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The average (arithmetic mean) monthly balance in Company X's [#permalink]

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09 Mar 2010, 15:32

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The average (arithmetic mean) monthly balance in Company X's petty cash account on any given date is the average (arithmetic mean) of the closing balances posted on the last business day of each of the past 12 months. On March 6, 1990, the average (arithmetic mean) monthly balance was $692.02. What was the average (arithmetic mean) monthly balance as of June 23, 1990 ?

(1) As of June 23, 1990, the total of all the closing balances posted on the last business day of each of the last 12 months was $45.64 less than it had been on March 6, 1990.

(2) The closing balances posted on the last business days of March, April, and May, 1990 were $145.90, $3,000.00, and $725.25, respectively.

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. EITHER statement BY ITSELF is sufficient to answer the question. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, more data pertaining to the problem is required.

The first sentence of the question stem defines the term "average monthly balance" (AMB) as it is used in this problem. But you don't need the individual closing balances for the last business days of June, 1989, through May, 1990, to find the AMB as of June 23, 1990. The arithmetic mean of any group of terms (numbers) is equal to its sum, divided by the number of terms. In this problem, the number of terms used to calculate an AMB is defined as 12 months; if you knew the sum of the closing balances for any 12-month period, dividing it by 12 would give you the AMB for that period. The question stem gives you the AMB as of March 6, 1990; multiplying $692.02 by 12 would give you the sum of the closing balances posted on the last business day of each month from March, 1989, through February, 1990. Since you want to find the AMB as of June 23, 1990, the problematic months are March, April, and May, 1990 (which are covered by the AMB for June 23, 1990, but not by the AMB for March 6, 1990) and March, April, and May, 1989 (which are covered by the AMB for March 6, 1990, but not by the AMB for June 23, 1990). If you knew the total of the closing balances for March-May, 1989, and the total of the closing balances for March-May, 1990, you could subtract the first total from 12($692.02) and add the second total in order to find the sum of the closing balances posted from June, 1989, through May, 1990.

Statement (1) finesses the situation by stating the difference between the sums for the two 12-month periods. We know that the sum of the closing balances posted on the last business day of each month from March 1989 through February 1990 was 12($692.02). Then Statement (1) says that the sum of the closing balances for June 23, 1990 was $45.64 less than 12($692.02), or 12($692.02) - $45.64. So the average monthly balance posted for June 23, 1990 can be found by simply dividing this quantity by 12.

Statement (2) does not include the closing balances posted on the last business days of March-May, 1989, so it alone is insufficient to answer the question.

____

The correct answer is A, but I fail to see why statement 2 is insufficent.... the explanation says that statement 2 does not include the closing balances , but isn't that the information that it DOES provide? Or am I missing something completely obvious?

Re: Prob/Stat - Average Monthly Balance [#permalink]

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10 Mar 2010, 00:23

SnehaC wrote:

The average (arithmetic mean) monthly balance in Company X's petty cash account on any given date is the average (arithmetic mean) of the closing balances posted on the last business day of each of the past 12 months. On March 6, 1990, the average (arithmetic mean) monthly balance was $692.02. What was the average (arithmetic mean) monthly balance as of June 23, 1990 ?

(1) As of June 23, 1990, the total of all the closing balances posted on the last business day of each of the last 12 months was $45.64 less than it had been on March 6, 1990.

(2) The closing balances posted on the last business days of March, April, and May, 1990 were $145.90, $3,000.00, and $725.25, respectively.

st 1) we know the total of the balances for hte past 12 months for june 23 and can find the average. Sufficient st 2) closing balances of march, april, may 1990 are given but we dont know the closing balances of hte other 9 months from june 1989 to feb 1990 .. so cannot find out the average as of june 23 1990 not sufficient

Re: Prob/Stat - Average Monthly Balance [#permalink]

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10 Mar 2010, 21:32

chix475ntu wrote:

SnehaC wrote:

The average (arithmetic mean) monthly balance in Company X's petty cash account on any given date is the average (arithmetic mean) of the closing balances posted on the last business day of each of the past 12 months. On March 6, 1990, the average (arithmetic mean) monthly balance was $692.02. What was the average (arithmetic mean) monthly balance as of June 23, 1990 ?

(1) As of June 23, 1990, the total of all the closing balances posted on the last business day of each of the last 12 months was $45.64 less than it had been on March 6, 1990.

(2) The closing balances posted on the last business days of March, April, and May, 1990 were $145.90, $3,000.00, and $725.25, respectively.

st 1) we know the total of the balances for hte past 12 months for june 23 and can find the average. Sufficient st 2) closing balances of march, april, may 1990 are given but we dont know the closing balances of hte other 9 months from june 1989 to feb 1990 .. so cannot find out the average as of june 23 1990 not sufficient

A

Agree. In statement 2, The closing balance of first 9 months is not available. From the question stem, we only can find te sum of closing balance of 12 months till march 1990. Now how much did the last 9 months contribute to this total is not given.