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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 ## Arthmetic subsequent value Problem Solving question tagged by: sam mwambazi ##### This topic has 1 expert reply and 0 member replies ## Arthmetic subsequent value Problem Solving question ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Does anyone know how to solve this question with an equation that is easy to understand? A certain drive-in movie theater has a total of 17 rows of parking spaces. There are 20 parking spaces in the first row and 21 parking spaces in the second row. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater? A. 412 B. 544 C. 596 D. 632 E. 692 ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 1981 messages Followed by: 237 members Upvotes: 1443 If each row had 2 more spaces than the previous, we could imagine this as [x, x + 2, x + 4, x + 6... x + n]. Because the 1st & 2nd rows have different spacing than the other rows, there's no way to do this in one simple step, but we can divide it into 2 steps. For this problem, the first & second rows are 1 apart, then everything afterwards is 2 apart. First, it helps to establish your pattern: 1st --> 20 2nd --> 21 3rd --> 23 4th --> 25 5th --> 27 For every term after the 2nd term, we've added 21 + 2(the # of terms between 2 and that term). For example, there are 3 terms between the 2nd to 5th term, inclusive. So 21 + 2(3) = 27. The 17th term will be the 15th term after the 2nd. So 21 + 2(15) = 51. (Or you could just list them all out. It wouldn't really take that long. In fact, it might be faster than trying to derive the pattern!). Now, we'll find the sum in 2 steps: 1. find the sum from the 2nd row (21) to the 17th row (51) 2. add the value from the 1st row To add up all of the odd integers from 21 to 51, we use the CONSECUTIVE SUM formula: sum = (average)(# of terms) The average of a consecutive set = the average of the endpoints --> (biggest + smallest)/2 The # of terms = the difference between the biggest and the smallest, divided by the step. Then add 1 to make it inclusive. So the # of odd terms --> (biggest - smallest)/2 + 1 So for odd integers from 21 to 51: average = (21 + 51)/2 = 72/2 = 36 # of terms = (51 - 21)/2 + 1 = 30/2 + 1 = 16 sum = (36)(16) = 576 To get the total for all the spaces, we need to add the 20 from the 1st row: 576 + 20 = 596. The answer is C. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. • Award-winning private GMAT tutoring Register now and save up to$200

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