Data Sufficiency

On Jane's credit card account, the average daily balance for a 30 day billing cycle is average(arithmetic mean) of the daily balances at the end 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 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 of the billing cycle.
2) The average daily balance through the 25th day of the billing cycle was $540.

aditiniyer wrote:On Jane's credit card account, the average daily balance for a 30 day billing cycle is average(arithmetic mean) of the daily balances at the end 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 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 of the billing cycle.
2) The average daily balance through the 25th day of the billing cycle was $540.

To calculate the average daily balance, we need to know which day Jane made her $300 payment. (Once she makes her payment, her balance will go from $600 to $300. If we call the number of days her balance is at 600 "s" and the number of days her balance is at 300 "t" then her average balance for the month will be [600s+ 300t]/30

Statement 1: clearly sufficient. If she made her payment on the 21st day of the month, she'd have s = 20 days with a balance of 600 and t = 10 days with a balance of 300 for the month. We can certainly calculate the average balance.

Statement 2: We know that we had days with a balance of 300 and days with a balance of 600. The overall average of those first 25 days was 540. Plot out the numbers on a number line:

300-------------540-----600
Gap:-----240--------60

For those first 25 days, the ratio of days during which the balance was 600: days balance was 300 would be 240/60 = 4/1. In other words, of those first 25 days, we had four times as many days with a balance of 600 as days with a balance of 300. Thus, there must have been 20 days with a balance of 600 and 5 days with a balance of 300, and the payment occurred on the 21st day. The same info we had in statement 1. Sufficient.

The answer is D

aditiniyer wrote:On Jane's credit card account, the average daily balance for a 30 day billing cycle is average(arithmetic mean) of the daily balances at the end 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 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 of the billing cycle.
2) The average daily balance through the 25th day of the billing cycle was $540.

Average = (sum of the daily balances)/(number of days) = (sum of the daily balances)/30.
To determine the average, we need to know the SUM of the daily balances.
Every day the balance is either $600 or $300: once the balance decreases to $300, it remains at $300 for the rest of the month.
Implication:
To calculate the sum of the daily balances, we need to know when Jane made the $300 payment.

Question stem, rephrased:
On what day did Jane make the $300 payment?

Statement 1: Jane's Payment was credited on the 21st of the billing cycle.
SUFFICIENT.

Statement 2: The average daily balance through the 25th day of the billing cycle was $540.
If we understand how DS problems are constructed, NO WORK IS NEEDED HERE.

Statement 1 indicates that the $300 payment was made on the 21st day.
Since the two statements cannot contradict each other, the information in Statement 1 -- a payment of $300 on the 21st day -- must also satisfy statement 2.
Implication:
If the $300 payment is made on the 21st day, then the average for the first 25 days will be $540.

By extension:
If the payment is made BEFORE the 21st day, then the average for the first 25 days will decrease below $540, since there will be fewer days with the higher amount ($600) and more days with the lower amount ($300).
If the payment is made AFTER the 21st day, then the average for the first 25 days will increase above $540, since there will be more days with the higher amount ($600) and fewer days with the lower amount ($300).
Implication:
For the first 25 days to have an average daily balance of $540, the $300 payment MUST be made on the 21st day, as indicated in Statement 1.
SUFFICIENT.

The correct answer is D.