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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 r and s are positive numbers and θ is one tagged by: AbeNeedsAnswers ##### This topic has 3 expert replies and 0 member replies ## If r and s are positive numbers and θ is one ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If r and s are positive numbers and θ is one of the operations, +, -, X, or ÷, which operation is θ ? (1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r. A Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2528 messages Followed by: 353 members Upvotes: 1090 GMAT Score: 780 We can just check each of the four arithmetic operations to see when each Statement will be true. If r = s, we can replace 's' with 'r', so for Statement 1: r+r = 2r r-r = 0 r*r = r^2 r/r = 1 and it's only when the operation is subtraction that we get 0 as a result, and the operation therefore must be subtraction. So Statement 1 is sufficient. For Statement 2: r + s = s + r is always true r - s does not equal s - r if r and s are different (one of them is positive, the other negative) r*s = s*r is always true r/s does not equal s/r if r and s are different positive numbers (one of them is less than 1, the other greater than 1) so we don't know if the operation is subtraction or division, and Statement 2 is not 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: 13041 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 AbeNeedsAnswers wrote: If r and s are positive numbers and θ is one of the operations, +, -, X, or ÷, which operation is θ ? (1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r. Given: r and s are positive numbers and θ is one of the operations, +, -, X, or ÷ Target question: Which operation is θ ? Statement 1: If r = s, then r θ s = 0 Keep in mind that r and s are POSITIVE So, we have POSITIVE θ POSITIVE = 0 POSITIVE + POSITIVE ≠ 0 So, θ cannot represent addition POSITIVE - POSITIVE = 0 So, θ COULD represent subtraction POSITIVE X POSITIVE ≠ 0 So, θ cannot represent multiplication POSITIVE ÷ POSITIVE ≠ 0 So, θ cannot represent division The answer to the target question is θ represents subtraction Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: If r ≠ s, then r θ s ≠ s θ r Let's test some values for each possible operation. 1 ≠ 2, yet 1 + 2 = 2 + 1. So, θ cannot be addition 1 ≠ 2, yet 1 x 2 = 2 x 1. So, θ cannot be multiplication If r and s are DIFFERENT positive numbers, then r - s will never equal s - r. So, θ COULD represent subtraction If r and s are DIFFERENT positive numbers, then r ÷ s will never equal s ÷ r. So, θ COULD represent division Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent _________________ Brent Hanneson – 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 GMAT’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: 497 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that R and S are POSITIVE NUMBERS and θ is one of the operations add, subtract, multiply or divide. We're asked which operation is θ. This question comes down to some basic Arithmetic and TESTing VALUES. (1) If R =S, then R θ S = 0. With the information in Fact 1, we have to check the 4 possible operations to see which one(s) fit the given equation. IF.... R=S=1.... 1 + 1 = 2 this is NOT a match 1 - 1 = 0 this IS a match (1)(1) = 1 this is NOT a match 1/1 = 1 this is NOT a match The ONLY operation that fits is SUBTRACTION, so that is the answer to the question. Fact 1 is SUFFICIENT (2) If R ≠ S, then R θ S ≠ S θ R Just as we did with Fact 1, we have to check the 4 possible operations to see which one(s) fit the given equation (meaning that the two calculations do NOT equal one another). IF.... R=1 and S=2.... 1 + 2 = 3 IS equal to 2 + 1 = 3 this is NOT a match 1 - 2 = - 1 DOES NOT equal 2 - 1 = 1 this IS a match for the given information (1)(2) = 2 IS equal to (2)(1) = 2 this is NOT a match 1/2 = 1/2 DOES NOT equal 2/1 = 2 this IS a match for the given information. Thus, the operation could be either SUBTRACTION OR DIVISION. Fact 2 is INSUFFICIENT Final Answer: A GMAT assassins aren't born, they're made, Rich • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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