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On Jane's credit card account, the average daily balance for [#permalink]

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21 Dec 2010, 09:26

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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.

Re: On Jane's credit card account, the average daily balance for [#permalink]

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21 Dec 2010, 10:24

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anilnandyala 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 substracted 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.

Re: On Jane's credit card account, the average daily balance for [#permalink]

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31 Dec 2010, 05:37

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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 ...

Re: On Jane's credit card account, the average daily balance for [#permalink]

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31 Dec 2010, 09:45

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jonblazon wrote:

Could someone please help me with this one?

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 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.

Thanks!

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:

Attachment:

Ques1.jpg [ 3.77 KiB | Viewed 11391 times ]

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:

Attachment:

Ques2.jpg [ 3.9 KiB | Viewed 11387 times ]

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.

Re: On Jane's credit card account, the average daily balance for [#permalink]

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22 Feb 2011, 13:11

VeritasPrepKarishma wrote:

jonblazon wrote:

Could someone please help me with this one?

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 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.

Thanks!

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:

Attachment:

Ques1.jpg

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:

Attachment:

Ques2.jpg

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)

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

Re: On Jane's credit card account, the average daily balance for [#permalink]

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18 Nov 2011, 14:05

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 to or subtracted from the account during the billing cycle, what was 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.

Struggling to solve this. Can you please help? OA is not provided. _________________

Re: On Jane's credit card account, the average daily balance for [#permalink]

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19 Nov 2011, 23:39

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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$.

Re: On Jane's credit card account, the average daily balance for [#permalink]

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04 Feb 2012, 14:17

Expert's post

enigma123 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 to or subtracted from the account during the billing cycle, what was 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.

Struggling to solve this. Can you please help? OA is not provided.

Merging similar topics. Please ask if anything remains unclear. _________________

Re: On Jane's credit card account, the average daily balance for [#permalink]

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05 Jul 2012, 19:06

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 ??

Re: On Jane's credit card account, the average daily balance for [#permalink]

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05 Jul 2012, 22:02

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smartmanav wrote:

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.

Re: On Jane's credit card account, the average daily balance for [#permalink]

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10 Oct 2012, 06:23

VeritasPrepKarishma wrote:

smartmanav wrote:

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.

Re: On Jane's credit card account, the average daily balance for [#permalink]

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28 Nov 2013, 05:50

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Re: On Jane's credit card account, the average daily balance for [#permalink]

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28 Nov 2013, 05:55

Bunuel wrote:

anilnandyala 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 substracted 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.

Bunuel, what is the purpose of the first sentence in the question. Has it been mentioned to simply confuse or am I missing something?

Re: On Jane's credit card account, the average daily balance for [#permalink]

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13 Dec 2014, 00:20

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Re: On Jane's credit card account, the average daily balance for [#permalink]

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16 Feb 2016, 20:55

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