Question basically ask on which day did Jane make the payment of $300.

Or algebraically: \(average \ daily \ balance=\frac{x*600+(30-x)*300}{30}\) --> for the first \(x\) days the balance will be $600 and then for \((30-x)\) days the balance will be $600-$300=$300 (meaning that Jane made a payment of $300 on the (x+1)st day). So all we need to know is on which day did Jane make the payment of $300, the value of x+1.

(1) Jane's payment was credited on the 21st day of the billing cycle --> directly gives the value of \(x+1\) --> \(x+1=21\) --> \(x=20\): for 20 days the balance was $600 and for the rest 10 days (from 21st) it was $300 --> we can find the average daily balance. Sufficient.

(2) The average daily balance through the 25th day of the billing cycle was $540 --> \(average_{25 \ days}=540=\frac{x*600+(25-x)*300}{25}\) --> we can find \(x\) --> we can find the average daily balance. Sufficient.

Answer: D.
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At the staring of the month we have 600$. Some where in the middle 300$ is withdrawn. If we know the date when this happened or the average on a date after the amount is withdrawn. We can find a soln.

S1: amount withdrawn on 21st. Hence :

av = (20*600+10*300)/30
av = 500. Sufficient

S2: given av as 540 on 25th. As the average is less than 600$ we know as of 26th the amount in the account is 300$.

hence
av= (25*540+5*300)/30
av= 500
Sufficient.

Hence D

1)you know that for the first 20 days you have a balance of 600, for the following a balance of 300 and then just averaging

2)you know that for the first 25 days the average balance is 540 and for the following days you have a balance of 300 each. Just take 25*540 + 5*300 and divide it by 30 again ...

Hope I could help you!

Long question stem... Though try to identify that the question is just testing you on weighted averages. For some days the account had $600, for rest of the days, the account had $300 in it. We need to find the average of the amount in the account (it is weighted because the two amounts could have been in the account for different durations.)

Stmnt 1 - We know now that the account had $600 for 20 days and $300 for the rest of the 10 days. You can easily find the average. Sufficient.

You don't need to since it is a DS question, but if you had to find the average, then Avg = (600*20 + 300*10)/30 = 500
or using scale method:

Stmnt 2 - Average for first 25 days = 540 so you can find for how many of these 25 days, the account balance was 600 and for how many was it 300. The rest of the 5 days, the balance was of course $300. Hence sufficient.

If you want to do the calculations:


No of days $300 balance : No of days $600 balance = 1:4
So out of 25 days, (1/5)*25 = 5 days, the balance was $300.
(4/5)*25 = 20 days the balance was $600.

Answer (D)
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Interesting approach but i find the algebraic formula easier. Esp for the second statement. This seems time consuming

I need more help here
read the 2nd statement : The average daily balance through the 25th day of the billing cycle was $540.

Perhaps the payment was deducted from her account n 27th day but they just provided the avg for first 25 days , in that case we will not be able to solve it. No ??

The average of the 25 days is $540. If the average were $600, only then can we say that the deduction was made after the 25th day. Since the average is less than $600, the deduction must have been made before the 25th day. Only then can the average be less than 600.

Now, it is simple to find the average (even though you don't need to)

For 25 days, the average balance was $540 and for 5 days, it was $300.

Avg = (540*25 + 300*5)/30 = 500
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To determine the average daily balance for the 30 days, we need to know the SUM of the 30 daily balances.
The daily balance starts at $600.
At some point, the daily balance decreases to $300 and stays at $300 for the remainder of the month.
Implication:
To calculate the sum of the daily balances for the 30 days, we need to know when the $300 payment was made.

Statement 1:
SUFFICIENT.

Statement 2:
For the first 25 days to yield an average of $540, we can determine exactly how many $600 days must be combined with $300 days.
Thus, we can determine when the $300 payment was made.
SUFFICIENT.



An additional way to evaluate Statement 2:
Statement 1 indicates that the $300 payment was made on the 21st day, implying that the balance decreases from $600 to $300 on the 21st day.
The two statements cannot contradict each other.
Thus, making the $300 payment on the 21st day (as required by Statement 1) MUST yield an average of $540 for the first 25 days (as required by Statement 2).
Otherwise, the two statements would be giving contradictory information.
Clearly, if the balance decreases from $600 to $300 EARLIER than the 21st (implying a greater number of $300 days) or LATER than the 21st (implying a greater number of $600 days), the average for the first 25 days will not remain $540.
Implication:
For the first 25 days to yield an average daily balance of $540, the balance must decrease from $600 to $300 on the 21st day.
Thus, the payment was made on the 21st day.
SUFFICIENT.
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Below post helped me understand this DS problem. Sir Ron Purewal RonPurewal has explained it very well. I posted this link here if it helps any one else.

https://www.manhattanprep.com/gmat/foru ... t6750.html
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From the question stem, we know that Jane made a payment of $300 sometime during her 30-day billing cycle. There were no other transactions in her account. The problem turns on deciphering when the payment of $300 was made. Once we know the exact day of the payment, we can easily calculate her average daily balance, as we will know the exact amounts in her accounts for each of the 30 days.

(1) Jane's payment was credited on the 21st day of the billing cycle.

We are given explicit information about when Jane's payment was made. SUFFICIENT

Her average daily balance in $ = [(20 days)*($600) + (10 days)*($300)]/30 days

(2) The average daily balance through the 25th day of the billing cycle was $540.

Did Jane make her payment sometime during the first 25 days or did she make her payment in the last 5 days of the billing cycle?

If Jane had not made her payment during the first 25 days, her average daily balance would have been (25 days)*($600)/25 days = $600. But we are told that the average daily balance was $540, which is less than $600. So we know that Jane made a payment of $300 sometime during the first 25 days.

Let 'x' be the number of days during the first 25 days when Jane had an average daily balance of $600. Then, '25 - x' will be the number of days when Jane had an average daily balance of $300. The average of these amounts computed over 25 days should equal $540.

[(25 days)*($600) + (25-x days)*($300)]/25 days = $540

Solve for x: x = 20 days.

Therefore, Jane made her payment on the 21st day of the billing cycle. This information is also consistent with the information provided in statement (1).

Note that we are not required to make these calculations. It is sufficient to know that we can calculate Jane's average daily balance with the $300 payment.

Statement (2) is SUFFICIENT

ANSWER: (D)

Why aren't we considering the factor that the total payment of $300 can be a summation of various smaller payments? Why are we considering only transaction? The stem never mentions that only one transaction was done.

Very good point -- it could be MULTIPLE small payments, adding up to 300 $

We know it was ONE payment of 300 $ because of the question stem, specifically this wording "Jane made a payment of $300"