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Beginning in January of last year, Carl made deposits of

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Beginning in January of last year, Carl made deposits of [#permalink]

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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 28 Jul 2012, 01:47, edited 3 times in total.
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Re: Tough OG12 DS#161 [#permalink]

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kotela wrote:
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.

Can anyone please help in solving this problem...??


To find the range we should know:
A. Balance before he started depositing, initial balance - we know that there was initial balance because for may balance was 2600 and maximum amount he could deposited for this period (from January till May) is: 5 months*120=600;
B. In which month Carl stopped depositing $120 and started withdrawing $50.

We have:
APRIL___MAY__JUNE
---?----$2,600----?---


(1) April balance < 2625 --> he deposited in May;

Because if he didn't then April balance would have been $2,600+50=$,2650 and we know that in April balance was<2625:
APRIL____MAY__JUNE
2,480----$2,600----?---


Notice that we can find the initial balance based on this info: $2,600=x(initial balance)+5months*120 --> x+600=2600 --> x=2000.

Though this statement is still insufficient as we still don't know in which month Carl stopped depositing and started withdrawing.

(2) June balance < 2675 --> he didn't deposited in June --> he withdrew in June.

Because if he deposited, then in June deposit would have been May balance +$120: $2,600+$120=$2,720>$2,675.
APRIL___MAY____JUNE
---?----$2,600---$2,550---

But again this statement is still insufficient as we still don't know when he started withdrawing, all we know it was not after June.

(1)+(2) We know that initial balance was $2,000 and that Carl deposited in May and started withdrawing in June:
APRIL_____MAY____JUNE
$2,480----$2,600---$2,550---


Thus we can find the range. Sufficient.

Answer: C.
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 23 Jan 2012, 11:50
Fairly tough question. I just guessed C once 2:30 hit on the timer. Luckily I got it right but it was an educated guess after following a similar approach as the user above me. I sometimes lose sight of strategy when faced with problem solving DS questions and think I always need some type of formula or chart when a picture/timeline is sufficient enough to answer the Q. Need to work on this better.
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 23 Jan 2012, 13:19
AzWildcat1 wrote:
Fairly tough question. I just guessed C once 2:30 hit on the timer. Luckily I got it right but it was an educated guess after following a similar approach as the user above me. I sometimes lose sight of strategy when faced with problem solving DS questions and think I always need some type of formula or chart when a picture/timeline is sufficient enough to answer the Q. Need to work on this better.


I'm new to test-taking strategies and was curious about your post.

Is it widely considered good strategy to limit each DS question to 2:30 ?
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 23 Jan 2012, 14:30
OjilEye wrote:
AzWildcat1 wrote:
Fairly tough question. I just guessed C once 2:30 hit on the timer. Luckily I got it right but it was an educated guess after following a similar approach as the user above me. I sometimes lose sight of strategy when faced with problem solving DS questions and think I always need some type of formula or chart when a picture/timeline is sufficient enough to answer the Q. Need to work on this better.


I'm new to test-taking strategies and was curious about your post.

Is it widely considered good strategy to limit each DS question to 2:30 ?


Well you don't want to spend too much time on one problem, so after grinding out the math for this problem I was able to reach the conclusion of C but was rather an educated guess than a certified answer.
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Re: Arithmetic Statistics [#permalink]

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Here's my shot: The given info is this: Carl's $ increased 120 for x months, then his $ decreased by 50 for 12-x months. In May, his $(May) = 2600.

So what other information do we need to determine the range? One way of calculating the range would be to know the $ in every month which would require knowing only one more piece of information: what month did Carl switch from from depositing to withdrawing?

Scenario 1)

$(April) < 2625
$(May) = 2600

This scenario tells us that Carl definitely deposited money in May, but we don't know if he continued to deposit. Insufficient.

[strike]AD[/strike]
BCE

Scenario 2)

$(May) = 2600
$(June) < 2675

This scenario tells us that Carl withdrew money in June, but we don't know when he started withdrawing money. Insufficient.

Scenario 1+2)

Obviously the two are sufficient together. We know when he switched from depositing to withdrawing. Seeing as how that's all we need to know to then go the long roundabout way of calculating the range, the answer is C.
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Re: Arithmetic Statistics [#permalink]

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New post 06 Jun 2012, 17:13
Thanks a lot - the wording of the question threw me off a bit - I wasn't sure how to calculate "the range" of account balances!
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 01 Dec 2012, 09:45
Hi,
Should'nt the answer be B. I may be wrong but we already know that $2600 was the closing balance for May, therefore, opening Balance $2000 + (120*5) = $2600, had he withdrawn in May it would not be possible to have a closing balance of $2600. Basis this and the information in Statement B we can confirm he did not start withdrawing mooney from the account before the month of June.
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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rahulmrsingh wrote:
Hi,
Should'nt the answer be B. I may be wrong but we already know that $2600 was the closing balance for May, therefore, opening Balance $2000 + (120*5) = $2600, had he withdrawn in May it would not be possible to have a closing balance of $2600. Basis this and the information in Statement B we can confirm he did not start withdrawing mooney from the account before the month of June.


To find the range we should know:
A. Balance before he started depositing, initial balance - we know that there was initial balance because for may balance was 2600 and maximum amount he could deposited for this period (from January till May) is: 5 months*120=600;
B. In which month Carl stopped depositing $120 and started withdrawing $50.

We have:
APRIL___MAY__JUNE
---?----$2,600----?---


(2) June balance < 2675 --> he didn't deposited in June --> he withdrew in June.

Because if he deposited, then in June deposit would have been May balance +$120: $2,600+$120=$2,720>$2,675.
APRIL___MAY____JUNE
---?----$2,600---$2,550---

But again this statement is still insufficient as we still don't know when he started withdrawing, all we know it was not after June.

Hope it's clear.
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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mydreammba wrote:
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.



Given :
Jan
Feb
Mar
Apr
May - $2600
Jun
Jul
Aug
Sep
Oct
Nov
Dec

Statement 1: April < 2625
Since either $50 withdrawl or $120 deposit is possible so for withdraw of $50 in May, April must have been $2600+50 = 2650 for a deposit of $50 which is not true as per statement 1 i.e. Deposit of $120 must have happened in all the months before MAY till MAY
Jan - $2120
Feb - $2240
Mar - $2360
Apr - $2480

May - $2600
Jun
Jul
Aug
Sep
Oct
Nov
Dec
It gives us the amount from Jan to may but not for months later so
NOT SUFFICIENT

Statement 2: June < 2675
Since either $50 withdrawl or $120 deposit is possible so for withdraw of $50 in May, June must have been $2600+120 = $2720 for a deposit of $120 which is not true as per statement 2 i.e. Withdrawl of $50 must have happened in all the months After MAY
Jan
Feb
Mar
Apr
May - $2600
Jun - $2550
Jul - $2500
Aug - $2450
Sep - $2400
Oct - $2350
Nov - $2300
Dec - $2250


It gives us the amount from May to Dec but not for months before MAY so
NOT SUFFICIENT

Combining the two statements

Jan - $2120
Feb - $2240
Mar - $2360
Apr - $2480

May - $2600
Jun - $2550
Jul - $2500
Aug - $2450
Sep - $2400
Oct - $2350
Nov - $2300
Dec - $2250

SUFFICIENT

Answer: option C
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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mydreammba wrote:
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.


Target question: What was the range of the monthly closing balances of Carl’s account last year?

Given: The closing balance of Carl’s account for May of last year was $2,600

IMPORTANT: To answer the target question we need only determine which month Carl STARTED withdrawing money.
For example, if he started withdrawing money on March 15, we could use the fact that he had $2600 at the end of May to determine how much he had in the bank every month of the year, and thus determine the range of closing balances.
Notice that, since this is a Data Sufficiency, we need not calculate the actual range. We need only determine which month the deposits stopped and the withdrawals started.

So, we can rephrase our target question as . . .

REPHRASED target question: In which month did Carl start withdrawing $50?

Statement 1: Last year the closing balance of Carl’s account for April was less than $2,625
Let's examine two cases:
case a: In May, Carl DEPOSITED $120. So, balance at end of April = $2600 - $120 = $2480. This is possible, since we're told that the balance is less than $2625
case b: In May, Carl WITHDREW $50. So, balance at end of April = $2600 + $50 = $2650. This is NOT possible, since we're told that the balance is less than $2625
So, Carl definitely deposited $120 in May (and deposited $120 in April, March, Feb, and Jan).
However, we don't know the first month that Carl started withdrawing $50
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Last year the closing balance of Carl’s account for June was less than $2,675.
Let's examine two cases:
case a: In June, Carl DEPOSITED $120. So, balance at end of June = $2600 + $120 = $2720. This is NOT possible, since we're told that the balance is less than $2675
case b: In June, Carl WITHDREW $50. So, balance at end of June = $2600 - $50 = $2550. This is possible, since we're told that the balance is less than $2675
So, Carl definitely withdrew $50 in June, which means he also withdrew $50 in July, August, Sept, etc. However, we don't know the FIRST month that Carl started withdrawing $50
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that Carl deposited $120 in May.
Statement 2 tells us that Carl withdrew $50 in June.
So, June was the first month that Carl started withdrawing $50
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C

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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 19 Dec 2015, 11:30
I still don't understand what the question is asking by "What is the range of monthly closing balances"?
Is is asking

1. Highest balance- lowest balance or
2. Difference between each successive monthly balances?

I could easily calculate the below data.

Jan - $2120
Feb - $2240
Mar - $2360
Apr - $2480
May - $2600
Jun - $2550
Jul - $2500
Aug - $2450
Sep - $2400
Oct - $2350
Nov - $2300
Dec - $2250
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 19 Dec 2015, 14:51
Quote:
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


Target question: What was the range of the monthly closing balances of Carl’s account last year?

Given: The closing balance of Carl’s account for May of last year was $2,600

IMPORTANT: To answer the target question we need only determine which month Carl STARTED withdrawing money.
For example, if he started withdrawing money on March 15, we could use the fact that he had $2600 at the end of May to determine how much he had in the bank every month of the year, and thus determine the range of closing balances.
Notice that, since this is a Data Sufficiency, we need not calculate the actual range. We need only determine which month the deposits stopped and the withdrawals started.

So, we can rephrase our target question as . . .

REPHRASED target question: In which month did Carl start withdrawing $50?

Statement 1: Last year the closing balance of Carl’s account for April was less than $2,625
Let's examine two cases:
case a: In May, Carl DEPOSITED $120. So, balance at end of April = $2600 - $120 = $2480. This is possible, since we're told that the balance is less than $2625
case b: In May, Carl WITHDREW $50. So, balance at end of April = $2600 + $50 = $2650. This is NOT possible, since we're told that the balance is less than $2625
So, Carl definitely deposited $120 in May (and deposited $120 in April, March, Feb, and Jan).
However, we don't know the first month that Carl started withdrawing $50
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Last year the closing balance of Carl’s account for June was less than $2,675.
Let's examine two cases:
case a: In June, Carl DEPOSITED $120. So, balance at end of June = $2600 + $120 = $2720. This is NOT possible, since we're told that the balance is less than $2675
case b: In June, Carl WITHDREW $50. So, balance at end of June = $2600 - $50 = $2550. This is possible, since we're told that the balance is less than $2675
So, Carl definitely withdrew $50 in June, which means he also withdrew $50 in July, August, Sept, etc. However, we don't know the FIRST month that Carl started withdrawing $50
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that Carl deposited $120 in May.
Statement 2 tells us that Carl withdrew $50 in June.
So, June was the first month that Carl started withdrawing $50
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 21 Dec 2015, 18:27
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

When you modify the condition and the question,
Attachment:
GCDS  mydreammba     Beginning in January (20151220).jpg
GCDS mydreammba Beginning in January (20151220).jpg [ 37.59 KiB | Viewed 7049 times ]

It turns out like the table above. You need to know the month when Carl completed his deposit because he is going to make withdrawals from the next month. So, there is 1 variable(the month Carl completed his deposit) and you need 1 equation to match with the number of equation, which is likely to make D the answer.

In case of 1), case 1 and case 2 are possible, which is not unique. Therefore, it is not sufficient.
In case of 2), case 1 and case 2 are possible, which is not unique. Therefore, it is not sufficient.

In 1) & 2), only is case 2 possible, which is unique. Therefore it is sufficient and the answer is C.


->For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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mydreammba wrote:
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.


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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 16 May 2017, 13:42
Hello Bunnel / GMATClub Experts,

Still not sure. Why cant we assume that Carl made deposits till May. We dont need S-1 and answer would be B. My analysis is as below:

Infer: 120$ deposits each month. May Balance is 2600. This is possible only if Carl made deposits for 5 * 120 = 600. Means there was initial balance of 2000. If Carl didnot make 5 deposits then May Balance cannot be 2600, but less. We need to find Max and Min balance. Max Balance would be May. So we need Min Balance

S-1) April Balance is less than 2625. This is obvious as May Balance is 2600 which is less than 2625
S-2) June balance was less than 2675. Means Carl made withdrawal otherwise June would be 2600+120. Now there will be 7 withdrawals from June to dec. So Min Balance is 2600 - 350.
This statement is sufficient to get Range. So answer is B.
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Re: Beginning in January of last year, Carl made deposits of [#permalink]

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New post 17 May 2017, 14:01
i like this question.
Missed it though. Could not translate (1) as Bunnuel did.
Was able to translate (2).
Well done Bunnuel
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Beginning in January of last year, Carl made deposits of [#permalink]

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New post 24 Jun 2017, 16:18
I see very elaborate answers, but facing this kind of questions even assuming one has enough time is enough to dampen confidence. A good approach is to ignore all the useless details, like last year Carl did this and that. Just know that we have a six months period out of which deposits were made consecutively before withdrawals started and May's balance was 2600

Statement 1 says April was <2625, meaning there was definitely no withdrawal in or before May, otherwise we need 2650 in April. However, still not sufficient to find the range. We don't know the last month and when the withdrawal started, but we now know that the starting balance was 2000, i.e 2600-5(120)

Statement 2 says June's balance was less than 2675. No new info here and we have no clue of what took place in April.

Now combining both statements we have info on May and we can confirm that a withdrawal took place in June as otherwise, we will have 2720. We also know that June's balance is 2550.

Having January's and June's balance we can confirm that the range is 550. Hence C.

I think the main takeaway is to see this as a CR question, tackle the assumptions and then make, hopefully, quick inferences. This sort of question needs quick comprehension and good thinking and not necessarily calculation. If this approach is taken, one should be able to arrive at C/E at least, then this is where freshness and focus take over, assuming the question comes at the end of the quant session.

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Beginning in January of last year, Carl made deposits of   [#permalink] 24 Jun 2017, 16:18
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