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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, y, and z are three-digit positive integers and if x = ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If x, y, and z are three-digit positive integers and if x = ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? (1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z. OA A Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12985 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? (1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z. OA A Source: Official Guide Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313. Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308 Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z. This rules out scenarios 2 and 3 (plus we already ruled out scenario 1). So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The units digit of x is equal to the sum of the units digits of y and z. This rules out scenario 3, but not scenario 2. Consider these two conflicting cases: Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z 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 GMAT Instructor Joined 22 Aug 2016 Posted: 1979 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? (1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z. OA A Source: Official Guide Say, x = abc; y = def; z = ghi We are given hat x = y + z. Thus, abc = def + ghi We have to determine whether a = d + g. This is true if there is no carryover from the tens digits' sum, or e + h â‰¤ 9. (1) The tens digit of x is equal to the sum of the tens digits of y and z. e + h = b; thus, there is no carryover to hundreds position. Sufficient (2) The units digit of x is equal to the sum of the units digits of y and z. c + f = i; thus, there is no carryover to tens position; however, we do not know if there will be a carryover from the tens position to hundreds position. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GMAT Classes in Manhattan | GMAT Tutoring New York | GRE Prep Seattle | Manhattan TOEFL | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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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