$$Average\ balance\ at\ the\ end\ of\ 30\ days=\frac{sum\ of\ daily\ balance}{30\ days}$$
Jane's credit card account had a balance of $600, and Jand made a payment of $300 during the cycle. So, we can say the balance on the credit card account is either $600 or $300 and once it decreases to $300, it stays at $300 for the rest of the month.

For the sum of the daily balance, we have to figure out when Jane made the $300 payment to estimate the sum of daily balances.

Statement 1: Jane's payment was credited on the 21st day of the billing cycle.
The account had a $600 balance for 20 days starting from the 21 daily balance became $300 for the next 30 days.
Sum of daily balance = (20 * 600) + (10 * 300)
= 12000 + 3000 = 15,000
$$Average\ balance\ at\ the\ end\ of\ 30\ days=\frac{15000}{30}=500$$
Statement 1 is SUFFICIENT

Statement 2: The average daily balance through the 25th day of the billing cycle was $540.
Let the number of days for $600 balance = x
no. of days for $300 balance = 25 - x
$$Average\ for\ 25\ days=\frac{\left(x\cdot600\right)+\left[\left(25-x\right)\cdot300\right]}{25}$$
$$$540=\frac{600x-300x+7500}{25}$$
13500 = 300x + 7500
300x = 6000
x = 6000/300 = 20 days
There will be 20 days for $600 and 10 days for $300 balance in the 30 days billing cycle.
Sum of daily balance = (20 * 600) + (10 * 300) = 15000
Average for 30 days = 15000/30 = 500
Statement 2 is SUFFICIENT.

Since each statement alone is SUFFICIENT, option D is the correct answer.