What is the three digit number?
I Three-fifth of that number is less than that number by 90
II. One-fourth of that number is 25% of that number

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 the 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
The first statement says, "Three-fifth of that number is less than that number by 90."

Let's denote the three-digit number as \( x \).

According to the statement, we can write the equation:
\[ \frac{3}{5}x = x - 90 \]

### Step 2: Solve the Equation from Statement I
Now, let's solve the equation:
1. Rearranging the equation gives:
\[ x - \frac{3}{5}x = 90 \]
2. Simplifying the left side:
\[ \frac{2}{5}x = 90 \]
3. Multiplying both sides by \( \frac{5}{2} \) to isolate \( x \):
\[ x = 90 \times \frac{5}{2} = 90 \times 2.5 = 225 \]

### Step 3: Check if \( x \) is a Three-Digit Number
The number we found is \( 225 \), which is indeed a three-digit number.

### Step 4: Analyze Statement II
The second statement says, "One-fourth of that number is 25% of that number."

We can express this mathematically as:
\[ \frac{1}{4}x = 0.25x \]

### Step 5: Simplify Statement II
1. Since \( 0.25 \) is equivalent to \( \frac{1}{4} \), the equation simplifies to:
\[ \frac{1}{4}x = \frac{1}{4}x \]
2. This is always true for any value of \( x \) and does not help us find a specific three-digit number.

### Conclusion
From the analysis:
- Statement I is sufficient to determine the three-digit number, which is \( 225 \).
- Statement II does not provide any new information to find the number.

Thus, the answer to the question is that only Statement I is sufficient.

### Final Answer
The answer is **Option A**: Statement I alone is sufficient, while Statement II alone is not sufficient.

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