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
OA D
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For a certain savings account, the table shows the
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theCodeToGMAT
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The answer is [D].
(1000x10 + 650x5 + 150x5 + (150+x)10))/30 = 1000
x = 1450
(1000x10 + 650x5 + 150x5 + (150+x)10))/30 = 1000
x = 1450
guerrero wrote: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
OA D
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ganeshrkamath
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June 1 to 10 => $1000 ___________ 10 daysguerrero wrote: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
OA D
June 11 to 15 => 1000 - 350 = $650 ___________ 5 days
June 16 to 20 => 650 - 500 = $150 ___________ 5 days
June 21 to 30 => $(150+x) ___________ 10 days
Average = (10*1000 + 5*650 + 5*150 + 10*(150+x))/30 = 1000
(10000 + 3250 + 750 + 1500 + 10x) = 30000
15500 + 10x = 30000
10x = 14500
x = $1450
Choose D
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GMATGuruNY
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The DAILY BALANCE is the amount in the account AT THE END OF THE DAY.guerrero wrote: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
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.
Last edited by GMATGuruNY on Mon Jan 26, 2015 8:13 pm, edited 1 time in total.
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Hi Guys,
I am struggling with this question, can you explain why have you multiplied 10 with 1000 for Jun 1-10? The mean of $1000 is for the 30 days so I cannot understand how we can use it for the first 10 days oe even the last 20 days.
Appreciate your help.
I am struggling with this question, can you explain why have you multiplied 10 with 1000 for Jun 1-10? The mean of $1000 is for the 30 days so I cannot understand how we can use it for the first 10 days oe even the last 20 days.
Appreciate your help.
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Hi smkhan,
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
