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On Jane's credit card account, the average daily balance for 30-day bi

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On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 02:05
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On Jane's credit card account, the average daily balance for 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-jane-s-credit-card-account-the-average-daily-balance-for-106680.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Sep 2014, 04:51, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 02:13
1)suff.
balance of first 20 days are 600, last 10 days are 300. We can find average.
2)suff.
balance of first 25 days are 450, last 5 days are 300. We can find average.

D.
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 09:55
maliyeci wrote:
1)suff.
balance of first 20 days are 600, last 10 days are 300. We can find average.
2)suff.
balance of first 25 days are 450, last 5 days are 300. We can find average.

D.

for stmt2 we cannot say that last 5 days the balance is 300.
Since the average balance is less than 600 for the first 25 days, the 300 credit has already been made on one of the days from 1-25.

However, if we consider the average for the first 25 days to be 450 then we can find the exact day on which the credit of 300 was made using:

(n-1)*600 + [ 25-(n-1)]*300 / 25 = 450, where n is the day on which 300 was credited
no need to calculate, but once we get this exact day we can calculate the monthly average since for n days balance was 600 and rest 30-n days the balance was 300...just like in stmt 1
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 10:30
Economist wrote:
maliyeci wrote:
1)suff.
balance of first 20 days are 600, last 10 days are 300. We can find average.
2)suff.
balance of first 25 days are 450, last 5 days are 300. We can find average.

D.

for stmt2 we cannot say that last 5 days the balance is 300.
Since the average balance is less than 600 for the first 25 days, the 300 credit has already been made on one of the days from 1-25.

However, if we consider the average for the first 25 days to be 450 then we can find the exact day on which the credit of 300 was made using:

(n-1)*600 + [ 25-(n-1)]*300 / 25 = 450, where n is the day on which 300 was credited
no need to calculate, but once we get this exact day we can calculate the monthly average since for n days balance was 600 and rest 30-n days the balance was 300...just like in stmt 1



I agree with the answer D. However, I think you can make it easier by calculating the balance directly:
\frac{25\times 450+5\times 300}{30}=425

But this value (425) contradicts the balance of 500 from stmt 1. I think the balance in statement 2 is wrong...it should be 540...that is the only value for the first 25 days that will give the average 30 day balance of 500.
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 10:57
LenaA wrote:
Economist wrote:
maliyeci wrote:
1)suff.
balance of first 20 days are 600, last 10 days are 300. We can find average.
2)suff.
balance of first 25 days are 450, last 5 days are 300. We can find average.

D.

for stmt2 we cannot say that last 5 days the balance is 300.
Since the average balance is less than 600 for the first 25 days, the 300 credit has already been made on one of the days from 1-25.

However, if we consider the average for the first 25 days to be 450 then we can find the exact day on which the credit of 300 was made using:

(n-1)*600 + [ 25-(n-1)]*300 / 25 = 450, where n is the day on which 300 was credited
no need to calculate, but once we get this exact day we can calculate the monthly average since for n days balance was 600 and rest 30-n days the balance was 300...just like in stmt 1



I agree with the answer D. However, I think you can make it easier by calculating the balance directly:
\frac{25\times 450+5\times 300}{30}=425

But this value (425) contradicts the balance of 500 from stmt 1. I think the balance in statement 2 is wrong...it should be 540...that is the only value for the first 25 days that will give the average 30 day balance of 500.


I think you have assumed that for the last 5 days the balance was 300. This is only possible if on the 25th day 300 was credited into the account.
At the beginning of the month bal was 600, on 25th day the average balance reduced, which means that the 300 credit has taken place in the first 25 days (not necessarily on the 25th day)...if it was on the first day itself then average will be less, if it is on 24th day for example then average will be higher. So in any case we need to find the exact day on which 600 became 600-300=300.

Anyhow, the answer is D.
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 11:22
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I did not assume that. I assumed that the charge ocurred during the first 25 days

If you denote x_i to be the balance on the day i, i={1,2,...30},

\frac{\sum_{i=1}^{25} x_i}{25}=450

\sum_{i=1}^{25} x_i=450\times 25

\frac{\sum_{i=1}^{30} x_i}{30}=\frac{\sum_{i=1}^{25} x_i+\sum_{i=26}^{30} x_i}{30}=\frac{450\times 25 + 300\times 5}{30}

Am i missing something
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 15:09
LenaA wrote:
I did not assume that. I assumed that the charge ocurred during the first 25 days

If you denote x_i to be the balance on the day i, i={1,2,...30},

\frac{\sum_{i=1}^{25} x_i}{25}=450

\sum_{i=1}^{25} x_i=450\times 25

\frac{\sum_{i=1}^{30} x_i}{30}=\frac{\sum_{i=1}^{25} x_i+\sum_{i=26}^{30} x_i}{30}=\frac{450\times 25 + 300\times 5}{30}

Am i missing something


Totally agree..Hats off to you SigmA LenaA :)
Economists :- I think you are thinking too much in this problem..it does not matter on which day payment was made in statement 2. We know that average is less than 600 and we know the number of days and average..
whether the payment made on 1st day, 2nd day or the 25th day..it does not matter..Sum of daily averages will be equal in all the cases if given average is constant..

one more thing guys :- if statememt 1 and statement 2 gives different answers , it does not mean something is wrong..it is possible in GMAT that by solving both statements, you can get different answers, however, it is very rare but possible..
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 19:25
LenaA wrote:
I did not assume that. I assumed that the charge ocurred during the first 25 days

If you denote x_i to be the balance on the day i, i={1,2,...30},

\frac{\sum_{i=1}^{25} x_i}{25}=450

\sum_{i=1}^{25} x_i=450\times 25

\frac{\sum_{i=1}^{30} x_i}{30}=\frac{\sum_{i=1}^{25} x_i+\sum_{i=26}^{30} x_i}{30}=\frac{450\times 25 + 300\times 5}{30}

Am i missing something

You are right in a way that you are trying to calculate the weighted average, this is what the question asks. BUT we DO NOT know the values in the second set (26-30).
Lets take your approach,

For the first 25 days the av balance was 450...meaning on the ...22,23,24 day the balance can be 450,450,450 or it can be 300,300,300..or any value depending on when the 300 was credited. Now as per your formula you took 300 as the average value for 26-30 days which is a problem. How did the balance suddenly reduce/increase if no transactions were made from 25-30 days? :)

We can use the above formula only if we know all values in both the sets. I hope I answered your question.
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 02 Sep 2009, 23:40
Economist, your missing point in the problem is that wording in option II (Average daily balance through the 25th day of the billing cycle was $450)
it is through not for ;)
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 19 Nov 2009, 05:07
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The question can be quite intimidating, but look closely and you will get the right meaning
What it says is that Jane’s average daily balance for a 30 day period is equal to (the sum of Jane’s balance on each day)/no. of days

Here Jane’s month starts off with 600$ and somewhere along the line she makes a payment of 300$. If we know, when she makes that payment we will be able to calculate her avg daily balance. Now, lets look at the statements

Statement A – Says that she makes the payment on the 21st day. Therefore, her avg daily balance is –
(600*20 + 10*300)/30 = SUFFICIENT

Statement B – Says that the avg daily balance that Jane has on the 25th day is 540$, which means that Jane has made the payment of 300$ somewhere in the middle of those 25 days.
We can calculate that day by –

(x*600 + (25-x)540)/25 = 540
Knowing x from the above equation, will lead us to the Daily balance

Hope this helps
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 29 May 2010, 17:40
Can anyone kindly suggest the difficulty level of this problem?
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 23 May 2011, 12:58
D. The average daily balance through the 25th day of the billing cycle was 540. (Suff)

Approach 1-600(25-x)+300(x)/25=540--> X represent the amount of days left ending balance of 300. Add 5 more days with a balance of 300 to get the total daily balance and divide by 30 days.

Approach 2- Average of 540--> 600 is 60 away from avg while 300 is 240 away-->So ratio of the difference can be expressed as 60:240 or 1:4 ---> Since 600 is the larger of the group value it takes on the larger portion. So you can conclude that 600 daily balances make up 4/5 of the average days and that 300 daily balances make up 1/5 of the average days.
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 24 May 2011, 01:08
D it is.

since there is just one transaction the question stem itself gives a clear answer here.
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 10 Jul 2011, 03:57
Can someone explain what the question says ? and simplify what its asking?
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 27 Sep 2014, 04:27
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Re: On Jane's credit card account, the average daily balance for 30-day bi [#permalink] New post 27 Sep 2014, 04:52
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Ibodullo wrote:
On Jane's credit card account, the average daily balance for 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.


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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-jane-s-credit-card-account-the-average-daily-balance-for-106680.html
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Re: On Jane's credit card account, the average daily balance for 30-day bi   [#permalink] 27 Sep 2014, 04:52
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