 and one more 7. Therefore, y = 7 x 2 = 14 Answer: E _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 VJesus12 wrote: If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be A. 2 B. 5 C. 6 D. 7 E. 14 OA=E Source: Official Guide Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime. For example, 36 = (2)(2)(3)(3) And 400 = (2)(2)(2)(2)(5)(5) Likewise, 3150y must have an EVEN number of each prime in its prime factorization. So, 3150y = (2)(3)(3)(5)(5)(7)y We have an EVEN number of 3's and 7's, but we have ONE 2 and ONE 7. If y = (2)(7), then we get a perfect square. That is: 3150y = (2)(2)(3)(3)(5)(5)(7)(7) So, if y = 14, then 3150y is a perfect square. Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 958 messages Followed by: 4 members $$3150 = 3*1050 = 3*3*350 = 3*3*35*10$$ $$= 3*3*5*7*5*2$$ $$=(3)^2*(5)^2*14$$ So we can say, if we want this number to be a perfect square this has to be multiplied with $$14$$. $$y=14$$. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free 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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