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.
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