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Bunuel,
I am confused about this part:

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;

why are we multiplying by 5? Aren't the withdrawals/deposit made on a particular day ? how do we know that the withdrawals were made for 5 continuos days?
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liarish
Bunuel,
I am confused about this part:

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;

why are we multiplying by 5? Aren't the withdrawals/deposit made on a particular day ? how do we know that the withdrawals were made for 5 continuos days?

Not sure that I understand your question. Anyway:

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.
Each day from June 16 to June 20 (5 days) the daily balance was $650-$500=$150, thus the sum of the balances 5*$150=$750.
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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.
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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.

Since no transactions were made from June 11 till June 16, then the daily balance from June 11 to June 15 was $650 (on each day).
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Great !! Thank you Bunuel and SpotlessMind.

This is exactly what I was confused about :
"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.. " that the previous balance remains same i.e continues until the next transaction.
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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.

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

Hey Guys,
I'm sorry but I'm not getting it..
In bank account, if I deposit $1000.00 on say Jan-01 and if for next 30 days there is no transaction then at the end 30 days my bank account will have $ 30000.00 as per your explanations.Does that make sense guys ?Keeping money idle in the bank and its getting multiplied with no. of days kept in the account...I mean certainly there will be addition of Interest but that will not fetch you 30 times your deposit in 30 days.

Then, why we're considering this theory..Bunuel I would request you help.

Please come up with a deep analysis on this.
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SpotlessMind
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.

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

Hey Guys,
I'm sorry but I'm not getting it..
In bank account, if I deposit $1000.00 on say Jan-01 and if for next 30 days there is no transaction then at the end 30 days my bank account will have $ 30000.00 as per your explanations.Does that make sense guys ?Keeping money idle in the bank and its getting multiplied with no. of days kept in the account...I mean certainly there will be addition of Interest but that will not fetch you 30 times your deposit in 30 days.

Then, why we're considering this theory..Bunuel I would request you help.

Please come up with a deep analysis on this.

No one is saying that.

If you deposit 1,000 on January 1 and there is no transaction after that, then you'll daily balance would be 1,000 each day but the sum of the balances would be 31*1,000, which does not mean that you'll have 31*1,000 at the end.
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June has 30 days

1)for the first 10 days the amount in the deposit is 1000
2)for the next 5 days is 650 (1000-350)
3)for the next 5 days is 150 (650-500)
4)for the final 10 days is x

The median is
\(\frac{1000*10+650*5+150*5+10*x}{30}=1000\)
\(10x=16000, x= 1600\)
So the amount for the last 10 days was 1600 $, but the question asks for the DEPOSIT, and knowing that in the account there were 150 $, the deposit is 1600-150=1450 $
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mun23
Need explanation of the attached file...........

Given:

1. The variable is the daily balance
2. The variable changes thrice i.e., it takes 4 values.
3. The average daily balance for the 30 days is given as 1000

Relevant topic: Weighted average. The clues for identifying this topic are the mention of arithmetic mean and the unequal days (i.e., the weights) for each value.

Solution:

\((10 *1000 + 5*650 + 5*150 + 10 * x )/ 30 = 1000\)

x= 1600

The deposit therefore is 1600-150=1450 ( because the balance was already 150 when the deposit was made and so has to be deducted to find the deposit)
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Attachment:
Untitled.png
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

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?

Responding to a pm: For the ease of calculations, you can use deviation from the mean concept for weighted averages.

Shortfall = Excess
350*20 + 500*15 = 10*x
x = 1450

Here is the 1 minute video solution: https://youtube.com/shorts/vtXoij2yKWA

The concept has been discussed in detail here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/0 ... -averages/
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Hi All,

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:

GMAT assassins aren't born, they're made,
Rich
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VeritasPrepKarishma
anon1
Attachment:
Untitled.png
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

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?

Responding to a pm: For the ease of calculations, you can use deviation from the mean concept for weighted averages.

Shortfall = Excess
350*20 + 500*15 = 10*x
x = 1450

The concept has been discussed in detail here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/09 ... -averages/

Hey VeritasPrepKarishma,

I read through your article and went through the solution you posted here. The only part I didn't get was : why did you multiply 350 and 500 with 20 and 15 respectively?

I multiplied 350 with 5 (as we are short of 350 for 5 days) and multiplied 850 with 5 (as we are short of 850 for 5 days)

Shortfall = Excess

350*5 + 850*5 = 10*x

x = 600

Can you tell me where I am going wrong?
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VeritasPrepKarishma
anon1
Attachment:
Untitled.png
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

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?

Responding to a pm: For the ease of calculations, you can use deviation from the mean concept for weighted averages.

Shortfall = Excess
350*20 + 500*15 = 10*x
x = 1450

The concept has been discussed in detail here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/09 ... -averages/

Hey VeritasPrepKarishma,

I read through your article and went through the solution you posted here. The only part I didn't get was : why did you multiply 350 and 500 with 20 and 15 respectively?

I multiplied 350 with 5 (as we are short of 350 for 5 days) and multiplied 850 with 5 (as we are short of 850 for 5 days)

Shortfall = Excess

350*5 + 850*5 = 10*x

x = 600

Can you tell me where I am going wrong?

The withdrawal of 350 was done on 11th june. So from 11th to 30th june, i.e. for 20 days, we had a shortfall of $350.
The withdrawal of $500 was done on 16th june. So from 16th to 30th June, i.e. for 15 days, we had a shortfall of $500. (Note that the 350 shortfall for these 15 days is already accounted for above when we said that 350 will be short for 20 days)

So the total shortfall is 350*20 + 500*15
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anon1

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 is the amount in the account AT THE END OF THE DAY.

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 \(= \frac{sum-of-the-daily-balances}{number-of-days} = \frac{16,000}{10} = 1600\).

Since the daily balance on June 20 = 150, the amount deposited on June 21 = 1600-150 = 1450.

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Here's how I think about it:

For the first 1/3 of the month, the average balance is $1,000.

For the second 1/3 of the month, the average is (650+150) / 2 = $400

That means the balance for the final 1/3 of the month needs to be $1,600, in order for the monthly balance to average $1k.

We already have $150, so the final deposit must be $1,600 - $150 = $1,450

Choice D
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Bunuel MartyMurray KarishmaB IanStewart

1) How does the phrase ‘The DAILY BALANCE is the amount in the account AT THE END OF THE DAY’ affect the solution strategy?
2) What other variations of this phrase could potentially be used and what difference would each make to the solution?

Thank you for your time and effort!
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