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.
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When $350 is withdrawn on June 11, the daily balance decreases to $650.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When another $150 is withdrawn on June 16, the daily balance decreases to $500.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.

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.)