Sam has $800 in his account. He will deposit $1 in his account one week from

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

Sam has $800 in his account. He will deposit $1 in his account one week from

by BTGModeratorVI » Thu Dec 03, 2020 2:47 pm

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Sam has $800 in his account. He will deposit $1 in his account one week from now, $2 two weeks from now, and each week thereafter he will deposit an amount that is $1 greater than the amount that he deposited one week before. If there are no other transactions, how much money will Sam have in his account 50 weeks from now?

A. $850
B. $1,200
C. $1,675
D. $2,075
E. $3,350

Answer: D
Source: official guide

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Source: Beat The GMAT — Problem Solving | Thu Dec 03, 2020 2:47 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: Sam has $800 in his account. He will deposit $1 in his account one week from

by Brent@GMATPrepNow » Thu Dec 03, 2020 3:05 pm

BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:47 pm
Sam has $800 in his account. He will deposit $1 in his account one week from now, $2 two weeks from now, and each week thereafter he will deposit an amount that is $1 greater than the amount that he deposited one week before. If there are no other transactions, how much money will Sam have in his account 50 weeks from now?

A. $850
B. $1,200
C. $1,675
D. $2,075
E. $3,350

Answer: D
Source: official guide

We have the following:

Initial amount of money: $800
Money after 1 week: $800 + $1
Money after 2 weeks: $800 + $1 + $2
Money after 3 weeks: $800 + $1 + $2 + $3
Money after 4 weeks: $800 + $1 + $2 + $3 + $4
.
.
.
Money after 50 weeks: $800 + $1 + $2 + $3 + $4 + . . . + $49 + $50
So we need to find the value of $1 + $2 + $3 + $4 + . . . + $49 + $50

Useful formula for the sum of the first n positive integers: 1 + 2 + 3 + ....+ n = n(n+1)/2

So 1 + 2 + 3 + ....+ 49 + 50 = 50(50+1)/2 = (50)(51)/2 = (25)(51) = 1275
So, $1 + $2 + $3 + $4 + . . . + $49 + $50 = $1275

So, the money after 50 weeks = $800 + $1275 = $2075

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Sam has $800 in his account. He will deposit $1 in his account one week from

by Scott@TargetTestPrep » Sun Dec 06, 2020 8:51 am

BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:47 pm
Sam has $800 in his account. He will deposit $1 in his account one week from now, $2 two weeks from now, and each week thereafter he will deposit an amount that is $1 greater than the amount that he deposited one week before. If there are no other transactions, how much money will Sam have in his account 50 weeks from now?

A. $850
B. $1,200
C. $1,675
D. $2,075
E. $3,350

Answer: D
Source: official guide

Solution:

The total amount of money Sam will have 50 weeks from now is:

800 + (1 + 2 + 3 + … + 50)

The sum (1 + 2 + 3 + … + 50) can be easily calculated by using the formula sum = average x number. The average of this equally-spaced set is (first + last)/2 = (1 + 50)/2, and we note that there are 50 terms (numbers) comprising the sum.

= 800 + (1 + 50)/2 x 50

= 800 + 51 x 25

= 800 + 1275

= $2075

Answer: D

Scott Woodbury-Stewart
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