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Bingging in January of last year, Carl made deposits of $120

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Bingging in January of last year, Carl made deposits of $120 [#permalink]

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New post 18 Jul 2009, 19:30
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Bingging in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year?

a. Last year the closing balance of Carl's account for April was less than $2,625
b. Last year the closing balance of Carl's account for June was less than $2,675
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Re: Closing balances [#permalink]

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New post 18 Jul 2009, 21:32
sondenso wrote:
Bingging in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year?

a. Last year the closing balance of Carl's account for April was less than $2,625
b. Last year the closing balance of Carl's account for June was less than $2,675


Good example. Makes you scratch your head.

First let's understand the example. Carl started depositing $120 from January (Jan). He continued it for some time. Then, withdraws $50 each month after that.

Closing balance of May is given = $2600. Obviously, there was some initial balance before January, before Carl started depositing $120 in a/c. (Maximum he can deposit in 5 months = 5 x $120 = $600.) But, we can not assume that he has deposited for all 5 months. He might have withdrawn $50.

To find the closing month balances of Jan to Dec. We need to know following 3 things -

a. Initial balance in a/c. Let's say 'X'.
b. Till what month Carl deposited $120.
c. In which month Carl started withdrawing $50.

1. April balance < $2625. But, in May it's $2600. So obviously, in May he has deposited $120. Now, we know, for sure, that Carl has deposited $120 for first 5 months.

X + ($120 x 5) = 2600.
X=2000.--------- Initial balance.

Still, it does not tell you when Carl started withdrawal of $50.

2. June balance < 2675. Obviously, after May (Balance = $2600), he has not deposited $120. He has started withdrawal of $50. This statement alone does not give us 'a' & 'b'.

Combining 1 & 2, we get all answers - a,b,c.

Hence, answer = 'C'. Both sentences together are necessary.

Though, solution seems long, it only takes a minute to solve it. :)

P.S. I am still skeptical about the solution. As the question mentions "range of the monthly closing balances". Can you please confirm if the answer is right ?
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Re: Closing balances   [#permalink] 18 Jul 2009, 21:32
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Bingging in January of last year, Carl made deposits of $120

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