Data Sufficiency

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

mikepamlyla wrote:Brent, thank you! Your explanations are great!!!!!

Just curious, what level question is this one? 600?

Thanks!

The questions in the OG13 are arranged in order of difficulty, from easiest to hardest.
This question is #143 out of 174 questions, so I'd place it around 600 to 650

Cheers,
Brent

mikepamlyla wrote:Thanks! If I am able to do All the problems in the OG for quant (PS and DS) in 2 min or less, would that be a good goal to try to achieve around a 700?

.

That sounds very promising. I think a high quant score is definitely within your reach.
How are your Verbal skills?
Have you taken a full-length practice test yet?

Cheers,
Brent