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
