The total monthly salary of Liam is $60,000. He spends y% of his monthly salary on housing rent, 25% of the remaining monthly salary on food and utilities, and half of the remaining monthly salary on stock investments. If Liam saves $18,000 at the end of the month, then the amount spent on stock investments is what percent more than the amount spent on housing rent?

The correct option is 50%.

Step 1: Understand the given values
Total monthly salary of Liam = $60,000
Savings at the end of the month = $18,000

Step 2: Determine the salary remaining after housing rent
Let $R$ be the remaining monthly salary after spending $y\%$ on housing rent.

Liam spends 25% of this remaining salary $R$ on food and utilities:
$\text{Amount spent on food and utilities}=0.25R=\frac{1}{4}R$
Remaining salary after food and utilities = $R-\frac{1}{4}R=\frac{3}{4}R$

Step 3: Calculate stock investments and savings
Liam spends half of the remaining salary on stock investments:
$\text{Amount spent on stock investments}=\frac{1}{2}\times \frac{3}{4}R=\frac{3}{8}R$

The remaining amount after stock investments represents Liam's monthly savings:
$\text{Savings}=\frac{3}{4}R-\frac{3}{8}R=\frac{3}{8}R$

We are given that the total savings equal $18,000. Equating the two expressions:
$\frac{3}{8}R=18000$

Solving for $R$:
$R=\frac{18000\times 8}{3}$
$R=6000\times 8=48000$

So, the remaining salary after paying for housing rent is $48,000.

Step 4: Calculate the amounts spent on housing rent and stock investments
Since total monthly salary is $60,000 and the salary remaining after housing rent is $48,000:
$\text{Amount spent on housing rent}=60000-48000=12000$

The amount spent on stock investments is:
$\text{Amount spent on stock investments}=\frac{3}{8}\times 48000=18000$

Step 5: Calculate how much percent more stock investment is than housing rent
We compare the stock investment ($18,000) to the housing rent ($12,000):
$\text{Percentage More}=\frac{\text{Stock Investments}-\text{Housing Rent}}{\text{Housing Rent}}\times 100$
$\text{Percentage More}=\frac{18000-12000}{12000}\times 100$
$\text{Percentage More}=\frac{6000}{12000}\times 100=50\%$

Therefore, the amount spent on stock investments is 50% more than the amount spent on housing rent.