On Jane's credit card account, the average daily balance for the 30day 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 30day 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.
Answer: D
Source: GMAT Prep
On Jane's credit card account, the average daily balance for the 30day billing cycle is the average (arithmetic mean)
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$$Average\ balance\ at\ the\ end\ of\ 30\ days=\frac{sum\ of\ daily\ balance}{30\ days}$$
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
$$Average\ for\ 25\ days=\frac{\left(x\cdot600\right)+\left[\left(25x\right)\cdot300\right]}{25}$$
$$$540=\frac{600x300x+7500}{25}$$
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.
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
$$Average\ for\ 25\ days=\frac{\left(x\cdot600\right)+\left[\left(25x\right)\cdot300\right]}{25}$$
$$$540=\frac{600x300x+7500}{25}$$
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.