Find x
I 20 % of x is equal to the `1/5` th part of an another number
II. `7/20` the part of x is equal to the 35 % of an another 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 I alone is not sufficient
C. If both statements I and II together are needed to answer the question
D. If cannot get the answer from the statements I and II together and need even more data

Answer

To solve the problem, we need to analyze the two statements provided and see if they give us enough information to find the value of \( x \).

### Step 1: Analyze Statement I
The first statement says that 20% of \( x \) is equal to the \( \frac{1}{5} \) part of another number.

We can express this mathematically:
\[ 0.20 \cdot x = \frac{1}{5} \cdot n \]
Where \( n \) is the other number.

### Step 2: Simplify Statement I
We know that 20% can be written as a fraction:
\[ 0.20 = \frac{20}{100} = \frac{1}{5} \]
Thus, we can rewrite the equation:
\[ \frac{1}{5} \cdot x = \frac{1}{5} \cdot n \]

### Step 3: Eliminate the Fraction
Multiplying both sides of the equation by 5 to eliminate the fraction gives us:
\[ x = n \]

### Step 4: Analyze Statement II
The second statement states that \( \frac{7}{20} \) of \( x \) is equal to 35% of another number.

We can express this mathematically:
\[ \frac{7}{20} \cdot x = 0.35 \cdot m \]
Where \( m \) is another number.

### Step 5: Simplify Statement II
We know that 35% can also be expressed as a fraction:
\[ 0.35 = \frac{35}{100} = \frac{7}{20} \]
Thus, we can rewrite the equation:
\[ \frac{7}{20} \cdot x = \frac{7}{20} \cdot m \]

### Step 6: Eliminate the Fraction
Multiplying both sides of the equation by 20 to eliminate the fraction gives us:
\[ 7x = 7m \]

### Step 7: Simplify Further
Dividing both sides by 7 gives us:
\[ x = m \]

### Step 8: Combine Information
From Statement I, we have \( x = n \) and from Statement II, we have \( x = m \). However, since \( n \) and \( m \) are different variables representing different numbers, we cannot determine a unique value for \( x \) without additional information about either \( n \) or \( m \).

### Conclusion
Since neither statement alone provides enough information to determine \( x \), and combining both statements does not eliminate the variables \( n \) and \( m \), we conclude that the data given in both statements is not sufficient to find the value of \( x \).

### Final Answer
The correct option is D: The data given in both statements is not sufficient to find the value of \( x \).

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