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143. 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. Ifthe
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.
Arithmetic Statistics
(1) If Carl began making $50 withdrawalson
or beforeMay 15, his account balance on
April 16 would be at least $50 greater than it
was on the last day of May. Thus, his account
balance on April 16 would be at least
$2,600 + $50 = $2,650, which is contrary to
the information given in (1). Therefore, Carl
did not begin making $50 withdrawals until
June 15 or later. Tiese observations can be
used to give at least two possible ranges.
Carl could have had an account balance of
$2,000 on January 1, made $120 deposits in
each of the first 11 months of the year, and
then made a $50 withdrawal on December
15, which gives a range of monthly closing
balances of (120)(10). Also, Carl could have
had an account balance of $2,000 on
January 1, made $120 deposits in each of the
first 10 months of the year, and then made
$50 withdrawals on November 15 and on
December 15, which gives a range of
monthly closingbalances of (120)(9); NOT----------------------------------------为什么选存10个月，11个月呢，存四个月五个月六个月之后就连续取的情况可以吗？
sufficient.
(2) On June 1, Carl's account balance was the
same as its closing balance was for May,
namely $2,600. Depending on whether Carl
made a $120 deposit or a $50 withdrawal on
June 15, Carl's account balance on June 16
was either $2,720 or $2,550. It follows from
the informationgiven in (2) that Carl's
balance on June 16 was $2,550. Therefore,
Carl began making $50withdrawals on or
before June 15. These observations can be
used to give at least two possible ranges.
Carl could have had an account balance of
$2,680 on January 1, made one $120 deposit
on January 15, and then made a $50
withdrawal in each of the remaining
11 months of the year (this gives a closing
balanceof $2,600 for May), which gives
a range of monthly closingbalances of
(50)(11). Also, Carl could have had an account ------------------------------------疑问同上面。
balance of $2,510 onJanuary 1, made$120
depositson January 15 and on February 15,
and then made a $50 withdrawal in each of
the remaining 10months of the year (this
gives a closing balance of $2,600 for May),
which gives a range of monthly closing
balances of (50)(10); NOT sufficient.
Given both (1) and (2), it follows from the
remarks above that Carl began making $50
withdrawals on June 15.Therefore, the changes to
Carl's account balance for each month of last year
are known. Since the closing balance for May is
given, it follows that the closingbalances for each
month of last year are known, and hence the
range of these 12 knownvalues can be determined.
Therefore, (1) and (2) together are sufficient.
The correct answer is C;
both statements together are sufficient. -----------------综合一二，我可以理解存到五月后就开始取，但是这个range就不明白什么意思
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发表于 2013-10-20 17:41:17
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