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

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parkhydel
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Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   28 Apr 2020, 07:08
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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

PS44321.02
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D
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BrentGMATPrepNow
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Re: Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   28 Apr 2020, 09:16
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parkhydel wrote:
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


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
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Re: Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   01 Jun 2020, 03:32
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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 \(S_{n} = \frac{n}{2}\)[First term + Last term]

\(S_{50} = \frac{50}{2}[1 + 50]\)

\(S_{50} = 25*51 = $1275\)

Total amount in his account = \($1275 + $800 = $2075\)

Therefore answer is Option D.
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Re: Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   13 Dec 2020, 06:04
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parkhydel wrote:
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

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
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Re: Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   28 Apr 2020, 07:18
parkhydel wrote:
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


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
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Re: Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   05 Jul 2020, 21:47
Explanation:
Initial Amount in Bank : 800
1$ 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
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Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   11 Feb 2021, 09:23
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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 :thumbsup:
Devmitra Sen(Math)
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Re: Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   22 May 2021, 01:03
Expert Reply
parkhydel wrote:
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


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Answer: Option D

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Re: Sam has $800 in his account. He will deposit $1 in his account one wee [#permalink] New post   25 Feb 2022, 09:58
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Hi GMATters,

Here is a link to my video explanation of this question:

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