Cheers123 wrote:On Jane's credit card account, the average daily balance for a 30 day billing cycle is the average of the daily balances at the end of each 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 the 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.

The average daily balance (call that the ADB) is the average of the daily balances at the end of each of the 30 days.
At the beginning of the cycle, the balance is $600.

Let's take it a few days:
end of day 1: $600
end of day 2: still $600
end of day 3: still $600.
etc.

At some point, jane makes a payment of $300, and the daily balances from then on will be only $300.

for example, from stat. (1) we get that the payment was done on the 21st: the balance for the first 20 days will be 600 each, and the balance for the remaining 10 days is 300 each. The ADB is calculated as 20*600 + 10*300 / 30 - add the daily balances on each of 30 days (600 for the first 20 days, 300 for the remaining 10), and divide by the number of days=30.

So stat. (1) is sufficient, and demonstrates the missing piece - In order to determine the ADB, all you really need to know is WHEN the payment of $300 was made, so that you have the number of days with $600 and the number of days with $300.

With this in mind, stat. (2) is also sufficient. Since the ADB until the 25th day is less than $600, it follows that the payment was made on some day before the 25th - otherwise the ADB wouldve been a perfect $600. When was the payment made? Assign x to the day the payment was made, so the account held $600 for x days, and $300 for the remaining 25-x days. The ADB for day 25 would then be:
[ x*600 + (25-x)300 ]/25 = 540

from which it is possible to derive x, and then solve for ADB of all 30 days, same as stat. (1).

The answer is D.

Appreciate your quick and detailed response, Geva.
I also approached the problem in a similar way but I found the second statement a bit confusing. Also, shouldn't x in the equation, x*600 + (25-x)*300 = 540, be 21, as mentioned in statement 1?

Sorry - forgot to divide by the number of days (25), as the ADB is the average. I'll edit the post above.

Incidentally, there's no real requirement for the two statements of a DS question to reach the exact same value. It is even, theoretically possible for the statements to contradict each other, but in such a case the question cannot require you to consider both statements together, as that would be illogical - both statements must be true. The answer cannot be C or E in such a case, and at least one of the statements must be sufficient.

I admit that I have not seen any official question do this, though.