GMATGuruNY wrote:

lavinia 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 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

We should ask ourselves the following questions:

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 remainder 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, the level at which it will remain 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.

Statement 1:
Tells us that the payment was made on the 21st day of the month. Sufficient.

Statement 2:
Ideally, we should recognize that for the average of the 25 days to be 540, we can determine exactly how many days at 600 and exactly how many days at 300 will be needed. Thus, we can determine on which day the $300 payment was made. Sufficient.

If we don't recognize what was discussed above, here's a neat trick:
If statement 2 also is sufficient, it will have to confirm the information given in statement 1: that the payment of 300 was made on the 21st day. Let's try it out:
Total for 20 days at $600/day = 20*600 = 12,000.
Total for 5 days at $300/day = 5*300 = 1500.
Average for all 25 days = (12000 + 1500)/25 = 540.
Success! Like statement 1, statement 2 tells us that the payment was made on the 21st day. Sufficient.

The correct answer is D.

lavinia 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 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!