Data Sufficiency

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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

lavinia 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

We should ask ourselves the following questions:

What is the question asking for?
The average daily balance for the whole month.

What information have we been given?
The balance starts at 600. At some point, the balance decreases to 300 and stays at 300 for the remainder of the month.

What do we need to answer the question?
Since average = total/number of days = total/30, we need to know the total of the balances for the whole month. The balance every day is either 600 or 300, the level at which it will remain for the rest of the month. So to determine the total for the whole month, all we need to know is on which day Jane made the $300 payment.

Statement 1:
Tells us that the payment was made on the 21st day of the month. Sufficient.

Statement 2:
Ideally, we should recognize that for the average of the 25 days to be 540, we can determine exactly how many days at 600 and exactly how many days at 300 will be needed. Thus, we can determine on which day the $300 payment was made. Sufficient.

If we don't recognize what was discussed above, here's a neat trick:
If statement 2 also is sufficient, it will have to confirm the information given in statement 1: that the payment of 300 was made on the 21st day. Let's try it out:
Total for 20 days at $600/day = 20*600 = 12,000.
Total for 5 days at $300/day = 5*300 = 1500.
Average for all 25 days = (12000 + 1500)/25 = 540.
Success! Like statement 1, statement 2 tells us that the payment was made on the 21st day. Sufficient.

The correct answer is D.

Thanks GmatGuruNY for this wonderful explanation. It was difficult to figure out that we are talking about one billing cycle- one month. They introduced so many words about the process, billing cycle to confuse the student. Tricky

Moreover, if I am not sure that stament 2 is sufficient can I still use the neat trick or it is risky? I believe that it can lead the studend to choose C instead of D.

GMATGuruNY wrote:

lavinia 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

We should ask ourselves the following questions:

What is the question asking for?
The average daily balance for the whole month.

What information have we been given?
The balance starts at 600. At some point, the balance decreases to 300 and stays at 300 for the remainder of the month.

What do we need to answer the question?
Since average = total/number of days = total/30, we need to know the total of the balances for the whole month. The balance every day is either 600 or 300, the level at which it will remain for the rest of the month. So to determine the total for the whole month, all we need to know is on which day Jane made the $300 payment.

Statement 1:
Tells us that the payment was made on the 21st day of the month. Sufficient.

Statement 2:
Ideally, we should recognize that for the average of the 25 days to be 540, we can determine exactly how many days at 600 and exactly how many days at 300 will be needed. Thus, we can determine on which day the $300 payment was made. Sufficient.

If we don't recognize what was discussed above, here's a neat trick:
If statement 2 also is sufficient, it will have to confirm the information given in statement 1: that the payment of 300 was made on the 21st day. Let's try it out:
Total for 20 days at $600/day = 20*600 = 12,000.
Total for 5 days at $300/day = 5*300 = 1500.
Average for all 25 days = (12000 + 1500)/25 = 540.
Success! Like statement 1, statement 2 tells us that the payment was made on the 21st day. Sufficient.

The correct answer is D.

lavinia wrote:Thanks GmatGuruNY for this wonderful explanation. It was difficult to figure out that we are talking about one billing cycle- one month. They introduced so many words about the process, billing cycle to confuse the student. Tricky

Moreover, if I am not sure that stament 2 is sufficient can I still use the neat trick or it is risky? I believe that it can lead the studend to choose C instead of D.

GMATGuruNY wrote:

lavinia 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

We should ask ourselves the following questions:

What is the question asking for?
The average daily balance for the whole month.

What information have we been given?
The balance starts at 600. At some point, the balance decreases to 300 and stays at 300 for the remainder of the month.

What do we need to answer the question?
Since average = total/number of days = total/30, we need to know the total of the balances for the whole month. The balance every day is either 600 or 300, the level at which it will remain for the rest of the month. So to determine the total for the whole month, all we need to know is on which day Jane made the $300 payment.

Statement 1:
Tells us that the payment was made on the 21st day of the month. Sufficient.

Statement 2:
Ideally, we should recognize that for the average of the 25 days to be 540, we can determine exactly how many days at 600 and exactly how many days at 300 will be needed. Thus, we can determine on which day the $300 payment was made. Sufficient.

If we don't recognize what was discussed above, here's a neat trick:
If statement 2 also is sufficient, it will have to confirm the information given in statement 1: that the payment of 300 was made on the 21st day. Let's try it out:
Total for 20 days at $600/day = 20*600 = 12,000.
Total for 5 days at $300/day = 5*300 = 1500.
Average for all 25 days = (12000 + 1500)/25 = 540.
Success! Like statement 1, statement 2 tells us that the payment was made on the 21st day. Sufficient.

The correct answer is D.

Use the trick described above only if you've already determined that statement 1 is sufficient, in which case you can eliminate B, C and E, since the correct answer can be only A or D.

Here are more traditional ways to determine that statement 2 is sufficient:
Total for 25 days = 25*540 = 13,500.
Total for 25 days at 600/day = 25*600 = 15,000.
Difference = 15,000 - 13,500 = 1500.
Thus, number of days at 300/day = 1500/300 = 5.
Thus, 25-5 = 20 days at 600/day, so the deposit was made on the 21st day.

We also could use alligation:
Proportion needed of $600 days = 540-300 = 240.
Proportion needed of $300 days = 600-540 = 60.
Ratio of ($600 days):(300 days) = 240:60 = 4:1.
Since there are 25 days, we'll need 20 $600 days and 5 $300 days, indicating that the deposit was made on the 21st day.

If you're not sure how to use alligation, please check my post in the following thread:

https://www.beatthegmat.com/percentage-p ... 70078.html

Answer should be D.

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

We know the day on which balance came down to $300 from $600.

Sufficient

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

For the second statment- since we already know that 25 day avg balance is $540 and we also know from question that balance for remaining 5 days will be $300, so we can find avg balance.

Sufficient

Another way to quickly determine that statement 2 is sufficient

Suppose x = no of days during which the balance was 600
Suppose y = no of days during which the balance was 300

Given
x + y = 25
600x + 300y = 540.25

Now we have two equations and two unknowns, therefore the statement is sufficient.

GMATGuruNY wrote:

lavinia 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

We should ask ourselves the following questions:

What is the question asking for?
The average daily balance for the whole month.

What information have we been given?
The balance starts at 600. At some point, the balance decreases to 300 and stays at 300 for the remainder of the month.

What do we need to answer the question?
Since average = total/number of days = total/30, we need to know the total of the balances for the whole month. The balance every day is either 600 or 300, the level at which it will remain for the rest of the month. So to determine the total for the whole month, all we need to know is on which day Jane made the $300 payment.

Statement 1:
Tells us that the payment was made on the 21st day of the month. Sufficient.

Statement 2:
Ideally, we should recognize that for the average of the 25 days to be 540, we can determine exactly how many days at 600 and exactly how many days at 300 will be needed. Thus, we can determine on which day the $300 payment was made. Sufficient.

If we don't recognize what was discussed above, here's a neat trick:
If statement 2 also is sufficient, it will have to confirm the information given in statement 1: that the payment of 300 was made on the 21st day. Let's try it out:
Total for 20 days at $600/day = 20*600 = 12,000.
Total for 5 days at $300/day = 5*300 = 1500.
Average for all 25 days = (12000 + 1500)/25 = 540.
Success! Like statement 1, statement 2 tells us that the payment was made on the 21st day. Sufficient.

The correct answer is D.

Mitch,

Thank you for the wonderful explanation. Is it based on the assumption that GMAT will not give two conditions which contradict each other?

______________
Samuel

leumas wrote:

GMATGuruNY wrote:

lavinia 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

We should ask ourselves the following questions:

What is the question asking for?
The average daily balance for the whole month.

What information have we been given?
The balance starts at 600. At some point, the balance decreases to 300 and stays at 300 for the remainder of the month.

What do we need to answer the question?
Since average = total/number of days = total/30, we need to know the total of the balances for the whole month. The balance every day is either 600 or 300, the level at which it will remain for the rest of the month. So to determine the total for the whole month, all we need to know is on which day Jane made the $300 payment.

Statement 1:
Tells us that the payment was made on the 21st day of the month. Sufficient.

Statement 2:
Ideally, we should recognize that for the average of the 25 days to be 540, we can determine exactly how many days at 600 and exactly how many days at 300 will be needed. Thus, we can determine on which day the $300 payment was made. Sufficient.

If we don't recognize what was discussed above, here's a neat trick:
If statement 2 also is sufficient, it will have to confirm the information given in statement 1: that the payment of 300 was made on the 21st day. Let's try it out:
Total for 20 days at $600/day = 20*600 = 12,000.
Total for 5 days at $300/day = 5*300 = 1500.
Average for all 25 days = (12000 + 1500)/25 = 540.
Success! Like statement 1, statement 2 tells us that the payment was made on the 21st day. Sufficient.

The correct answer is D.

Mitch,

Thank you for the wonderful explanation. Is it based on the assumption that GMAT will not give two conditions which contradict each other?

______________
Samuel

Yes.
If the correct answer is D, the two statements must confirm the same information.
Thus, if statement 1 is sufficient, we can use the information in statement 1 to evaluate statement 2.
BUT WE MUST BE CAREFUL.
If the value in statement 1 satisfies statement 2, we cannot choose D until we have confirmed that NO OTHER value will satisfy statement 2.

In statement 2 in the problem above, when the payment is made on the 21st day, the average daily balance for the first 25 days is 540.
Thus, if the payment is made on ANY OTHER DAY, the average daily balance for the first 25 days will NOT be 540.
Thus, we can be sure that no other value will satisfy statement 2: the payment was made on the 21st day.
Sufficient.

By the way, if we understand that this is a weighted average question, no real math is needed.
Check my explanation here:

https://www.beatthegmat.com/arithmetic-mean-t82854.html

Thanks mitch.

Is there a simple solution for the below OG 12 DS 161 Q, which is little similar to the one above:

Beginning in January of last year, Carl made deposits
of $120 into his account on the 15th of each month
for several consecutive months and then made
withdrawals of $50 from the account on the 15th of
each of the remaining months of last year. There were
no other transactions in the account last year. If the
closing balance of Carl's account for May of last year
was $2,600, what was the range of the monthly
closing balances of Carl's account last year?
(1) Last year the closing balance of Carl's account
for April was less than $2,625.
(2) Last year the closing balance of Carl's account
for June was less than $2,675

GMATGuruNY wrote:

leumas wrote:

GMATGuruNY wrote:

lavinia 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.

Answer: D

How do you approach such a lengthy problem in less than 2 min?

Thanks!

We should ask ourselves the following questions:

What is the question asking for?
The average daily balance for the whole month.

What information have we been given?
The balance starts at 600. At some point, the balance decreases to 300 and stays at 300 for the remainder of the month.

What do we need to answer the question?
Since average = total/number of days = total/30, we need to know the total of the balances for the whole month. The balance every day is either 600 or 300, the level at which it will remain for the rest of the month. So to determine the total for the whole month, all we need to know is on which day Jane made the $300 payment.

Statement 1:
Tells us that the payment was made on the 21st day of the month. Sufficient.

Statement 2:
Ideally, we should recognize that for the average of the 25 days to be 540, we can determine exactly how many days at 600 and exactly how many days at 300 will be needed. Thus, we can determine on which day the $300 payment was made. Sufficient.

If we don't recognize what was discussed above, here's a neat trick:
If statement 2 also is sufficient, it will have to confirm the information given in statement 1: that the payment of 300 was made on the 21st day. Let's try it out:
Total for 20 days at $600/day = 20*600 = 12,000.
Total for 5 days at $300/day = 5*300 = 1500.
Average for all 25 days = (12000 + 1500)/25 = 540.
Success! Like statement 1, statement 2 tells us that the payment was made on the 21st day. Sufficient.

The correct answer is D.

Mitch,

Thank you for the wonderful explanation. Is it based on the assumption that GMAT will not give two conditions which contradict each other?

______________
Samuel

Yes.
If the correct answer is D, the two statements must confirm the same information.
Thus, if statement 1 is sufficient, we can use the information in statement 1 to evaluate statement 2.
BUT WE MUST BE CAREFUL.
If the value in statement 1 satisfies statement 2, we cannot choose D until we have confirmed that NO OTHER value will satisfy statement 2.

In statement 2 in the problem above, when the payment is made on the 21st day, the average daily balance for the first 25 days is 540.
Thus, if the payment is made on ANY OTHER DAY, the average daily balance for the first 25 days will NOT be 540.
Thus, we can be sure that no other value will satisfy statement 2: the payment was made on the 21st day.
Sufficient.

By the way, if we understand that this is a weighted average question, no real math is needed.
Check my explanation here:

https://www.beatthegmat.com/arithmetic-mean-t82854.html

leumas wrote:Thanks mitch.

Is there a simple solution for the below OG 12 DS 161 Q, which is little similar to the one above:

Beginning in January of last year, Carl made deposits
of $120 into his account on the 15th of each month
for several consecutive months and then made
withdrawals of $50 from the account on the 15th of
each of the remaining months of last year. There were
no other transactions in the account last year. If the
closing balance of Carl's account for May of last year
was $2,600, what was the range of the monthly
closing balances of Carl's account last year?

(1) Last year the closing balance of Carl's account
for April was less than $2,625.

(2) Last year the closing balance of Carl's account
for June was less than $2,675

May = 2600.

Statement 1: Last year the closing balance of Carl's account
for April was less than $2,625.
If 120 was deposited in May, then April = 2600-120 = 2480.
If 50 was withdrawn in May, then April = 2600+50 = 2650.
Since April < 2625, we know that a deposit of 120 was made in May, implying that 120 was deposited every month January through at least May.
Thus, we can determine the balance of every month January - April:
April = 2480, March = 2480-120 = 2360, etc.
No information about June - December.
Insufficient.

Statement 2: Last year the closing balance of Carl's account
for June was less than $2,675.
If 120 was deposited in June, then June = 2600+120 = 2720.
If 50 was withdrawn in June, then June = 2600-50 = 2550.
Since June < 2675, we know that a withdrawal of 50 was made in June, implying that 50 was withdrawn every month June - December.
Thus, we can determine the balance of every month June - December:
June = 2550, July = 2550-50 = 2500, etc.
No information about January - April.
Insufficient.

Statements 1 and 2 combined:
Statement 1 tells us the closing balances January - April.
The question stem tells us the closing balance in May.
Statement 2 tells us the closing balances June - December.
Combining the information above, we can determine the closing balance of every month and determine the range for the whole year.
Sufficient.

The correct answer is C.

You know that her average daily balance is just a sum of the balance on every day divided by 30. And you know that she starts with a balance of $600 and that will be her daily balance every day until she pays $300. Once she pays $300 her daily balance will be $300.

Statement A: She was credited with the $300 on the 21st. So you know that for the first 20 days her balance was 600 and for the last 10 it was 300. So, (600*20+300*10)/30=DAB. You don't have to do the math just know that you can get there. Statement A is sufficient.

Statement B: You know that if the daily balance is <600 that the payment was made at some point between the 1st and 25th day. And you know that from every point after the payment is made that the account has $300 on it. So you know that the average daily balance of the account for the entire billing cycle is (5*300+25*540)/30=DAB. Again you don't have to do the math but know you have an answer. So, B is also sufficient.

Answer is D.

The answer is D. To solve the question we need to know when the payment was made.

St1: Tells us the date of the payment. Sufficient.

St2: Again indirectly tells us the date of the payment. Sufficient.

I guess for solving DS questions under 2 mins, it is important that you develop the ability to figure out the answer without solving the whole question.

Just my 2cents. Very cliched advice...i do understand.

According to me, both the statements are sufficient. The answer should be D.

In data sufficiency one need not solve the problem, just check if it is solvable. Also don't worry if both answers are not same, they should give only one answer (Definite answer).
S1 is sufficient as one can find the avg if one knows how many times the account balance should be multiplied.
S2 is sufficient as one can find out the day when the account was credited.
Hence (D) is answer. No ned to solve hence can be solved in 1 minute.