a tough OG arithmetic word problem

[Redhorsep]

Hi,

I came across this problem in OG 11ed and just the wording totally threw me off:

On Jane's credit card account, the average daily balance for a 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.

I was stumped because this didn't seem like a regular arithmetic problem so I couldn't apply the simple formula for it directly. And even just reading the answer is so difficult to understand. Would someone please offer an easy way to solve this?

I also wonder on the real test if it's humanly possible to do this in 2 minutes, if not, is there a way to make an educated guess on the problem? If none is possible, what level of difficulty do you think this is at and will letting it go seriously affect my quant performance since I'm aiming for 700+?

Thanks!

[Gmatism]

I think it's A.

(1) Jane was holding $600 until the day 21 and then for the remaining 9 days she held $300.00 in her account. From that you can calculate the average.

(2) Not sufficient since it doesn't tell us anything about the days from 25 thru 30.

What is the correct answer BTW?

[Anurag@Gurome]

Hi,

I came across this problem in OG 11ed and just the wording totally threw me off:

On Jane's credit card account, the average daily balance for a 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.

I was stumped because this didn't seem like a regular arithmetic problem so I couldn't apply the simple formula for it directly. And even just reading the answer is so difficult to understand. Would someone please offer an easy way to solve this?

I also wonder on the real test if it's humanly possible to do this in 2 minutes, if not, is there a way to make an educated guess on the problem? If none is possible, what level of difficulty do you think this is at and will letting it go seriously affect my quant performance since I'm aiming for 700+?

Thanks!

We need to find the average daily balance on Jane's account for the whole month. It is given in the question that no other amounts were added to or subtracted from the account during the billing cycle, so the balance remains unchanged, that is $300, for the remaining month. This means that we can reword the question as "On which day did Jane make the payment?"

Statement 1 directly gives the answer to the question, which is the 21st day of the billing cycle; SUFFICIENT.

Statement 2: Let us assume that Jane makes the payment on Nth day.
Then for N - 1 days, the balance was $600.
For 25 - (N - 1) or 26 - N days, the balance was $300.
The average balance = [(N - 1)600 + (26 - N)300]/25 = 540, which can be solved to find the value of N; hence SUFFICIENT.

The correct answer is D.