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Math Expert V
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A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Question Stats: 75% (02:30) correct 25% (02:49) wrong based on 904 sessions

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A certain drive-in 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 drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Bunuel wrote:
A certain drive-in 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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GMAT 1: 600 Q47 V26 Re: A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Bunuel wrote:
A certain drive-in 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 drive-in movie theater has total of 17 rows of parking space  [#permalink]

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2
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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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+(16-1)*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 drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Top Contributor
2
Attached is a visual that should help.
Attachments Screen Shot 2016-08-10 at 7.45.53 PM.png [ 155.8 KiB | Viewed 16346 times ]

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A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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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 + {n-1} * Difference) = 15/2 * (2*23 + 14*2) = 555

Sum of all terms = 20 + 21 + 555 = 596
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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) = $$\frac{n}{2}*(2a + (n-1)d)$$

Substituting the values, we get

Sn = $$\frac{16}{2}*(2*21 + (16-1)2) = 8 * (42+30) = 8 * 72 = 576$$

Total number of parking spaces are 20+576 = 596(Option C)
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A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Bunuel wrote:
A certain drive-in 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
Intern  S
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Re: A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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MENNAWALID wrote:

Posted from my mobile device

I believe you are searching for a formula.
This one is a simple AP formula.

Sum= n/2{2a+(n-1)d}
here a=21
n=16
d=2

So now we get = 16/2{2*21+(16-1)*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 drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Bunuel wrote:
A certain drive-in 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.

17-2= 15 Rows
First term= 21
]Last term = (No of Rows * Difference) + First Term= 15*2=30

Therefore AP is 21.....51
No of rows for AP = [51-21]/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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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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

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Manager  B
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A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Bunuel wrote:
A certain drive-in 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:

23 33
25 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 drive-in movie theater has total of 17 rows of parking space  [#permalink]

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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+(n-1)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+(16-1)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.

HiBunuel,
Looks like the best tag for this question would be Sequences.

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Re: A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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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 drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Bunuel wrote:
A certain drive-in 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(17-2) = 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

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Re: A certain drive-in movie theater has total of 17 rows of parking space  [#permalink]

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Bunuel wrote:
A certain drive-in 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.

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