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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 ## a, b, c, and d are positive integers. If the remainder... tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## a, b, c, and d are positive integers. If the remainder... a, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d? (A) 20 (B) 19 (C) 18 (D) 16 (E) 15 The OA is E. I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi LUANDATO, We're told that A, B, C and D are positive integers, A/B gives us a remainder of 9 and C/D gives us a remainder of 5. We're asked which of the following is NOT a possible value for B+D. This is a great 'concept question' - and you can solve it without doing much math IF you understand the concept that this question is built around. When dealing with remainders, the possible value of the remainder is 'limited' by what the denominator is. For example: If you divide an integer by 2, then the ONLY possible remainders will be 0 and 1. (re: 2/2 = 1r0 and 3/2 = 1r1, then the cycle repeats). If you divide an integer by 3, then the ONLY possible remainders will be 0, 1 and 2. (re: 3/3 = 1r0 and 4/3 = 1r1 and 5/3 = 1r2 then the cycle repeats). Etc. The pattern is that the largest possible remainder will be '1 LESS' than the denominator. We can use that concept 'in reverse' to answer this question. Here, in one calculation we're getting a remainder of 9 (so the denominator must be AT LEAST 10) and in the other calculation we're getting a remainder of 5 (so the denominator must be AT LEAST 6). Thus, the minimum value of B+D is 10+6 = 16. Therefore, 15 is NOT a possible value. Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply LUANDATO wrote: a, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d? (A) 20 (B) 19 (C) 18 (D) 16 (E) 15 The OA is E. I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced. Important Rule: The divisor is always greater than the remainder. If the remainder is 9 when a is divided by b, then we know that b, the divisor is greater than 9, so the minimum value is 10. If the remainder is 5 when c is divided by d, we know that d, the divisor, is greater than 5, the minimum value is 6 If the mi value of b is 10 and min value of d is 6, then the min value of b + d is 16. Therefore the sum could never be 15. The answer is E _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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