What is the three digit number?
I. Two-fifth of the number is half of 204
II. 20% of the number is 51.

Options

A. If the Statement I alone is sufficient to answer the question but the Statement II alone is not sufficient
B. If the Statement II alone is sufficient to answer the question but the Statement alone is not sufficient
C. If both Statements I and II together are needed to answer the question
D. If either the Statement I alone or Statement II alone is sufficient to answer the question

Answer

To solve the problem of finding the three-digit number based on the given statements, we will analyze each statement step by step.

### Step 1: Analyze Statement I
Statement I states that two-fifths of the number is half of 204.

1. Let's denote the three-digit number as \( x \).
2. According to the statement, we can write the equation:
\[ \frac{2}{5}x = \frac{1}{2} \times 204 \]
3. Calculate half of 204:
\[ \frac{1}{2} \times 204 = 102 \]
4. Now substitute this back into the equation:
\[ \frac{2}{5}x = 102 \]
5. To find \( x \), multiply both sides by \( \frac{5}{2} \):
\[ x = 102 \times \frac{5}{2} = 102 \times 2.5 = 255 \]

### Step 2: Analyze Statement II
Statement II states that 20% of the number is 51.

1. Again, let \( x \) be the three-digit number.
2. According to the statement, we can write the equation:
\[ 0.2x = 51 \]
3. To find \( x \), divide both sides by 0.2:
\[ x = \frac{51}{0.2} = 51 \times 5 = 255 \]

### Conclusion
From both statements, we have calculated the three-digit number \( x \) to be 255. Thus, both statements are sufficient to determine the three-digit number.

### Final Answer
The three-digit number is **255**.