For a certain savings account, the table shows the three transactions

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.

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).

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.

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.

[
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.[/quote]

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.[/quote]

Hey Guys,
I apologize if I sound harsh..seriously didn't mean that way..!

But I'm still unable to get it..Are you considering that every day after Day 1, for the rest of the month you''ll be depositing $1000 each day..otherwise how can you sum up and get it $31000 at the end of the month where it's mentioned that there is no transaction hence no inflows to the account after Day1 till the end of the month.

So,$1000 deposit on Day1, no further inflow/outflow till Day31...sum is 31000.! By what logic we're concluding this? I'm completely lost..
Would request your help Bunuel...!

Again, you won't have 31,000 at the end. Each day your daily balance will be 1,000. The sum of the balances will be 31,000. Cannot explain this any better.

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 $

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)

Its NOT about cash inflow. ITS BECAUSE THE PROMPT MENTIONS THE AVERAGE OF BALANCES
For example
If I have a balance of $1000 for 3 days in my a/c the average is
$(1000X3)/3 = 1000

If I had withdrawn $500 on the second day BY THE LOGIC OF THE PROMPT THE AVERAGE WILL BE
$(1000+500+500)/3 = $667

Hope its clear

Since there is only three things happening on the account...

$1000 to start off with, -$350 ($750 left), -$500 ($250 left) how much do we need to deposit to take the avg back to $1000?

1000+750+250 = 2000, divide this by 3 (2000/3) and we get roughly 666. Then $1000 - $666 = $444, so the account must go up to $1000 + 444 =1444 (since 666 is roughly) its 1450 that was deposited on that day.

I had the same doubt as liarish

Thank You Bunuel The explanation was crisp.

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/

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

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?