Beginning in January of last year, Carl made deposits of $120 into his

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.

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we already know that $2600 was the closing balance for May, therefore, opening Balance $2000 + (120*5) = $2600, had he withdrawn in May it would not be possible to have a closing balance of $2600.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.

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

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

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,

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.

MATH REVOLUTION VIDEO SOLUTION:

Opening Balance

Jan 15 - Deposit $120
...
Month X - Deposit $120
Month Y - Withdrawal $50
...
Dec 15 - Withdrawal $50

Closing balance of May 31st = $2600

We don't know in which month he stopped depositing and started withdrawing.

(1) Closing balance for April was less than $2625

There are two possibilities:

If he had deposited in May, then closing balance of April would have been $2480.
If he had withdrawn in May, then closing balance of April would have been $2650.

Since closing balance of April is less than 2625, it must have been $2480. So in May, he must have deposited $120. Till when he kept depositing, we don't know. Not sufficient.

(2) Closing balance for June was less than $2675

There are again two possibilities:

If he had deposited in June, then closing balance of June would have been $2720.
If he had withdrawn in June, then closing balance of June would have been $2550.

Since closing balance of June is less than 2675, it must have been $2550.

So he must have withdrawn in June. Not sufficient alone.

Using both statements, we know that he deposited in May and withdrew in June so this is what it looks like:


Jan 15 - Deposit $120

...

May 15 - Deposit $120
May 31 - Closing balance $2600

June 15 - Withdrawal $50

...

Dec 15 - Withdrawal $50

So now we can easily go back each transaction and see the opening balance on Jan 1 by subtracting the deposits: 2600 - 120 - 120 - 120 - 120 - 120 = $2000
Closing balance on Jan 31 = 2120
and it increases from here on with each deposit till it becomes maximum on May 31 - $2600.
Thereafter, withdrawals start so it decreases till it reaches 2600 - 7*50 = 2250 on Dec 31.

So the range of closing balances is 2600 - 2120 = $480
Both statements together are sufficient.
Answer (C)

Notice that we're not given a starting balance or ending balance -- we're simply told the closing balance of Carl's account for May of last year was $2,600.

Since we do not have either the starting or ending balance, each statement alone will be insufficient. The answer must be C or E.

Statement 2 tells us the closing balance for June was less than $2,675. This statement tells us that Carl started making withdrawals in June. We need statement 1 to ensure that Carl did not start withdrawing money earlier in the year. Since we know the closing balance for May, we can determine the balance of the previous months.

Answer is C.

avigutman is there a way to solve this with a reasoning approach? This took me 5 minutes to solve with minor errors but leading to the right answer. (Probably the second time I'm seeing this after few months)

Jitu20 imagine that you're making consecutive leaps of 120 units to the right on the number line, and after some unknown number of such leaps you start taking consecutive steps of 50 units to the left. We know that you make a total of 12 moves (leaps and steps), but we don't know the breakdown (how many of each).
We know that after 5 moves you were exactly at 2,600 on the number line, and we want to know the total distance that you covered on the number line throughout your 12 moves.
What would you need to know in order to figure that out?
.
.
.
You'd need to know exactly when you switched from leaps to steps!

Statement (1) says you were to the left of 2,625 after four moves. But we know that after 5 moves you were at 2,600, so your fifth move must have still been a leap (a step would have brought you to the left of 2,575). You haven't switched to steps yet! When will it happen? We don't know.

Statement (2) says you were to the left of 2,675 after six moves. But we know that after 5 moves you were at 2,600, so your sixth move must have been a step (a leap would have brought you to 2,720). But when exactly did you switch from leaps to steps? We don't know.

Combining the statements, your sixth move must have been your first step, so the answer is C.

Solution:

We need to determine the range of the monthly closing balances of Carl's account last year. This hinges on knowing the last month he deposited the money or the first month he started to withdraw his money. For example, since we know the closing balance of May was $2,600 and if we know May is the last month he deposited $120 (and hence June is the first month he started to withdraw $50), we can determine that $2600 must be the highest monthly closing balance of last year and either January or December will have the lowest monthly closing balance. Since January’s closing balance was 2600 - 5 x 120 = $2000 and December’s closing balance was 2600 - 7 x 50 = $2250, we see that January has the lowest monthly closing balance. Therefore, the range of the monthly closing balances would be 2600 - 2000 = $600. However, keep in mind that the range could change if Carl made the last deposit in a month other than May. Therefore, we need to determine the last month he deposited the money or the first month he started to withdraw his money.

Statement One Alone:

Since the closing balance of Carl's account for April was less than $2,625, we know that he made a deposit of $120 in May. That is because if he made a withdrawal of $50 in May, then April’s closing balance would have been $2,650, which is more than $2,625. However, since we don’t know whether May was the last month he made the deposit (for example, he could have made another deposit in June), we can’t determine the range of the monthly closing balances of Carl's account last year. Statement one alone is not sufficient.

Statement Two Alone:

Since the closing balance of Carl's account for June was less than $2,675, we know that he made a withdrawal of $50 in June. That is because, had he made a deposit of $120 in June, then June’s closing balance would have been $2,720, which is more than $2,675. However, since we don’t know whether June was the first month he made the withdrawal (for example, he could have made another withdrawal in May), we can’t determine the range of the monthly closing balances of Carl's account last year. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that made a deposit of $120 in May and made a withdrawal of $50 in June. This tells us that May must be the last month he made a deposit and June must be the first month he made a withdrawal. Therefore, the range of monthly closing balances must be $600 (see stem analysis). Both statements together are sufficient.

Answer: C

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