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805+ Level|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 10:53
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AllocationChecking DepositChecking IncentiveChecking BalanceSavings DepositSavings Interest RateSavings InterestSavings BalanceTotal Balance
€14,000 in Checking, €6,000 in Savings€14,000€500€14,500€6,0003%€180€6,180€20,680
€12,000 in Checking, €8,000 in Savings€12,000€300€12,300€8,0004%€320€8,320€20,620
€8,000 in Checking, €12,000 in Savings€8,000None€8,000€12,0004%€480€12,480€20,480
€6,000 in Checking, €14,000 in Savings€6,000None€6,000€14,0004%€560€14,560€20,560


The best allocation to maximize Hana's year-end balance is €14,000 in Checking and €6,000 in Savings, with a total of €20,680.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 10:54
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The answer is 10,000 and 10,000

if you put 14k in C and 6k in S --> you will get 20,680 at the end of the year
if you put 12k in C and 8k in S --> you will get 20,620 at the end of the year
if you put 10k in C and 10k in S --> you get 20,700 and thus the answer.
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Checking account:
6k-10k --> added value = 100
10k-14k --> added value = 300
>=14k --> added value = 500

Savings account:
>=8k --> interest 4%
else interest 3%

So, any deposit greater than 6k and less than 10k for checking account interest will be reduced for savings account and added value will be constant.
Same for greater than 10k and 14k also.

So, (10k, 10k) is the only pair satisfying the profit maximization.

Answer: (€10,000, €10,000)
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 10:55
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6000+14000 = 6100+14560 = 20660
8000+12000 = 8100+12480 = 20580
10000+10000 = 10300+10400 = 20700
12000+8000 = 12300+8320 = 20620
14000+6000 = 14500+6180 = 20680

Going with the options check
so 10000, 10000 in both CA and SA
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 10:57
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After logging in all the possible values of 6k,8k and 12k

14k in checking + 6k in savings = 20680
12k in checking + 8k in savings = 20620
6k in checking + 14k in savings = 20660
8k in checking + 12k in savings = 20580
10k in checking + 10k in savings = 20700



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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 10:58
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After substituting in all the possible values of 6000,8000 and 12000


10,000 in checking account + 10,000 in savings account = 20700
which is the highest value

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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 11:03
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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If she invests 8k in Savings account, total interest earned in a year would be 320$.
If she invests 6k in Savings account, total interest earned in a year would be 180$.
Difference= 140$.

If she invests 12k in Checkings account, credit union will add 300$ whereas if she invests 14k, Credit union will add 500$.
Difference= 200$.

Definitely than the first case. Therefore, she'll invest 14k in Checkings account and 6k in Savings account total maximise her earnings.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 11:11
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Basically this is a trade-off comparison between checking account ("CA") and saving account ("SA"):

$6k checking account vs. $6k saving account: CA earns $100 and SA earns 6000 x 3% = $180 --> prefer SA
$10k checking account vs. $10k saving account: CA earns $300 and SA earns 10000 x 4% = $400 --> prefer SA
$14k checking account vs. $14k saving account: CA earns $500 and SA earns 14000 x 4% = $560 --> prefer SA

So we look for an answer that maximize deposits into SA. Answer: CA = $6k, SA = $14k
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 11:17
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Incentives in each case:

Case 1: 6k checking, 14k savings → 100 + 560 = 660
Case 2: 8k checking, 12k savings → 100 + 480 = 580
Case 3: 10k checking, 10k savings → 300 + 400 = 700
Case 4: 12k checking, 8k savings → 300 + 320 = 620
Case 5: 14k checking, 6k savings → 500 + 180 = 680

The best combination is Case 3: 10k checking and 10k savings, as it provides the highest total incentive
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 12:09
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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Best way to go with options.

So if Savings is 6000, So CA(Current) 14000 => 500+180 680.
if SA 8000, So CA 12000 => 320+300 => 620.
if SA 10000, CA 10000=> 400+300=>700.
if SA 12000, CA 8000 => 480+100 =>580
if SA 14000, CA 6000 => 5600


IMO SA 10000, CA 10000.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 12:51
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Checking account

Returns for 6k =< Deposit < 10k => 100

Returns for 10k =< Deposits < 14k => 300

Returns for Deposits >= 14k => 500

Savings account
Returns for Deposit < 8k => 3% of Deposit per year
Returns for Deposit >= 8k => 4% of Deposit per year

Inorder to optimise the profits from both - she has to balance it between both accounts

Total amount to invest = 20k

Taking the least limits of checking - as it only has fixed payout and no interest rates

a) 6k in checking and 14k in savings

Returns = 100 + 14k * 0.04 * 1 = 100 + 560 = 660

b) 10k in checking and 10k in savings

Returns = 300 + 10k * 0.04 * 1 = 300 + 400 = 700

c) 14k in checking and 6k in savings

Returns = 500 + 6k * 0.03 * 1 = 500 + 180 = 680

Out of these 10k,10k is the best option
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 12:59
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Answer is Checking = 10,000 and Savings = 10,000.

This gives total year-end balance of (10,000+300)+(10,000*1.04)=20,700.

We can check the other combinations of 20,000.

Checking = 6,000 and Savings = 14,000 gives total of 20,660.
Checking = 8,000 and Savings = 12,000 gives total of 20,580.
Checking = 12,000 and Savings = 8,000 gives total of 20,620.
Checking = 14,000 and Savings = 6,000 gives total of 20,680.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 13:08
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Scanning the options, we can see that there are only two combinations possible to make the total €20,000. €6,000 and €14,000 or €8,000 and €12,000. Lets calculate the year end balance:
Combination 1: €6,000 and €14,000
Investing €14,000 in Checking account = €500
Investing €6,000 in Savings = Interest - €6,000*3% = 180
Total Year end balance = €20,000 + €680

Combination 1: €8,000 and €12,000
Investing €12,000 in Checking account = €300
Investing €8,000 in Savings = Interest - €8,000*4% = 320
Total Year end balance = €20,000 + €620

The year end balance is maximum in the first combination
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 13:10
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Quote:
Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.
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We can proceed with 2 scenarios-

Scenario 1-
8000 in savings and 12000 in checking account
Money earned on 8000= 0.04*8000=320
Money earned on 12000= 300
Total= 620

Scenario 2-
14000 in checking account and 6000 in savings account
Money earned on 14000=500
Money earned on 6000= 6000*0.03= 180
Total= 680

Scenario 2>Scenario 1

Hence answer- checking: 14000, Savings:6000
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 13:18
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Solving this by putting different values from the options in checking & savings account. We get

i) When checking account = 6000 & Savings account = 14000
Amount received = 680

ii) When checking account = 8000 & Savings account = 12000
Amount received = 620

iii) When checking account = 10000 & Savings account = 10000
Amount received = 700

iv) When checking account = 12000 & Savings account = 8000
Amount received = 580

v) When checking account = 14000 & Savings account = 6000
Amount received = 660

Hence, deposits in checking account = 10000 & Savings account = 10000
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 13:43
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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We can create logical groupings and see which amount within the group attracts maximum savings.

For example, whether Hana deposits €6,000 or €8,000 in checking account they will receive a fixed interest of €100.
Interest earned in savings account will be more when a deposit of €6,000 is made.

Total interest earned = 100 + 0.04 * 14000 = €660

The second group will be €10,000, €12,000 and €14,000. Hana will receive the same interest in check-in account when she makes deposits. However, among €10,000, €12,000 and €14,000, a deposit of €10,000 will attract maximum in interest.

Total Interest earned = 300 + 0.04 * 10000 = €700

Hence, to maximize the distribution dividing €10,000 on both checking and savings account makes sense.

Checking Account = €10,000
Savings Account = €10,000
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 14:44
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As with most table questions, the key solution is to try different values for the variables given. In this case the function to maximize is ROI, among different savings or checking accounts. Find the yiled of different combinations and select the answer.

But the key to be fast is to apply logic, think about the most profitable case scenario were she would put all her money, and then, apply restrictions, in this case 2 accounts must contain money, 14k in the checkings account, yielding $400 which is more than any % elsewhere and the remaining of the money in a savings account, yielding 3%, which is more than any other combination i find logic.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 15:15
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Now if savings account > 8k -> 4% yield. Otherwise savings is 3%
Checking account depends but is not a %, is an absolute gain.

Now if Hana invested 20k in 2 different accounts, one checkins and the other is savings. She'd be better off by investing and ensuring the +500 of a checkings account with more than 14K and deposit the rest (6k) at 3%.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 15:40
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checking account=6000, savings account=14000, balance: 100+560=660
checking account=10000, savings account=10000, balance: 300+400=700
checking account=14000, savings account=6000, balance: 500+180=680

Her total year-end balance will be maximized when checking account=10000 and savings account=10000
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 15:55
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Bunuel
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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Let X be the amount of money

Checking Account (CA)
6000 <= X < 10000 then +100
10000 <= X < 14000 then +300
14000 <= X then +500

Savings Account (SA)
8000 <= X then 4% annual return
X < 8000 then 3% annual return

Hana makes an initial deposit of 20000 in both accounts combined. We need to maximize the year-end balance.

You can try various combinations and these are the final values that you get:
CA 6000 and SA 14000 = 660
CA 8000 and SA 12000 = 580
CA 10000 and SA 10000 = 700
CA 12000 and SA 8000 = 620
CA 14000 and SA 6000 = 680

Clearly, we can see that we get the maximum value when an equal amount of money is deposited in both the Checking Account and the Savings Account (10000 each).
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