Statistics based Problem - Simple Explanation please !

[aditiniyer]

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 2600$, 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 2625$.
2)Last year the closing balance of Carl's account for June was less than 2675$.

[GMATGuruNY]

Several solutions are posted here:
https://www.beatthegmat.com/statistics-d ... 87701.html

[Brent@GMATPrepNow]

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

[Scott@TargetTestPrep]

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 2600$, 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 2625$.
2)Last year the closing balance of Carl's account for June was less than 2675$.

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