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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 k is divided by 5, the remainder is 2. ##### This topic has 2 expert replies and 0 member replies ### Top Member ## When positive integer k is divided by 5, the remainder is 2. ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7? A. 2 B. 3 C. 4 D. 5 E. 6 OA B Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7? A. 2 B. 3 C. 4 D. 5 E. 6 When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. When positive integer k is divided by 5, the remainder is 2 The possible values of k are: 2, 7, 12, 17, 22, 27, 32, 37, 42, . . . When k is divided by 6, the remainder is 5. The possible values of k are: 5, 11, 17, 23, 29, 35, 41. . . . Since 17 is the only number (less than 40) that both lists share, it must be the case that k = 17 What is the remainder when k is divided by 7? 17 divided by 7 = 2 with remainder 3 Answer: B 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! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7? A. 2 B. 3 C. 4 D. 5 E. 6 OA B Source: Magoosh We are given that k < 40. Since, when positive integer k is divided by 5, the remainder is 2: k = 5Q + 2 So k can be 2, 7, 12, 17, 22, 27, 32, or 37. Since, when k is divided by 6, the remainder is 5: k = 6P + 5 So k can be 5, 11, 17, 23, 29, or 35. Thus, we see that k must be 17, and 17/7 = 2 remainder 3. Alternate Solution: Since, when positive integer k is divided by 5, the remainder is 2: k = 5Q + 2 Since, when k is divided by 6, the remainder is 5: k = 6P + 5 We see that k - 2 = 5Q = 6P + 3 is divisible by both 5 and 3; therefore, k - 2 must be divisible by 15. The only numbers divisible by 15 and which would produce a k-value less than 40 are 0, 15 and 30. If k - 2 is 0, 15 or 30; then k is 2, 17 or 32, respectively. We see that only k = 17 produces a remainder of 2 when divided by 5 and a remainder of 5 when divided by 6. The remainder when k = 17 is divided by 7 is 3. 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 • 5 Day FREE Trial Study Smarter, Not Harder 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 • 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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