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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 ## When positive integer x is divided by positive interger y, ##### This topic has 2 expert replies and 0 member replies ### Top Member ## When positive integer x is divided by positive interger y, ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y? A. 560 B. 616 C. 672 D. 728 E. 784 OA B Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y? A. 560 B. 616 C. 672 D. 728 E. 784 OA B Source: Veritas Prep Since x/y = 59.32 = 59 32/100 = 59 8/25, we see that the possible remainders are of the form 8k where k is a positive integer. Therefore, the first two-digit remainder is 8(2) = 16 and the last two-digit remainder is 8(12) = 96. We can now use the formula sum = average x quantity to find the sum of all possible two-digit remainders. We see that average = (16 + 96)/2 = 56 and quantity = (96 - 16)/8 + 1 = 11. Therefore, the sum is: 56 x 11 = 616 Answer: B _________________ 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 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 Top Reply When one positive integer is divided by another, we typically represent what is left over as a REMAINDER or as a DECIMAL. There is a relationship between the two representations: Remainder/Divisor = Decimal. When 5 is divided by 2: Remainder representation: 5/2 = 2 R1 Decimal representation: 5/2 = 2.5 Remainder/Divisor = 1/2 Decimal = 0.5 Since the two values are equal: Remainder/divisor = decimal It can be helpful to write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM. BTGmoderatorDC wrote: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y? A. 560 B. 616 C. 672 D. 728 E. 784 In the problem above: Remainder = R Divisor = 7 Decimal = 0.32 = 32/100 = 8/25 Plugging these values into remainder/divisor = decimal, we get: R/y = 8/25 The resulting equation implies that the remainder must be a MULTIPLE OF 8. For any EVENLY SPACED SET: Count = (biggest - smallest)/(increment) + 1. Average = (biggest + smallest)/2. Sum = (count)(average). The INCREMENT is the difference between successive values. Here, we must sum the 2-digit multiples of 8 between 16 and 96, inclusive. Since the integers are multiples of 8, the increment = 8. Thus: Count = (96-16)/8 + 1 = 11 Average = (96+16)/2= 56 Sum = (count)(average) = 11*56 = integer with a units digit of 6 The correct answer is B. Similar remainder problems: http://www.beatthegmat.com/dealing-with-remainders-t269971.html http://www.beatthegmat.com/quotient-remainder-problem-t101371.html http://www.beatthegmat.com/remainder-t176105.html http://www.beatthegmat.com/remainder-t111428.html _________________ 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. • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 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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