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A certain drivein movie theater has total of 17 rows of parking space
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03 Jul 2016, 11:26
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A certain drivein movie theater has 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
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A certain drivein movie theater has total of 17 rows of parking space
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07 May 2017, 06:43
Bunuel wrote: A certain drivein movie theater has 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 we are dealing with consecutive integers! therefore average=median first two rows = 20+21 = 41 next 15 rows > Median = (23,25,27,29,31,33,35, 37,39,41,43,45,47,49,51) we can stop listing them down at 37, since median = 8th term Hence, 41 + 37* 15 = 596
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Re: A certain drivein movie theater has total of 17 rows of parking space
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03 Jul 2016, 11:37
Bunuel wrote: A certain drivein movie theater has 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 Sent from my iPhone using GMAT Club Forum mobile app



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Re: A certain drivein movie theater has total of 17 rows of parking space
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04 Jul 2016, 00:03
596
first row 20 then other 16 rows form an Ap with first term 21 and last 51.Avg is 36 so 36*16+20=596



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Re: A certain drivein movie theater has total of 17 rows of parking space
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10 Jul 2016, 17:19
A certain movie theater has a total of 17 rows of parking space
Number of parking Spaces in first row 20 Number of parking Spaces in first row 21 Number of parking Spaces in first row 23
It is evident that from Second row the other 16 rows form an Airthematic Progression with first term 21 The last term of AP i.e \(T16\) = 21+(161)*2 = 51. Sum of Arithmetic series =16*(51+21)/2 = 576
The sum of the series = 576+20
so 36*16+20=596
Hence Option C



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Re: A certain drivein movie theater has total of 17 rows of parking space
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10 Aug 2016, 19:47
Attached is a visual that should help.
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Screen Shot 20160810 at 7.45.53 PM.png [ 155.8 KiB  Viewed 16346 times ]
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A certain drivein movie theater has total of 17 rows of parking space
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16 Oct 2016, 04:56
First Row = 20
Second Row =21
Third Row = 21 + 2
Fourth Row = 21 + 4
Third till Last Row are in a sequence with difference of 2 between each terms. Hence, Sum of all terms in this sequence of 15 terms = N/2 * (2* First Term + {n1} * Difference) = 15/2 * (2*23 + 14*2) = 555
Sum of all terms = 20 + 21 + 555 = 596



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A certain drivein movie theater has total of 17 rows of parking space
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07 May 2017, 07:13
First row will have 20 parking spaces. Second column onwards is an AP with Starting term(a) = 21, Common difference(d) = 2, and Number of terms(n) = 16 Sum of n terms(Sn) = \(\frac{n}{2}*(2a + (n1)d)\)Substituting the values, we get Sn = \(\frac{16}{2}*(2*21 + (161)2) = 8 * (42+30) = 8 * 72 = 576\) Total number of parking spaces are 20+576 = 596(Option C)
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A certain drivein movie theater has total of 17 rows of parking space
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09 Jun 2017, 15:36
Bunuel wrote: A certain drivein movie theater has 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 20+16*[21+(21+15*2)]/2=596 total spaces C



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Re: A certain drivein movie theater has total of 17 rows of parking space
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07 Jul 2017, 12:31
MENNAWALID wrote: Please I need an answer than is shown by a rule.
Posted from my mobile device I believe you are searching for a formula. This one is a simple AP formula. Sum= n/2{2a+(n1)d} here a=21 n=16 d=2 So now we get = 16/2{2*21+(161)*2} => 16(21+15) => 16*36 => 576 Add the 20 from the first row to get 596 as your total.



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Re: A certain drivein movie theater has total of 17 rows of parking space
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16 Dec 2017, 03:25
Bunuel wrote: A certain drivein movie theater has 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 Total Rows : 17 Info given on 1st two Rows : 20, 21 Spaces . Rest of the spaces will increase per row by 2 spaces. Hence this becomes an AP question. 172= 15 Rows First term= 21 ]Last term = (No of Rows * Difference) + First Term= 15*2=30Therefore AP is 21.....51 No of rows for AP = [5121]/2 +1=16 Sum of AP= Mean * No of terms involved in AP = [51+21]/2 * 16= 576 Now we have 20 Spaces from firt Row therefore total spaces = 576 +20=596 The only difficulty you might face is figuring out why first 15 rows were used and then 16. 15 were used from 3rd to 17th row. Because we had info of 2nd row. (i.e. 21 spaces) While in AP, we used info from 2nd row to 17th, hence 16 rows. Easier of way finding a mean for AP is via Median ,23,25.....51. Middle term is 37 Sum of AP becomes : 37 * 15 = 555 Now add first 2 row spaces = 555 + 20+21= 596.



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Re: A certain drivein movie theater has total of 17 rows of parking space
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29 Jan 2018, 16:12
Hi All, This question can be solved with a bit of Arithmetic and 'bunching.' We're told that the first two rows of parking spaces contain 20 and 21 spaces respective, then the following 15 rows increase by 2 each (re: 23, 25, 27, etc.). We're asked for the TOTAL number of parking spaces. The first two rows total 20+21 = 41 spaces. The remaining 15 rows are the odd numbers from 23 through 51, inclusive. By adding the smallest and largest of those numbers, we get: 23 + 51 = 74 By adding the next smallest and next biggest, we get: 25 + 49 = 74 This pattern is consistent, so we'll end up with 7 "pairs" of numbers that add up to 74 and one number "in the middle" that doesn't 'pair up': 37. Thus, the total number of spaces is... 41 + 7(74) + 37 = 596 Final Answer: GMAT assassins aren't born, they're made, Rich
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A certain drivein movie theater has total of 17 rows of parking space
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21 Feb 2018, 19:59
Bunuel wrote: A certain drivein movie theater has 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 Fastest way: 2 3 3 325 35 27 37 29 39 31 41 if you see the patterns, the last digits repeat, 15 digits, thus the last digit would be 3+5+7+9+1 = 25 + 0 (1st row) + 1 (2nd row) = 26, 6 is the last digit, only answer 596. I think, for Gmat you will have to see yourself as a hacker, if we try algebra or some tedious calculations we might run short of time in the end. ironically it took me 5 mins, as I lost my myself in this question initially try to do long calculations.



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Re: A certain drivein movie theater has total of 17 rows of parking space
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16 Aug 2018, 14:01
Here, If we see we are given a condition that after the second row each row number has 2 more parking spaces than the previous one. So we see an AP forming from 2 till the last 17 We can find the that in last row there would how many parking spaces. In last row there would be a16=a1+(n1)d { since we have considered 21 as our first term and 51 as our last term, so we have 16 terms } where a1= 21 n=16, d=2 = 21+(161)2 =51 Sum of all the parking spaces from row 2 to 17 = (21+51)*16/2 = 72*8= 576 now adding the first row it will be 576+20=596. Hi Bunuel, Looks like the best tag for this question would be Sequences. Probus
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Re: A certain drivein movie theater has total of 17 rows of parking space
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18 Sep 2018, 15:41
Just a tip: when you come to final calculations (or in the beginning) glance at answer choices before making arithmetics. In this case I came up with 72*8+20. As you can see, the last digit has to be 6. The only answer that ends with 6 is C. So I skipped the part with calculations and picked option C. This approach helps to save your energy when you are doing tests and saves you from silly mistakes related to arithmetics.



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Re: A certain drivein movie theater has total of 17 rows of parking space
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23 Oct 2018, 07:33
Bunuel wrote: A certain drivein movie theater has 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 From 2nd to the 17th row we get a sequence in the form of \(X_n = X_2 + 2 (X_n  2)\) 21 + 2(172) = 21 + 2*15 = 21 + 30 = 51 51 + 21 = 72/2 = 36 Number of terms from 2nd to 17th = 17  2 = 15 + 1 = 16 36 * 16 = 576 576 + 20 = 596 Answer choice C



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Re: A certain drivein movie theater has total of 17 rows of parking space
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04 Apr 2019, 18:35
Bunuel wrote: A certain drivein movie theater has 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 We can see that the 3rd row has 21 + 2(1) = 23 parking spaces, the 4th row has 21 + 2(2) = 25 parking spaces and so on. Therefore, the 17th row has 21 + 2(15) = 51 sparking spaces. Therefore, the total parking spaces of row 2 to row 17 is: 21 + 23 + 25 + … + 51 Since the terms of the above sum are evenly spaced, we can use the formula sum = average x quantity. The average is (21 + 51)/2 = 72/2 = 36. The quantity is 17  2 + 1 = 16. Therefore, the sum is 36 x 16 = 576. We still have to add the number of parking spaces in the first row, so the total number of parking spaces in all 17 rows is 576 + 20 = 596. Answer: C
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Re: A certain drivein movie theater has total of 17 rows of parking space
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