on jane's credit card account, the average daily balance for a 30-day billing cycle is the average of the daily balances at the end of each of the 30 day. 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) Average daily balance through the 25th day of the billing cycle was $450. [editor: this should say 540, not 450.]

This answer is said to be D but I have absolutely no idea how to even begin to compute statement (2). We still have to consider the $300 payment made @ sometime during the billing cycle. How can statement (2) be viable if we don't know when to apply the payment. Do we apply it on the second day? On the 29th day? How does this exactly work?

the key to this question is rephrasing.
instead of the question that's actually posed here, you can ask the following question: on which day did jane make the payment?

there are two ways you can get this rephrase:
* use intuition
the later jane makes the payment, the higher the average daily balance on her account. therefore, any unique value for the account balance must correspond to a unique day on which the payment was made, and vice versa. so, knowing the day on which the payment was made is equivalent to knowing the average daily balance, and vice versa.
* use algebra
if jane makes the payment on day #n, then there are (n - 1) days for which the balance is $600, and 30 - (n - 1) = (31 - n) days for which the balance is $300. therefore, the average balance is (600(n - 1) + 300(31 - n)) / 30. this is a linear expression, so it can be solved uniquely for n. therefore, asking for the value of this expression is equivalent to asking for n itself.

so, there's the rephrase: on which day did jane make the payment?

--

once you have this:

statement (1) is immediately sufficient; you don't even have to do anything.

statement (2) can be handled using exactly the same techniques used for the rephrase above:
* use intuition
the later jane makes the payment, the higher the average daily balance on her account. therefore, any unique value for the account balance must correspond to a unique day on which the payment was made, and vice versa. so, knowing the day on which the payment was made is equivalent to knowing the average daily balance, and vice versa. so, since you know the balance, you know on which day the payment was made, so this is sufficient.
* use algebra
if jane makes the payment on day #n, then there are (n - 1) days for which the balance is $600, and 25 - (n - 1) = (26 - n) days for which the balance is $300. therefore, the average balance is (600(n - 1) + 300(26 - n)) / 25. this is a linear expression, so it can be solved uniquely for n. therefore, if you are given the value of this expression, then, perforce, you also have the value of n..

so each statement is individually sufficient.
[editor: fixed an arithmetic error that was in this post before.]

so Ron, how is one supposed to answer questions like these within 2 mins?

Seems to me if one is relying on their intuition then it should be way up there and if it is algebra one is relying on then 2 mins does not seem sufficient, unless ofcourse one already knew how to solve the problem before hand!

They dont want to know the answer buddy. they want to know whether the data can answer the question.

The key to answering this question is tht in the 2nd option where it says the average is 450$ for 25 days makes it obvious tht somewhere in the 1st 25 days payment of 300$ was made so forget the 300$. its quite simple now. avg for 25 days is 450. rest of the days is 300. there's ur answer champ.

you don't strictly have to answer questions within two minutes.
two minutes is the average time per problem. since this is an average, it goes without saying that you can exceed two minutes (say, 2:30-2:45), somewhat regularly, on more difficult problems. after all, you'll have easier problems on which you take less than two minutes.

the real problems arise if you let yourself take more than 3 minutes. you should pretty much always cut the rope at 3 minutes, unless you're working on a solution that is 100% GUARANTEED to work.



i'm sorry; i don't know what you mean by "way up there". could you explain please?



remember that this is data sufficiency, not problem solving. you don't have to do the algebra.
a big, big part of solving data sufficiency problems efficiently, especially data sufficiency word problems, is realizing when you do and don't actually have to solve all the way through.

Thank you Chintan and Ron.

Ron, what I meant by "way up there" was someone with very high level of intuition..anyways forget that, thats water under the bridge :)

Gotcha. But note that Ron's point still holds, even with the timing element: the secret to this problem is rephrasing. Sure, it takes practice, but this problem CAN be done in under 2 minutes. There are a handful of "minor type" word translation problems that you might explore, so as to practice your flexibility.

Ron,

Don't you think : 30 - (n - 1) = should be equated to (31-n) rather than to (29 - n).

Ranveer

nice catch.

i went back and edited that particular error out of the post. thanks.

We are taught that Statement 1 and 2 are always true..In this case there seems to be a discrepancy..St 1 says the entire payment ($300) was paid on the 21st, while statement 2 says $150 paid by the 25th day and we still have a 150 to go..how is this possible? What am I interpreting wrong here?

thanks

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

(2) Average daily balance through the 25th day of the billing cycle was $450.

read statement (2) again; it says that the AVERAGE daily balance THROUGH the 25th day.
this means that if you take ALL 25 of the daily balances from the 1st-25th (some of which are $600 and the rest of which are $300), and average them, you'll get this figure.

you're misreading it as "THE daily balance ON the 25th".

Can the MGMAT Instructors kindly suggest the difficulty level of this problem?

Difficulty level is determined by who gets it right and who gets it wrong, not by the subjective sense of difficulty, the sophistication of the operations involved, how long it takes, anything else. Lots of very good test-takers get this wrong, and it's a crap shoot for all but very good test-takers, so I suspect it's 700-800.

You might be able to infer something about the difficulty by the context in which you encountered the question. Did it follow correct answers to a number of other difficult questions? That would be more evidence that it's difficult.

If you're asking so that you don't waste time preparing for questions harder than any you're likely to see on the test, fine. Don't worry during the test about difficulty, though. It's hard to judge, and the attempt will waste your time and energy.