During a particular period, an investor received $1000 a

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Apr 24, 2018 2:13 pm

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During a particular period, an investor received $1000 a week the first week then $1000 two weeks later and then $1000 four weeks later and so on. If this pattern continued indefinitely, how many weeks did it take her to receive $5,000?

A. 5
B. 16
C. 31
D. 32
E. 63

The OA is C.

Please, can anyone assist me with this PS question? Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Apr 24, 2018 2:13 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Apr 24, 2018 9:53 pm

Hi All,

We're told that during a particular period, an investor received $1000 a week the first week then $1000 two weeks later and then $1000 four weeks later and so on. We're asked for the number of weeks that it took her to receive $5,000 in total. This question can probably best be solved with 'brute force' and drawing a little table:

Start:
After 1 week, $1000 received --> Total = $1000
After 2 more weeks, another $1000 received --> Total = $2000, Total time = 3 weeks
After 4 more weeks, another $1000 received --> Total = $3000, Total time = 7 weeks
After 8 more weeks, another $1000 received --> Total = $4000, Total time = 15 weeks
After 16 more weeks, another $1000 received --> Total = $5000, Total time = 31 weeks

Thus, after 31 total weeks, $5000 in total would be received.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Sionainn@PrincetonReview: GMAT Instructor; Posts: 41; Joined: Mon Mar 12, 2018 9:54 amFollowed by: 1 member

by Sionainn@PrincetonReview » Tue Apr 24, 2018 9:54 pm

Once you get over your suspicions that your investment is in the hands of Bernie Madoff as it is taking longer and longer to get the same return on investment, notice that the time it takes to return $1,000 is doubling. $1,000 after 1 week, $1,000 after 2 weeks, $1,000 after 4 weeks, $1,000 after 8 weeks and $1,000 (bringing the total to $5,000) after 16 weeks. 16+ 8 + 4 + 2 + 1 =31 or choice C.

Take care,
Sionainn Marcoux
BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Apr 25, 2018 10:12 am

The pattern can be expressed in terms of powers of 2 = 2^0 + 2^1 + 2^2 + 2^3 + 2^4 = 1 + 2 + 4 + 8 + 16 = 31.

We calculate the sum of powers of 2 till 2^4 as we need only $5000 hence till 5 terms from 2^0 to 2^4.

So to receive $5000, it took 31 weeks. Option C.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Apr 26, 2018 2:51 pm

BTGmoderatorLU wrote:During a particular period, an investor received $1000 a week the first week then $1000 two weeks later and then $1000 four weeks later and so on. If this pattern continued indefinitely, how many weeks did it take her to receive $5,000?

A. 5
B. 16
C. 31
D. 32
E. 63

We can start by making a list (or table) that tracks the amount of money she received during a particular week and the total amount of money she has received:

Week 1: $1,000 --- Total: $1,000
2 weeks later or week 3: $1,000 --- Total: $2,000
4 weeks later or week 7: $1,000 --- Total: $3,000
8 weeks later or week 15: $1,000 --- Total: $4,000
16 weeks later or week 31: $1,000 --- Total: $5,000

Thus, it takes her 31 weeks to receive a total of $5,000.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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