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Credit card problem!

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Credit card problem!

by MI3 » Sun Jul 17, 2011 3:11 am
Q. On Jane's credit card account, the average daily balance for a 30-day billing cycle is average (arithmetic mean) of the daily balances at the end of the 30 days. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was average daily balance on Jane's account for the billing cycle?
(1) Jane's payment was credited on the 21st day of the billing cycle.
(2) The average daily balance through the 25th day of the billing cycle was $540.

IMO - A, am i correct?
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by beatthegmat.garry » Sun Jul 17, 2011 8:18 am
IMO its D

statement 1:

The $300 payment was credited on 21st day of the billing cycle. So we can find the average as
(600*21+300*9 )/30=daily average
Hence statement 1 is sufficient

Statement 2:

The average until 25 day was $540.

Since average is less than 600 and much more than 300 it means that payment has been applied but recently.

We can assume that on day x the payment was applied.

Hence,

600*x+300(25-x)=25*540
x=20.

Hence on day 20 the $300 payment was applied to the account.
So its easier now to find the average balance at the end of 30 day billing cycle.

So statement 2 is sufficient.

Hence D.

Thanks !
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by GMATGuruNY » Sun Jul 17, 2011 11:36 am
I posted a solution here:

https://www.beatthegmat.com/arithmetic-mean-t82854.html

The posted solution requires almost no math.
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