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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 ## Set M is composed of the positive even integers up to 100. tagged by: swerve ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Set M is composed of the positive even integers up to 100. ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Set M is composed of the positive even integers up to 100. Set N is composed of the odd integers from -1 to 99. What is the value of (the sum of set M)-(the sum of set N)? A. 49 B. 50 C. 51 D. 100 E. 101 The OA is C Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 swerve wrote: Set M is composed of the positive even integers up to 100. Set N is composed of the odd integers from -1 to 99. What is the value of (the sum of set M)-(the sum of set N)? A. 49 B. 50 C. 51 D. 100 E. 101 The OA is C Source: Magoosh Set M is composed of the positive even integers up to 100. Set M = {2, 4, 6, 8, . . . . 96, 98, 100} Set N is composed of the odd integers from -1 to 99 Set N = {-1, 1, 3, 5, . . . 95, 97, 99} What is the value of (the sum of Set M) - (the sum of Set N)? SUM of set M = 2 + 4 + 6 + 8 + . . . .+ 96 + 98 + 100 SUM of set N = -1 + 1 + 3 + 5 + . . . 95 + 97 + 99 ASIDE: Notice that there are 100 POSITIVE integers from 1 to 100 inclusive HALF of them are EVEN and HALF are ODD So, set M consists of 50 integers and set N consists of 51 integers (since set N also has one NEGATIVE odd number) (the sum of Set M) - (the sum of Set N) = (2 + 4 + 6 + 8 + . . . .+ 96 + 98 + 100) - (-1 + 1 + 3 + 5 + . . . 95 + 97 + 99) = (2 + 4 + 6 + 8 + . . . .+ 96 + 98 + 100) - (1 + 3 + 5 + . . . 95 + 97 + 99) + 1 [I did this because I want to PAIR each of the 50 values in set M with each of the 50 values in set B] = (2 - 1) + (4 - 3) + (6 - 5) + . . . + (98 - 97) + (100 - 99) + 1 = (1) + (1) + (1) + . . . + (1) + (1) + 1 = 50 + 1 [since we have 50 PAIRS of even and odd numbers] = 51 Answer: C 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 25 May 2010 Posted: 15383 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 swerve wrote: Set M is composed of the positive even integers up to 100. Set N is composed of the odd integers from -1 to 99. What is the value of (the sum of set M)-(the sum of set N)? A. 49 B. 50 C. 51 D. 100 E. 101 For any EVENLY SPACED SET: Count = (biggest - smallest)/(increment) + 1. Average = (biggest + smallest)/2. Sum = (count)(average). The INCREMENT is the difference between successive values. Even integers between 2 and 100, inclusive: Here, the integers are EVEN, so the increment = 2. Count = (100-2)/2 + 1 = 50. Average = (100+2)/2= 51. Sum = (50)(51). Odd integers between -1 and 99, inclusive: Here, the integers are ODD, so the increment = 2. Count = (99-(-1))/2 + 1 = 51. Average = (99+(-1))/2= 49. Sum = (51)(49). Subtracting the second sum from the first, we get: (50*51) - (51*49) = 51(50-49) = 51*1 = 51. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 swerve wrote: Set M is composed of the positive even integers up to 100. Set N is composed of the odd integers from -1 to 99. What is the value of (the sum of set M)-(the sum of set N)? A. 49 B. 50 C. 51 D. 100 E. 101 The OA is C Source: Magoosh The number of integers in set M is (100 - 2)/2 + 1 = 50 The number of integers in Set N is (99 - (-1))/2 + 1 = 51 We can pair the 50 numbers from set M with the first 50 numbers from set N as follows: 2, -1 4, 1 6, 3, etc. We see that each number in set M is 3 more than each number in set N. Thus, comparing the first 50 numbers in each set, the sum of those numbers in Set M is 3 x 50 = 150 greater. However, set N has an extra number, which is 99. So the overall sum of the integers in set M is actually 150 - 99 = 51 greater than the sum of the integers in set N. Answer: C _________________ 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. 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