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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 ## sum of these 24 integers? tagged by: rajeet123 ##### This topic has 4 expert replies and 1 member reply ## sum of these 24 integers? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 1,234 1,243 1,324 ..... .... +4,321 The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers? A. 24,000 B. 26,664 C. 40,440 D. 60,000 E. 66,660 Junior | Next Rank: 30 Posts Joined 11 Jun 2019 Posted: 13 messages Using the symmetry in the numbers involved (All formed using all possible combinations of 1,2,3,4), and we know there are 24 of them. We know there will be 6 each with the units digits as 1, as 2, as 3 and as 4. And the same holds true of the tens, hundreds and thousands digit. The sum is therefore = (1 + 10 + 100 + 1000) * (1*6 +2*6 +3*6 +4*6) = 1111 * 6 * 10 = 66660 Answer: e OR Formulas for such kind of problems (just in case): 1. Sum of all the numbers which can be formed by using the nn digits without repetition is: (n-1)!âˆ-(sum of the digits)âˆ-(111... n times)(n-1)!âˆ-(sum of the digits)âˆ-(111... n times) 2. Sum of all the numbers which can be formed by using the nn digits (repetition being allowed) is: nn-1âˆ-(sum of the digits)âˆ-(111... n times)nn-1âˆ-(sum of the digits)âˆ-(111... n times). ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13046 messages Followed by: 1253 members Upvotes: 5254 GMAT Score: 770 rajeet123 wrote: 1,234 1,243 1,324 ..... .... +4,321 The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers? A. 24,000 B. 26,664 C. 40,440 D. 60,000 E. 66,660 _________________ 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 08 Dec 2008 Posted: 13046 messages Followed by: 1253 members Upvotes: 5254 GMAT Score: 770 rajeet123 wrote: 1,234 1,243 1,324 ..... .... +4,321 The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers? A. 24,000 B. 26,664 C. 40,440 D. 60,000 E. 66,660 Since we're adding 24 numbers, we know that: Six numbers will be in the form 1--- Six numbers will be in the form 2--- Six numbers will be in the form 3--- Six numbers will be in the form 4--- Let's first see what the sum is when we say all 24 numbers are 1000, 2000, 3000 or 4000 The sum = (6)(1000) + (6)(2000) + (6)(3000) + (6)(4000) = 6(1000 + 2000 + 3000 + 4000) = 6(10,000) = 60,000 Since the 24 numbers are actually greater than 1000, 2000, etc, we know that the actual sum must be greater than 60,000 Answer: E 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: 15388 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 For any set that is SYMMETRICAL ABOUT THE MEDIAN: sum = (count)(median) rajeet123 wrote: 1,234 1,243 1,324 ..... .... +4,321 The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exactly once in each integer. What is the sum of these 24 integers? A. 24,000 B. 26,664 C. 40,440 D. 60,000 E. 66,660 The set is composed of integers in the following ranges: 1234...1432 2134...2431 3124...3421 4123...4321. Each range contains the same number of integers. Thus, the median of the set is equal to the average of the two integers in red: (2431 + 3124)/2 = 5555/2. Notice that the set is SYMMETRICAL ABOUT THE MEDIAN: ...2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241... Thus: sum = (count)(median) = 24 * 5555/2 = 12 * 5555 = 66,660. The correct answer is E. For a similar problem that can be solved with the same line of reasoning, check my post here: http://www.beatthegmat.com/on-consecutive-non-consecutive-series-t85395.html Alternate solution: Each digit will appear in each position 24/4 = 6 times. Thus, in each position, there will be six 1's, six 2's, six 3's, and six 4's. Sum of the digits in each position = 6(1+2+3+4) = 60. Sum of the thousands place = 60*1000 = 60,000. Sum of the hundreds place =60*100 =6,000. Sum of the tens place = 60*10 = 600. Sum of the units place = 60*1 = 60. Sum of all the integers = 60000 + 6000 + 600 + 60 = 66,660. _________________ 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 rajeet123 wrote: 1,234 1,243 1,324 ..... .... +4,321 The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers? A. 24,000 B. 26,664 C. 40,440 D. 60,000 E. 66,660 Since there are 24 different integers, each of the digits (1, 2, 3 and 4) will appear in each of the place values (thousands, hundreds, tens and ones) exactly 6 times. Therefore, the sum of the 24 integers will be as follows: 6(1000 + 2000 + 3000 + 4000) + 6(100 + 200 + 300 + 400) + 6(10 + 20 + 30 + 40) + 6(1 + 2 + 3 + 4) 6(10,000) + 6(1,000) + 6(100) + 6(10) 60,000 + 6,000 + 600 + 60 66,660 Answer: E _________________ 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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