NEW HERE? LEARN MORE
closeclose
Last visit was: 02 May 2024, 15:01 It is currently 02 May 2024, 15:01
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93015
Own Kudos [?]: 620779 [3]
Given Kudos: 81728
Send PM
CAT Tests Forum Quiz Mode
Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink] New post   04 Dec 2018, 01:46
1
Kudos
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

60% (02:41) correct 40% (02:56) wrong based on 162 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
E
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8023
Own Kudos [?]: 4109 [2]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink] New post   04 Dec 2018, 04:32
2
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




WeekCurrent Week Pay Previous Week pay Total pay of the Week
Week 1 $1 $0 $1
Week 2 $1 $1 $2
Week 3 $1 $3 $4
Week 4 $1 $7 $8
Week 5 $1 $15 $16
Week 6 $1 $31 $32
Week 7 $1 $63 $64
Week 8 $1 $127$128

total $255 IMO E
User avatar
G
baru
Manager
Manager
Joined: 18 Jan 2018
Posts: 214
Own Kudos [?]: 286 [1]
Given Kudos: 72
Location: India
Concentration: General Management, Healthcare
Schools: ISB '21 Booth '22 IIMB
GPA: 3.87
WE:Design (Manufacturing)
Send PM
GMAT ToolKit User
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink] New post   04 Dec 2018, 23:47
1
Kudos
Paid amount for Week 1 = 1 ,
Week 2 = 1+1 = 2,
week 3 = 1+2+1 = 4 ( 2*2 , week2 *2)
week 4 = 1+2+4+ 1 = 8 ( 4*2 , Week3 *2)
similary pattern is 1,2,4,8,16,32,64,128

So week 8 = 128 , instead of adding all here for the Total amount ,
we can do ( week 9 -1 ) = 128*2 -1 = 255 ( As give namount paid per week = Total paid till then + 1 )
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18801
Own Kudos [?]: 22121 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink] New post   23 Jun 2020, 13:58
1
Kudos
Expert Reply
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.)

Answer: E
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32792
Own Kudos [?]: 824 [0]
Given Kudos: 0
Send PM
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink] New post   10 Oct 2021, 07:34
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.
GMAT Club Bot
gmatclubot
Re: Mitchell plans to work at a day camp over the summer. Each week, he wi [#permalink]
10 Oct 2021, 07:34
Moderators:
Bunuel
Math Expert
93014 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions