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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 ## Is the sum of four particular integers even? tagged by: AbeNeedsAnswers ##### This topic has 3 expert replies and 0 member replies ## Is the sum of four particular integers even? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is the sum of four particular integers even? (1) Two of the integers are odd and two are even. (2) The average (arithmetic mean) of the four integers is an integer. D Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2475 messages Followed by: 350 members Upvotes: 1090 GMAT Score: 780 Statement 1 tells us exactly what kind of integers we have, so using the familiar even/odd rules, we can work out if the sum will be even or odd (since odd+odd is even, and even+even is even, the sum will turn out to be even, though since it's a DS question, we don't actually care what the answer is, only that we can find an answer, so there's no reason to bother even doing that much work). Statement 2 tells us that if we divide the sum by 4, we get an integer. So the sum is divisible by 4, and is thus certainly divisible by 2, which is another way of saying that it's even. So the answer is D. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 AbeNeedsAnswers wrote: Is the sum of four particular integers even? (1) Two of the integers are odd and two are even. (2) The average (arithmetic mean) of the four integers is an integer. Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is the sum of four particular integers even? Statement 1: Two of the integers are odd and two are even. We have: SUM = ODD + ODD + EVEN + EVEN = (ODD + ODD) + (EVEN + EVEN) = EVEN + EVEN = EVEN The answer to the target question is YES, the sum is even Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The average (arithmetic mean) of the four integers is an integer. Let the 4 numbers be a, b, c, and d We can write: (a + b + c + d)/4 = k, where k is some integer So, we can also write: a + b + c + d = 4k Since 4k is EVEN, we know that a + b + c + d is EVEN The answer to the target question is YES, the sum is even Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: D 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: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that we have four INTEGERS. We're asked if the sum of those four integers is EVEN. This is a YES/NO question and can be solved with either Number Property rules or TESTing VALUES. (1) Two of the integers are ODD and two are EVEN. Fact 1 gives us enough information to deal with some specific Number Properties. Adding two ODD numbers will give us a sum that is EVEN (for example, 3+5 = 8) Adding two EVEN numbers will give us a sum that is EVEN (for example, 2+4 = 6) Thus, adding two ODDs and two EVENs will give us EVEN+EVEN = EVEN. The answer to the question is ALWAYS YES. Fact 1 is SUFFICIENT (2) The average (arithmetic mean) of the four integers is an integer. Fact 2 references the 'Average Formula', so we should think in those terms. If we refer to the values as A, B, C and D, we can set up an average as: (A+B+C+D)/4 = Integer (A+B+C+D) = (4)(Integer) From this equation, we know that the sum of the four integers will be 4 times an integer. Multiplying ANY integer by an EVEN number will give us a product that is EVEN. For example: 4(-1) = -4 4(0) = 0 4(1) = 4 4(2) = 8 4(3) = 12 Etc. Thus, the answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • FREE GMAT Exam Know how you'd score today for$0

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