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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 ## What is the smallest positive integer K such that the... tagged by: swerve ##### This topic has 3 expert replies and 1 member reply ### Top Member ## What is the smallest positive integer K such that the... What is the smallest integer K such that the product of 1575 x K is a perfect square? A. 7 B. 9 C. 15 D. 25 E. 63 The OA is A. Here's a question I came across and am having problems solving. Any expert that can help me with it, would be greatly appreciated! Thanks. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi swerve, We're asked to find the SMALLEST integer K such that (1575)(K) is a perfect square. This question can be solved with Prime Factorization. A 'perfect square' means that we're multiplying an integer by itself. For example: (2)(2) = 4 (10)(10) = 100 In the second example, we can 'break down' the 10s into prime numbers... (2x5)(2x5) = 100 The same concept applies here: we have to use the smallest K possible to create two equal terms.... (1575)(K) = (5)(315)(K) = (5)(5)(63)(K) = (5)(5)(7)(9)(K) = (5)(5)(7)(3)(3)(K) Based on the above prime factorization, each of the two terms will have to include one 3, one 5 and one 7.... (3x5x7)(3x5xK) Thus, K the smallest possible value of K is 7. Final Answer: A GMAT assassins aren't born, they're made, Rich Master | Next Rank: 500 Posts Joined 29 Nov 2017 Posted: 100 messages Upvotes: 14 swerve wrote: What is the smallest integer K such that the product of 1575 x K is a perfect square? A. 7 B. 9 C. 15 D. 25 E. 63 The OA is A. Here's a question I came across and am having problems solving. Any expert that can help me with it, would be greatly appreciated! Thanks. here we have to find with how many perfect square numbers i.e. 4,9,16,25,... it is divisible. any number whose sum of digits is divible by 9 must itself be divisible by 9. if we add the digits of the number we get 1+5+7+5=18 which is a multiple of 9 so it must be divisible by 9. dividing with 9 we get (1575 x k)/9 = 175 x k any figure which ends in 25, or 50, or 75 or 00 must be divisible by 25 further dividing with 25 we get = 7 x k therefore k must be equal to 7 to make it a perfect square. hence 7 is the smallest number to make it a perfect square. so correct answer is A ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Here's a trick: break 1575K into two identical square roots. For instance, say we have 36. 36 = 2 * 2 * 3 * 3 = (2 * 3) * (2 * 3), or two identical square roots. Now let's try that with 1575K. 1575K => 25 * 63 * K => 5 * 5 * 3 * 3 * 7 * K => (5 * 3 * 7) * (5 * 3 * K) So if K = 7, we'll have two identical roots. Touchdown! Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Another approach (not quite as good, but you never know what's helpful!): pull the integers roots out of 1575K. √1575K => √1575 * √K => √(25*9*7) * √K => √25 * √9 * √7 *√K => 5 * 3 * √7 * √K => 5 * 3 * √7K So if √7K = an integer, we're set. If K = 7, then √7K = √49 = 7, an integer, so K = 7 is a solution. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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