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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 d is a positive integer and f is the product of the first ##### This topic has 1 expert reply and 0 member replies ### Top Member ## If d is a positive integer and f is the product of the first ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d? (1) 10^d is a factor of f (2) d>6 OA C Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d? (1) 10^d is a factor of f (2) d>6 30! = 30*29*28*....*3*2*1. Statement 1: To determine the greatest possible value for d, we need to know the number of 10's contained within 30! Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 30! will yield a 10. The prime-factorization of 30! is composed of FAR MORE 2'S than 5's. Thus, the number of 10's depends on the NUMBER OF 5's contained within 30!. To count the number of 5's, simply divide increasing POWERS OF 5 into 30. Every multiple of 5 between 1 and 30, inclusive, provides at least one 5: 30/5 = 6 --> 6 5's. Every multiple of 5Â² between 1 and 30, inclusive. provides a SECOND 5: 30/5Â² = 1 --> 1 more 5. Thus, the total number of 5's contained within 30! = 6+1 = 7. Implication: Within the prime-factorization of 30! are a total of 7 10's, with the result that up to 7 10's can divide into 30!. Thus, dâ‰¤7. Since d can be different values, INSUFFICIENT. Statement 2: Since d can be any integer value greater than 6, INSUFFICIENT. Statements combined: Since d must be an integer such that 6 < d â‰¤ 7, d=7. SUFFICIENT. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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