On Jane's credit card account, the average daily balance for 30-day billing cycle is the average (arithmetic mean) of the...

Understanding the Question

We need to find the average daily balance for Jane's 30-day billing cycle.

Here's what we know:

• Jane starts with a balance of $600
• She makes one $300 payment during the cycle
• After the payment, her balance drops to $300
• The average daily balance is the arithmetic mean of all 30 daily balances

The key insight: The average depends entirely on when Jane makes her payment. If she pays early in the cycle, she'll have more days at the lower $300 balance, resulting in a lower average. If she pays late, she'll have more days at the higher $600 balance, resulting in a higher average.

For sufficiency, we need to determine the exact timing of the payment to calculate the precise average.

Analyzing Statement 1

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

This gives us complete timing information:

• Days 1-20: Balance = $600 (20 days)
• Days 21-30: Balance = $300 (10 days)

With this information, we can determine the exact average. We know precisely how many days Jane maintained each balance level, which is all we need to calculate the weighted average.

[STOP - Sufficient!] Statement 1 alone is sufficient.

This eliminates choices B, C, and E.

Analyzing Statement 2

Now we forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us: "The average daily balance through the 25th day of the billing cycle was $540."

This partial information creates two critical problems:

Problem 1: We can't pinpoint when the payment occurred
The $540 average (which falls between $300 and $600) tells us the payment must have happened sometime before day 25. However, multiple payment dates could yield this same 25-day average. For example:

• Payment on day 15 could give us a 25-day average of $540
• Payment on day 20 could also give us a 25-day average of $540
• Different combinations of timing could produce the same partial average

Problem 2: We have no information about days 26-30
Even if we could somehow deduce the exact payment date from the 25-day average, we still don't know what happens in the final 5 days. Without knowing the balance for days 26-30, we cannot calculate the full 30-day average.

Statement 2 is NOT sufficient to answer the question.

This eliminates choice B.

The Answer: A

Statement 1 alone is sufficient because it tells us exactly when the payment occurred, allowing us to calculate the precise 30-day average. Statement 2 alone is not sufficient because it only gives us partial information about the first 25 days and tells us nothing about the final 5 days.

Since Statement 1 alone is sufficient and Statement 2 alone is not sufficient, the answer is Choice A.