To determine the range of monthly closing balances, we must know the month in which the $120 deposits no longer occur (i.e. the month in which the $50 withdrawals begin). Without knowing this, we don't have an upper or lower limit for the range.
We're given that Carl's balance at the end of May was $2,600.
We're also told that the only possible transaction on May 15th was one of the following:
(1) deposit of $120
(2) withdrawal of $50
If a deposit of $120 occurred on May 15th, the closing balance at the end of April was $2,600 - $120 = $2,480
If a withdrawal of $50 occurred on May 15th, the closing balance at the end of April was $2,600 + $50 = $2,650.
Statement (1) tells us that the closing balance at the end of April was less than $2,625.
Since only a closing balance of $2,480 fits this scenario, we can deduce that a deposit of $120 occurred on May 15th.
What information can we glean from this?
Since we know that only $120 deposits will occur each month until $50 withdrawals begin, and that deposits will no longer occur once those withdrawals begin, we can deduce that a $120 deposit occurred in January, February, March, April, and May.
This means that the starting balance for the year was $2,600 - ($120)*5 = $2,000.
However, we don't know if May is the final month in which a $120 deposit occurs. For all we know, the $120 deposits continue for several more months. Alternatively, May might be the final month for $120 deposits. This means we don't know how much more the balance will grow, or how much it will be reduced over the course of the year.
Therefore,
Statement (1) is INSUFFICIENT.
In Statement (2), we're told that the balance at the end of June was less than $2,675.
We know that the balance at the end of May was $2,600.
Between the end of May and the end of June, either a $120 deposit or $50 withdrawal occurred.
If a $120 deposit occurred, the balance at the end of June would have been $2,600 + $120 = $2,720
If a $50 withdrawal occurred, the balance at the end of June would have been $2,600 - $50 = $2,550.
Since only $2,550 < $2,675, we know that a $50 withdrawal occurred in June.
However, using only Statement (2), we don't know the first month in which the $50 withdrawals began.
For all we know, the $50 withdrawals could've begun a few months earlier. Depending on the month in which the withdrawals began, the range of closing balances for the year will vary.
Hence,
Statement (2) is INSUFFICIENT
Combining the statements, we know that a $120 deposit took place in May, and a $50 withdrawal took place in June.
In other words, we know the exact point at which the deposits end and the withdrawals begin.
This allows us to determine the exact range of monthly closing balances for the year.
Statement (1) + Statement (2) = SUFFICIENT.
Answer:
C
tonebeeze wrote:I am having difficulty understanding this problem. Can someone help provide clarity. Thanks
161. 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.
I'm really old, but I'll never be too old to become more educated.
