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

Question

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

PS44321.02

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

PS44321.02

BrentGMATPrepNow · Accepted Answer

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 = \frac{n(n+1)}{2}

So  1 + 2 + 3 + ....+ 49 + 50 = \frac{50(50+1)}{2}= \frac{(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

ScottTargetTestPrep · Answer

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

Kinshook · Answer

Given: 
1. Sam has $800 in his account. 
2. 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.

Asked: If there are no other transactions, how much money will Sam have in his account 50 weeks from now?

After n weeks, Sam will have = $800 + $1 + $2 + .......... $n = $800 + $n(n+1)/2
After 50 weeks, Sam will have = $800 + $50*51/2 = $800 + $1275 = $2075

IMO D

perfectreview · Answer

The amount deposited in the first week = $1

The amount deposited in the second week = $1 + $1 = $2

The amount deposited in the third week = $2 + $1 = $3

and so on for 50 weeks.

So the amounts will be like this $1, $2, $3, ................... $50

These terms in A.P if we observe.

So sum of the terms is  S_{n} = \frac{n}{2}

S_{50} = \frac{50}{2}

S_{50} = 25*51 = $1275

Total amount in his account =  $1275 + $800 = $2075

Therefore answer is  Option D .

rajatchopra1994 · Answer

Explanation:
Initial Amount in Bank : 800
1$ added in 1week then 2$ ... so on till 50 weeks. so, Series will become 1,2,3,4,.............,50
Sn = 50 (1+50)/2
Sn = 25x51 = 1275
So total amount in saving = 800 + 1275
=2075$

IMO-D

CrackverbalGMAT · Answer

SOLUTION : A NEW OG 2021 QUESTION In the first week, the amount saved = 1$ Money saved by the end of 2 weeks = 1$ + 2$ Money saved by the end of 3 weeks = 1$ +2$ + 3$ ..In the same pattern, the money saved by the end of 50th week = 1$ + 2$ +3$ +......50$ = (50* 51)/2 (The sum of 1+2+3+4+..n= n(n+1)/2 ) = 1275$ Total money saved by him in his account = 800$ (saved previously) + 1275$ = 2075$ (OPTION D) Hope this helps

Devmitra Sen(Math)

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=8VZHXGAVtZc

PGTLrowanhand · Answer

Hi GMATters,

Here is a link to my video explanation of this question:  https://www.youtube.com/watch?v=IVAkXk0UPz8

Rowan

bumpbot · Answer

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

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