Last visit was: 14 Jul 2024, 08:03 It is currently 14 Jul 2024, 08:03
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Mitchell plans to work at a day camp over the summer. Each week, he wi

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640716 [3]
Given Kudos: 85011
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 7963
Own Kudos [?]: 4214 [2]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Manager
Joined: 18 Jan 2018
Posts: 206
Own Kudos [?]: 287 [1]
Given Kudos: 72
Location: India
Concentration: General Management, Healthcare
GPA: 3.87
WE:Design (Manufacturing)
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19130
Own Kudos [?]: 22627 [1]
Given Kudos: 286
Location: United States (CA)
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink]
1
Kudos
Bunuel wrote:
Mitchell plans to work at a day camp over the summer. Each week, he will be paid according to the following schedule: at the end of the first week, he will receive \$1. At the end of each subsequent week, he will receive \$1, plus an additional amount equal to the sum of all payments he’s received in previous weeks. How much money will Mitchell be paid in total during the summer, if he works for the entire duration of the 8-week-long camp?

A. 126
B. 127
C. 252
D. 254
E. 255

Solution:

We can tabulate the amount Mitchell earns each week.

Week 1: \$1

Week 1: 1 + 1 = \$2

Week 3: 1 + (1 + 2) = \$4

Week 4: 1 + (1 + 2 + 4) = \$8

At this point, we see that the amount he earns in certain week is double the amount he earns the previous week. Therefore,

Week 5: \$16 Week 6: \$32 Week 7: \$64 Week 8: \$128

So the total he earns at the end of the 8-week-long camp is:

1 + 2 + 4 + … + 128 = 2^8 - 1 = \$255

(Note: We are using the formula 1 + 2 + 4 + … 2^n = 2^(n + 1) - 1 and notice that 128 = 2^7.)

Non-Human User
Joined: 09 Sep 2013
Posts: 33968
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink]
Moderator:
Math Expert
94342 posts