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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 x is an integer greater than 0, what is the remainder tagged by: AbeNeedsAnswers ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If x is an integer greater than 0, what is the remainder ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x is an integer greater than 0, what is the remainder when x is divided by 4 ? (1) The remainder is 3 when x + 1 is divided by 4. (2) The remainder is 0 when 2x is divided by 4. A Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12919 messages Followed by: 1248 members Upvotes: 5254 GMAT Score: 770 AbeNeedsAnswers wrote: If x is an integer greater than 0, what is the remainder when x is divided by 4 ? (1) The remainder is 3 when x + 1 is divided by 4. (2) The remainder is 0 when 2x is divided by 4. Target question: What is the remainder when x is divided by 4 ? Statement 1: The remainder is 3 when x + 1 is divided by 4. ------ASIDE---------------------- There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3 -------------------------------- We don't know how many times 4 divides into x+1. So, let's just say 4 divides into x+1 k times. So, we can write: x + 1 = 4k + 3 (for some integer k) Subtract 1 from both sides to get x = 4k + 2 Since 4k is a multiple of 4, we can see that x is 2 greater than some multiple of 4 So, when we divide x by 4, the remainder will be 2 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The remainder is 0 when 2x is divided by 4. We can write: 2x = 4k (for some integer k) Divide both sides by 2 to get: x = 2k This tells us that x is an even integer. There are several values of x that satisfy statement 2. Here are two: Case a: x = 2. In this case, the answer to the target question is when we divide x by 4, the remainder will be 2 Case b: : x = 4. In this case, the answer to the target question is when we divide x by 4, the remainder will be 2 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A 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 Elite Legendary Member Joined 23 Jun 2013 Posted: 10196 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that X is an INTEGER GREATER than 0. We're asked for the remainder when X is divided by 4. This question is based around some basic Arithmetic rules (and you can TEST VALUES to define the patterns involved). To start, here are the first several positive integers - and what happens when you divide by 4... 1/4 = 0r1 2/4 = 0r2 3/4 = 0r3 4/4 = 1r0 5/4 = 1r1 6/4 = 1r2 7/4 = 1r3 8/4 = 2r0 Etc. (1) The remainder is 3 when (X + 1) is divided by 4. Based on the pattern defined above, if we get a remainder of 3 when dividing (X+1) by 4, then removing the "+1" would move us one position 'up' in the pattern - meaning that the remainder when X/4 will ALWAYS equal 2. You can see this in a couple of examples: IF... X = 2, then (2+1)/4 = 0r3 and 2/4 = 0r2 X = 6, then (6+1)/4 = 1r3 and 6/4 = 0r2 Etc. Fact 1 is SUFFICIENT (2) The remainder is 0 when 2x is divided by 4. Fact 2 asks us to focus on values that would create a remainder of 0. That will occur with any multiple of 4. However, Fact 2 asks us to consider "2X" and that does not necessarily mean that X is a multiple of 4... IF... X = 2, then (2)(2)/4 = 1r0 and 2/4 = 0r2 X = 4, then (2)(4)/4 = 2r0 and 4/4 = 1r0 Thus, the answer to the question could be 2 OR 0. Fact 2 is INSUFFICIENT Final Answer: A GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Free Practice Test & Review How would you score if you took the GMAT 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 Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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