anilnandyala wrote:
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 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.
To determine the average daily balance for the 30 days, we need to know the SUM of the 30 daily balances.
The daily balance starts at $600.
At some point, the daily balance decreases to $300 and stays at $300 for the remainder of the month.
Implication:
To calculate the sum of the daily balances for the 30 days, we need to know when the $300 payment was made.
Statement 1:
SUFFICIENT.
Statement 2:
For the first 25 days to yield an average of $540, we can determine exactly how many $600 days must be combined with $300 days.
Thus, we can determine when the $300 payment was made.
SUFFICIENT.
An additional way to evaluate Statement 2:
Statement 1 indicates that the $300 payment was made on the 21st day, implying that the balance decreases from $600 to $300 on the 21st day.
The two statements cannot contradict each other.
Thus, making the $300 payment on the 21st day (as required by Statement 1) MUST yield an average of $540 for the first 25 days (as required by Statement 2).
Otherwise, the two statements would be giving contradictory information.
Clearly, if the balance decreases from $600 to $300 EARLIER than the 21st (implying a greater number of $300 days) or LATER than the 21st (implying a greater number of $600 days), the average for the first 25 days will not remain $540.
Implication:
For the first 25 days to yield an average daily balance of $540, the balance must decrease from $600 to $300 on the 21st day.
Thus, the payment was made on the 21st day.
SUFFICIENT.