The Average Daily Balance

This topic has expert replies
User avatar
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Tue Jan 10, 2012 12:12 pm

by amanpreet » Thu Feb 16, 2012 2:18 pm
The neat trick is awesome...
thank u so much.
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.

User avatar
Legendary Member
Posts: 934
Joined: Tue Nov 09, 2010 5:16 am
Location: AAMCHI MUMBAI LOCAL
Thanked: 63 times
Followed by:14 members

by [email protected] » Thu Feb 16, 2012 10:50 pm
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




May be that I solved it in a different way...


Statement 1 Alone:
= [20 X 600 + 10 X 300]/30

= 15000/30 = $500




Statement 2 Alone:

solve using algebra...

If $540 was the average balance for the first 25 days and $600 was the balance at the beginning of the month and $300 was the balance at the end of the 30 days period...

Hence lets say $600 was the balance for x number of days...

So $300 would be the balance for 25-x days...

Hence the equation would come as:

600x + 300(25-x) = 13500

300x = 6000

after solving this equation, you get the answer as 20

Then it becomes the same as the statement 1...
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.

User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Fri Feb 17, 2012 12:53 am
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!
This question has already been discussed for quite a good number of times...

(1) If Jane's payment was credited on the 21st day of the billing cycle, then the average daily balance for the 30-day billing cycle can be given by

$(20 X 600 + 10 X 300)/30. Sufficient

(2) Let Jane's payment was credited on the nth day of the billing cycle, then the average daily balance through the 25th day of the billing cycle can be given by

$[(n - 1) X 600 + (25 - n + 1) X 300]/25 = $540 (given);

n can be uniquely found out and hence the average daily balance for a 30-day billing cycle. [spoiler]Sufficient

D
[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Master | Next Rank: 500 Posts
Posts: 171
Joined: Tue Jan 08, 2013 7:24 am
Thanked: 1 times

by rajeshsinghgmat » Fri Feb 15, 2013 4:50 am
D the answer.

User avatar
Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue Jul 16, 2013 9:00 am
Location: West Virginia
Thanked: 9 times

by Java_85 » Sun Sep 08, 2013 8:09 am
IMO D

Senior | Next Rank: 100 Posts
Posts: 45
Joined: Fri Aug 30, 2013 7:51 pm

by ndqv » Fri Sep 27, 2013 7:00 am
1) Credited on 21st day
Average daily balance (ADB) for the cycle = (600*20 + 300*10)/30 = 500

2) ADB through 25th day is 540
600d + (25-d)300 = 540*25 = 13500
(payment was made on the dth day)
=> d=20

Both are sufficient => Choose D

User avatar
Junior | Next Rank: 30 Posts
Posts: 16
Joined: Tue Nov 12, 2013 11:20 am
Location: Appleton, WI
Thanked: 1 times
Followed by:3 members

by marshelle.slayton » Tue Oct 28, 2014 9:37 am
Make sure to focus on what the problem is asking for and what you need to calculate the answer. In this case a calculation is not needed because you have all of the pieces to the puzzle. The more DS questions you do, the better and fast you can become and determining if you have enough information! I used to not like DS problems and now they are faster and easier than PS questions.