• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Arthmetic subsequent value Problem Solving question

This topic has 1 expert reply and 0 member replies

Arthmetic subsequent value Problem Solving question

Post

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

  • +1 Upvote Post
  • Quote
  • Flag
Post
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!

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Top First Responders*

1 Brent@GMATPrepNow 60 first replies
2 fskilnik@GMATH 60 first replies
3 Jay@ManhattanReview 46 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 24 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

122 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

94 posts
3 image description Max@Math Revolution

Math Revolution

84 posts
4 image description Jay@ManhattanReview

Manhattan Review

79 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

63 posts
See More Top Beat The GMAT Experts