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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 non-negative integers such that x < y & tagged by: Brent@GMATPrepNow ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If x, y and z are non-negative integers such that x < y & ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x, y and z are non-negative integers such that x < y < z, then the equation x + y + z = 11 has how many distinct solutions? A) 5 B) 10 C) 11 D) 22 E) 78 Answer: B Difficulty level: 600-650 Source: www.gmatprepnow.com _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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 08 Dec 2008 Posted: 12838 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 Brent@GMATPrepNow wrote: If x, y and z are non-negative integers such that x < y < z, then the equation x + y + z = 11 has how many distinct solutions? A) 5 B) 10 C) 11 D) 22 E) 78 I created this question to show that there can be times when the best (i.e., fastest) way to solve a counting question is by listing and counting How do we know when it's not a bad idea to use listing and counting? The answer choices will tell us (ALWAYS scan the answer choices before beginning any answer choices) Here, the answer choices are reasonably small, so listing and counting shouldn't take long. ASIDE: Yes, 78 (answer choice E) is pretty big. However, if you start listing possible outcomes and you eventually list more than 22 outcomes (answer choice D), you can stop because the answer must be E. Okay, let's list possible outcomes in a systematic way. We'll list outcomes as follows: x, y, z Since x is the smallest value. Let's list the outcomes in which x = 0. We get: 0, 1, 10 0, 2, 9 0, 3, 8 0, 4, 7 0, 5, 6 Now, the outcomes in which x = 1. We get: 1, 2, 8 1, 3, 7 1, 4, 6 Now, the outcomes in which x = 2. We get: 2, 3, 6 2, 4, 5 Now, the outcomes in which x = 3. We get: 3, 4...hmmm, this won't work. So, we're done listing! Count the outcomes to get a total of 10 Answer: B Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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 25 Apr 2015 Posted: 2456 messages Followed by: 18 members Upvotes: 43 Brent@GMATPrepNow wrote: If x, y and z are non-negative integers such that x < y < z, then the equation x + y + z = 11 has how many distinct solutions? A) 5 B) 10 C) 11 D) 22 E) 78 Since 11/3 < 4, so x, being the smallest of all 3 variables, must be no more than 3. If x = 0, then we have y + z = 11. Since y < z, y can be any integers from 1 to 5 inclusive. So we have 5 distinct solutions when x = 0. If x = 1, then we have y + z = 10. Since y < z, y can be any integers from 2 to 4 inclusive. So we have 3 distinct solutions when x = 1. If x = 2, then we have y + z = 9. Since y < z, y can be any integers from 3 to 4 inclusive. So we have 2 distinct solutions when x = 2. If x = 3, then we have y + z = 8. Since y > x, y is at least 4. If y â‰¥ 4, then z â‰¤ 4. However, this will contradict the fact that y < z. So we donâ€™t have any possible solutions when x = 3. Therefore, there are a total of 5 + 3 + 3 = 10 distinct solutions. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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