Question: 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

“A certain drive-in movie theatre has total of 17 rows of parking spaces.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
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.

Correct Answer: C

Approach Solution 2:
A certain movie theatre 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 Arithmetic 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

Correct Answer: C

Approach Solution 3:
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) = n/2 ∗ (2a+(n−1)d)

Substituting the values, we get

Sn = 16/2 * (2∗21+(16−1)2)=8∗(42+30)=8∗72=576

Total number of parking spaces are 20+576 = 596

Correct Answer: C

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