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Unclear of daily bank account average concept
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utkalnayak
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I do not understand how daily average functions for a bank account. Attached is a problem I came across and have no idea how the solution is explained. Can anybody please help ?
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Utkal
Utkal
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GMATGuruNY
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The DAILY BALANCE is the amount in the account AT THE END OF THE DAY.For a certain savings account, the table shows the three transactions for the month of June. The daily balance for the account was recorded at the end of each of the 30 days in June. If the daily balance was $1,000 on June 1 and if the average (arithmetic mean) of the daily balances for June was $1,000, what was the amount of the deposit on June 21?
A. $1,000
B. $1,150
C. $1,200
D. $1,450
E. $1,600
The AVERAGE DAILY BALANCE = (sum of the daily balances)/(number of days).
Thus:
SUM OF THE DAILY BALANCES = (number of days)(average daily balance).
Since the daily balance for the first 10 days ($1000) is the same as the average daily balance for the entire month ($1000), we can ignore the first 10 days.
We need to determine the amount that must be deposited on June 21 so that the average daily balance for the LAST twenty days is $1000.
Sum of the daily balances for June 11-30 = (number of days)(daily balance) = 20*1000 = 20,000.
When $350 is withdrawn on June 11, the daily balance decreases to $650.
Sum of the daily balances for June 11-15 = (number of days)(daily balance) = 5*650 = 3250.
When another $150 is withdrawn on June 16, the daily balance decreases to $500.
Sum of the daily balances for June 16-20 = (number of days)(daily balance) = 5*150 = 750.
Thus:
Sum of the daily balances for June 21-30 = (sum for June 11-30) - (sum for June 11-15) - (sum for 16-20) = 20,000 - 3250 - 750 = 16000.
Daily balance for June 21-30 = (sum of the daily balances)/(number of days) = 16,000/10 = 1600.
Since the daily balance on June 20 = 150, the amount deposited on June 21 = 1600-150 = 1450.
The correct answer is D.
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Hi utkalnayak,
For this question, we have to deal with the average the daily balance at the END of each day for the entire 30 days.
For the first 10 days, the average is $1,000
For the next 5 days, the average is $650
For the next 5 days after, the average is $150
For the final 10 days, the average is $X
We're told that the average for the ENTIRE month is $1,000, so we need to use the Average Formula:
[10(1,000) + 5(650) + 5(150) + 10(X)]/30 = 1,000
This math can be done in a couple of different ways, but you'll eventually get to....
[14,000 + 10X]/30 = 1,000
14,000 + 10X = 30,000
10X = 16,000
X = 1600
Since X is the BALANCE for the last 10 days and there was already $150 in the account BEFORE the deposit was made, the deposit must be $1,450
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
For this question, we have to deal with the average the daily balance at the END of each day for the entire 30 days.
For the first 10 days, the average is $1,000
For the next 5 days, the average is $650
For the next 5 days after, the average is $150
For the final 10 days, the average is $X
We're told that the average for the ENTIRE month is $1,000, so we need to use the Average Formula:
[10(1,000) + 5(650) + 5(150) + 10(X)]/30 = 1,000
This math can be done in a couple of different ways, but you'll eventually get to....
[14,000 + 10X]/30 = 1,000
14,000 + 10X = 30,000
10X = 16,000
X = 1600
Since X is the BALANCE for the last 10 days and there was already $150 in the account BEFORE the deposit was made, the deposit must be $1,450
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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DavidG@VeritasPrep
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An alternate approach:
First see how much of a shortfall there is below our 1000 target
We'll have five days at 350 below our target. So we're 5*350 = 1750 below target.
Then we'll have five days at 850 below target (350 + an additional 500). This puts an additional 5*850 =4250 below target.
Total below target: 1750 + 4250 = 6000.
So we have to offset that $6000 shortfall.
Well, on the 21st, we'll have 10 days to get back to our target, meaning we'll need to be an average of 600 above target on those days, or 1000 + 600 = 1600.
And we know we'll have $150 on the 21st (we started with 1000, and we withdrew a total of 850), so we'll need an additional 1450 in the account.
(And note that 1600 is sitting there as a trap answer if you forget that we've still got 150 in the account on the 21st.)
First see how much of a shortfall there is below our 1000 target
We'll have five days at 350 below our target. So we're 5*350 = 1750 below target.
Then we'll have five days at 850 below target (350 + an additional 500). This puts an additional 5*850 =4250 below target.
Total below target: 1750 + 4250 = 6000.
So we have to offset that $6000 shortfall.
Well, on the 21st, we'll have 10 days to get back to our target, meaning we'll need to be an average of 600 above target on those days, or 1000 + 600 = 1600.
And we know we'll have $150 on the 21st (we started with 1000, and we withdrew a total of 850), so we'll need an additional 1450 in the account.
(And note that 1600 is sitting there as a trap answer if you forget that we've still got 150 in the account on the 21st.)
