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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 p, r, and s are consecutive integers in ascending tagged by: AbeNeedsAnswers This topic has 3 expert replies and 0 member replies If p, r, and s are consecutive integers in ascending Timer 00:00 Your Answer A B C D E Global Stats Difficult If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ? (1) Twice x is equal to the sum of p, r, and s. (2) The sum of p, r, and s is zero. D GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2475 messages Followed by: 350 members Upvotes: 1090 GMAT Score: 780 The average of an equally spaced set is equal to the median of that set, so here, if p, r, s are consecutive integers in increasing order, their average is simply r, so r = x and the question is just asking if we can find r. Notice also that the sum of the three integers is therefore 3r (because by the definition of an average, the sum equals the average times the number of terms). So Statement 1 just tells us that 2r = 3r, or that r = 0, and is sufficient. Statement 2 tells us that 3r = 0, or that r = 0, and is also sufficient. _________________ 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: If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ? (1) Twice x is equal to the sum of p, r, and s. (2) The sum of p, r, and s is zero. D Given: p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers Since p, r and s are EQUALLY spaced, the mean of the 3 numbers = the median of the 3 numbers. Since p < r < s, we know that r = the mean = the median. In other words, r = x (since we're told x is the mean) So, p = x - 1 And s = x + 1 (since p, r, and s are consecutive integers) Target question: What is the value of x? Statement 1: Twice x is equal to the sum of p, r, and s. We can write: 2x = p + r + s Replace p with x-1, replace r with x, and replace s with x+1 to get: 2x = (x-1) + x + (x+1) Simplify: 2x =3x Solve: x = 0 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The sum of p, r, and s is zero. We can write: p + r + s = 0 Replace p with x-1, replace r with x, and replace s with x+1 to get: (x-1) + x + (x+1) = 0 Simplify: 3x =0 Solve: x = 0 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 P, R and S are CONSECUTIVE integers in ASCENDING order and X is the AVERAGE (arithmetic mean) of the three integers. We're asked for the value of X. To start, it's worth noting that since we're dealing with 3 CONSECUTIVE integers, the sum will always be '3 times' the value of the 'middle' numbers, so the average of those 3 numbers will be the value of the "middle" number - in this case, "R" will be the average. This means that X = R, so if we find the value of X or R, then we have answered the question. We can also set up the 'Average Formula': (P + R + S)/3 = X. This can be rewritten into any of the following: P + R + S = 3X P + R + S = 3R P + S = 2R This question can be approached in a couple of different ways; here's a way to use a mix of Algebra and Number Properties. (1) Twice X is equal to the sum of P, R and S. With the information in Fact 1, we can create the following equation: 2X = P + R + S Comparing this equation to the initial equations we wrote, something interesting should stand out: How can (P + R + S) be equal to 3X AND 2X. Those appear to be 2 different results... and there's only one situation in which they are NOT.... when X = 0. Thus, the 3 values would be -1, 0 and 1 and the average is 0. Fact 1 is SUFFICIENT (2) The sum of P, R and S is zero. Fact 2 gives us the SUM of the three terms, so we can easily calculate the average... X = (0)/3 = 0. Fact 2 is SUFFICIENT Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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