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Can't solve this!

by ketaki6 » Thu Jul 28, 2011 7:41 pm
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 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.

a. Statement 1 alone
b. Statement 2 alone
c. Both together
d. Each alone sufficient
e. 1 and 2 not sufficient together


I understand 1. But I just don't get how 2. works out. Help please.
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by sanju09 » Sat Jul 30, 2011 3:26 am
ketaki6 wrote: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 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.

a. Statement 1 alone
b. Statement 2 alone
c. Both together
d. Each alone sufficient
e. 1 and 2 not sufficient together


I understand 1. But I just don't get how 2. works out. Help please.

(1) If Jane's payment was credited on the 21st day of the billing cycle, then the average daily balance for the 30-day billing cycle can be given by

$(20 × 600 + 10 × 300)/30. Sufficient

(2) Let Jane's payment was credited on the nth day of the billing cycle, then the average daily balance through the 25th day of the billing cycle can be given by

$[(n - 1) × 600 + (25 - n + 1) × 300]/25 = $540 (given);

n can be uniquely found out and hence the average daily balance for a 30-day billing cycle. [spoiler]Sufficient

D[/spoiler]
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by GMATGuruNY » Sat Jul 30, 2011 4:12 am
ketaki6 wrote: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 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.

a. Statement 1 alone
b. Statement 2 alone
c. Both together
d. Each alone sufficient
e. 1 and 2 not sufficient together


I understand 1. But I just don't get how 2. works out. Help please.
To determine the average of the daily balances for the whole month, we need to determine when Jane made the $300 payment.

Statement 1: Jane's payment was credited on the 21st day of the billing cycle.
Sufficient.

Statement 2: The average daily balance through the 25th day of the billing cycle was $540.
If statement 2 also is sufficient, it must confirm the same information given in statement 1: that the payment was made on the 21st day.
Total for 20 days with an average daily balance of 600 = 20*600 = 12000.
After the payment is made, total for 5 days with an average daily balance of 300 = 5*300 = 1500.
Average for the first 25 days = (12000+1500)/25 = 13500/25 = 540.
Thus, the payment was made on the 21st day.
If the payment had been made on any other day, the total for the first 25 days would change, yielding an average higher or lower than 540.
Sufficient.

The correct answer is D.
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by ketaki6 » Sat Jul 30, 2011 9:13 am
Thanks a lot. The mistake I made was I assumed payment to the account means payment towards his account. So instead of doing 600 - 300, I did 600 + 300.
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