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OG 12th Ed: DS#161 - Is there a faster way?

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OG 12th Ed: DS#161 - Is there a faster way?

by sashish007 » Sun Nov 21, 2010 9:55 am
Hi there - I solved a bunch of OG problems in a timed-session BUT this problem sucked up all my time.
Is there a faster method than the OG explains, please?

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Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month 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 $2600, what was the range of 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.
-----------------------------------

Thanks in advance!
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Source: — Data Sufficiency |
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by David@VeritasPrep » Sun Nov 21, 2010 7:01 pm
This is clearly not an easy question, given where it is located in the OG (161 out of 174), but it is the type of question that I love because it does not rely on pure math but illustrates the quantitative reasoning aspect of the GMAT.

So as I read this question I said, "good this is a data sufficiency so I don't need to calculate the range, I just need to know when Carl stops adding $120 dollars and starts withdrawing $50 each month.

There are two facts that are very important here - 1) Carl either adds or subtracts each month - there are no months that he has no activity and 2) he adds from the beginning (January) until he stops adding, then he starts withdrawing and he withdraws every month until the end of the year.

So if we can find two things we can solve:

A) the month when the adding stops and the subtracting begins and

B) the balance on any particular month.

So let's evaluate the statements, Statement 1 let's you know that May is still in the addition column since we know from the question stem that the balance at the end of May is $2600 and statement 1 tells us the balance at the end of April was less than $2625. This is not high enough to subtract $50 and get the $2600 balance at the end of May. So May is still an addition month. However, we do not yet know when the subtraction starts. So this is not sufficient.

Statement 2 tells us that balance at the end of June was less than $2675. Combined with that helpful fact from the question stem (the balance at the end of May was $2600) we know that June had to be a subtraction month since the balance would be $2720 at the end of June if it was an addition month. However, we don't know from this statement if June was the first subtraction month.

When you take them together you see that May is addition and June is the first subtraction - so you have the first thing we were looking for. And the question stem gives you the balance for the end of May so we have the second thing we were looking for as well. Remember - no need to solve it, it is enough to know that you can.

I hope that seems clear...I enjoyed it!
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by sashish007 » Sun Nov 21, 2010 11:01 pm
Thank you David, this is a much better explanation!

I will have to say that OG is not entirely perfect when explaining certain answers. The phrase "at least two possible ranges" baffled me whereas it meant that "more than one range is possible for either statement alone". And if answer explanations take so much time, the question is an even bigger leap! So, I had to resort to a home-grown recipe last night to explain myself, although it is heavily quantitative:

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To find the range we should know:
1. Balance before he started depositing - initial balance = x (we know that there was initial balance because for may balance is 2600 and maximum amount he could deposited from this period is 5 months *5=600)
2. Till what month he deposited $120
3. From which month he started withdrawing $50

(1) April balance< 2625 --> he deposited in May (because if he didn't April balance=2600+50=2650 and we know that in April balance was<2625) So for may balance=2600=x(initial balance)+5months*120 --> x+600=2600 --> x=2000. We know initial balance, but we still don't know: till what month he deposited $120 and from which month he started withdrawing $50
Not sufficient
(2) June balance < 2675 --> he didn't deposited in June --> he withdraw in June (if he deposited, in June deposit would be May balance 2600+120=2720>2675)
Not sufficient

(1)+(2) we know:
Initial balance: x=2000
Till what month he deposited $120: till May
From which month he started withdrawing $50: from June
Sufficient C.
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by maihuna » Sun Jan 02, 2011 12:43 pm
David@VeritasPrep wrote:This is clearly not an easy question, given where it is located in the OG (161 out of 174), but it is the type of question that I love because it does not rely on pure math but illustrates the quantitative reasoning aspect of the GMAT.stops and the subtracting begins and
as well. Remember - no need to solve it, it is enough to know that you can.

I hope that seems clear...I enjoyed it!
I am mostly concern on this concept as a PS problem, is there a way to solve if the same Q is frame as an PS, we know gmat does it.
Charged up again to beat the beast :)
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by David@VeritasPrep » Sun Jan 02, 2011 1:25 pm
maihuna -

Please re-read my explanation and that of sasish007. You can see that we were each just one quick step from actually solving. We know that the balance at the end of May was $2600 from the question stem. From the facts in statement 1 and 2 we know that $120 was added each month right up to May and that beginning in June $50 was subtracted. So the low end of the range would be $2600 - ($120*5) for the months Jan. Feb. March, April and May = these are the months when $120 was added so now we subtract to get the beginning balance for January. So the smallest amount was $2600 - $600 = $2000. So this is the low mark in the bank. We know that subtracting $50 for 7 months will not get us lower than we were in January.

Now the high mark need not be calculated since we are told that $2600 is the balance in May and since we are now subtracting to the end of the year then they high balance would be $2600.

So the way I see it, the answer is $2000 to $2600.

Does that help?
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