On Jane's credit card account, the average daily balance for 30-day billing cycle is the average (arithmetic mean) 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 substracted 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.
What is the question asking for?
The average daily balance for the whole month.
What information have we been given?
The balance starts at 600. At some point, the balance decreases to 300 and stays at 300 for the rest of the month.
What do we need to answer the question?
Since average = total/number of days = total/30, we need to know the total of the balances for the whole month.
The balance every day is either 600 or 300; once the balance changes to 300, it remains at 300 for the rest of the month.
So to determine the total for the whole month, all we need to know is
on which day Jane made the $300 payment.
Question rephrased: When did Jane make the $300 payment?
Statement 1: Jane's payment was credited on the 21st day of the billing cycle.
Tells us just what we need.
Sufficient.
Statement 2: The average daily balance through the 25th day of the billing cycle was $540.
This is a weighted average situation.
For the average of the 25 days to be 540, a certain number of days must be at 600, with the remaining days at 300.
Thus, we can determine on which day the $300 payment was made. No need to do any math.
Sufficient.
The correct answer is
D.
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