Follow the steps to solve the given problem :
Step 1. Put x = 2 and y = 3
Step 2. Multiply x by 2
Step 3. Multiply y by 3
Step 4. If y = greatest possible 3 digit perfect square, then stop, else follow step 5.
Step 5. Go to step 2.
What is the maximum possible value of x ?

Options

A. 32
B. 64
C. less than 50
D. None of these

Answer

To solve the given problem step by step, let's follow the instructions provided:

### Step 1: Assign values to x and y
We start by putting the values:
- Let \( x = 2 \)
- Let \( y = 3 \)

### Step 2: Multiply x by 2
Next, we multiply \( x \) by 2:
- \( x = 2 \times 2 = 4 \)

### Step 3: Multiply y by 3
Now, we multiply \( y \) by 3:
- \( y = 3 \times 3 = 9 \)

### Step 4: Check if y is the greatest possible 3-digit perfect square
The greatest possible 3-digit perfect square is \( 31^2 = 961 \). Since \( y = 9 \) is not equal to 961, we proceed to step 5.

### Step 5: Go to step 2
Since \( y \) is not the greatest possible 3-digit perfect square, we return to step 2 and repeat the process.

Now, we will continue this process until \( y \) reaches the greatest possible 3-digit perfect square.

We can summarize the steps as follows:
1. Multiply \( x \) by 2 repeatedly.
2. Multiply \( y \) by 3 repeatedly.
3. Check if \( y \) equals 961.

Continuing this process:
- After the first iteration: \( x = 4 \), \( y = 9 \)
- After the second iteration: \( x = 8 \), \( y = 27 \)
- After the third iteration: \( x = 16 \), \( y = 81 \)
- After the fourth iteration: \( x = 32 \), \( y = 243 \)
- After the fifth iteration: \( x = 64 \), \( y = 729 \)
- After the sixth iteration: \( x = 128 \), \( y = 2187 \)

At this point, \( y \) exceeds 961, so we stop and check the last valid \( y \):
- The last valid \( y \) was 729 when \( x = 64 \).

### Conclusion
The maximum possible value of \( x \) when \( y \) is the greatest possible 3-digit perfect square (961) is:
- \( x = 64 \)