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Difficulty:
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58% (03:05) correct
42%
(03:07)
wrong
based on 1370
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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
Attachment:
Untitled.png [ 14.66 KiB | Viewed 41381 times ]
Okay, so june 1 - june 10, the sum of the daily balance in this time period here is 10,000 (because initial balance is 1000, and nothing changes)
june 11-15 - the sum here is 3250 (1000-350)*5
june 15-20 the sum here is 750 (1000-350-500)*5
the sum of all those is 14,000.
Since we want to find a deposit, whose sum makes the total sum of all the balances 30,000 / 30 = 1,000
I did 30,000 - 14,000 which gives me 16,000.
so the sum of the balances for rest of the days (10) must equal 16,000. I do 16,000/10
and that's 1,600. E. But thats wrong. The answer is D
What am I donig wrong here? and what is the false logic?
23 Nov 2012, 03:10
Kudos
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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 daily balance from June 1 to June 10 (10 days) was $1,000 --> the sum of the balances 10*$1,000 = $10,000;
The daily balance from June 11 to June 15 (5 days) was $1,000-$350=$650 --> the sum of the balances 5*$650 = $3,250 ;
The daily balance from June 16 to June 20 (5 days) was $650-$500=$150 --> the sum of the balances 5*$150 = $750;
The daily balance from June 21 to June 30 (10 days) was $150 --> the sum of the balances 10*($150 + x).
We need the sum of the balances for 30 days to be $30,000 (since the average for 30 days was $1,000), thus we need
\(10,000+3,250+750+10*($150+x)=30,000\);
\(x=$1,450\).
Answer: D.
OR:
For 5 days the total balance was less by 5*$350 = $1,750;
For another 5 days the total balance was less by 5*($350 + $500) = $4,250;
The final 10 days of June should compensate \($1,750 + $4,250 = $6,000\), thus the sum of the balances for the final 10 days must be \($10,000+$6,000=$16,000\):
\(($100-($350+$500)+x)*10=$16,000\);
\(x=$1,450\).
Answer: D.
Hope it's clear.
24 Dec 2012, 00:46
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liarish
Sorry for not being clear.
I mean that the table says that the date of transaction is June 11. So what I am thinking is that balance on June 11 is 1000-350 = 650. Not that balance from June 11-June 16 is is (1000-350= 650 )*5. What language in the question is telling us that its for 5 continuos days (June 11-16)? ie. I am confused about the "Each" part in the following statement.
Each day from June 11 to June 15 (5 days) the daily balance was $1,000-$350=$650, thus the sum of the balances 5*$650=$3,250.
I mean that the table says that the date of transaction is June 11. So what I am thinking is that balance on June 11 is 1000-350 = 650. Not that balance from June 11-June 16 is is (1000-350= 650 )*5. What language in the question is telling us that its for 5 continuos days (June 11-16)? ie. I am confused about the "Each" part in the following statement.
Each day from June 11 to June 15 (5 days) the daily balance was $1,000-$350=$650, thus the sum of the balances 5*$650=$3,250.
Hi,
I think I got your point Liarish,
Let me try to explain.. the point to understand is that we are dealing with account balance"so if someone withdarws money on day 1, the balance will remain the same unless there is an other inflow/outflow cash transaction.. keep that in mind..
from june 1 -10 the account had Rs 1000/- on all 10 days -> so balance for the above 10 days = 1000x10 --------- (1)
Now June 11 the guy withdraws 350/- bucks.. so the balance in his account is 650. and since no transaction happens in the account for the next 5 days the balance will remain the same.. hence the balance for the above 5 days = 5x650 --------- (2)
Now june 16th he withdraws another 500 , so now his account bal = 150 and it will remain the same for the next 5 days.. so balance for the above 5 days = 150x5 --------- (3)
and on 21st he puts "X".. so the amount in his account is 150+x and it will remain the same till 30th... so total balance for the last 10 days= (150+X)x10 --------- (4)
no the sum of all the (1,2,3,4) would be equal to 1000x30 as the average balance for the month is 1000(given)
on solving for X we get the answer.. Gud Work Bunuel
