The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ?
Find the number of males and females in a party
I. The ratio of males and females is 3:2
II. The number of males is 50% more than the number of females

Options

A. If statement I alone is sufficient but statement il alone is not sufficient
B. If statement II alone is sufficient but statement i alone is not sufficient
C. If each statement alone (either I or II) is sufficient
D. If statement and I together are not sufficient

Answer

To determine whether the statements provided are sufficient to find the number of males and females in a party, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Question**:
We need to find the number of males and females in a party.

2. **Analyzing Statement I**:
- Statement I states that "The ratio of males to females is 3:2."
- This means for every 3 males, there are 2 females. However, without knowing the total number of individuals or the actual number of males or females, we cannot determine the exact counts of males and females.
- **Conclusion**: Statement I alone is **not sufficient** to answer the question.

3. **Analyzing Statement II**:
- Statement II states that "The number of males is 50% more than the number of females."
- If we denote the number of females as \( F \), then the number of males \( M \) can be expressed as:
\[ M = F + 0.5F = 1.5F \]
- This means that for every 2 females, there are 3 males (since \( 1.5F \) is the same as \( \frac{3}{2}F \)). However, similar to Statement I, we do not have the actual counts of males or females.
- **Conclusion**: Statement II alone is **not sufficient** to answer the question.

4. **Combining Statements I and II**:
- From Statement I, we have the ratio \( M:F = 3:2 \).
- From Statement II, we derived \( M = 1.5F \), which can also be expressed in ratio form as \( M:F = 3:2 \).
- Both statements lead us to the same ratio, but we still do not have the actual number of males or females.
- **Conclusion**: Even when combining both statements, we still cannot determine the exact numbers of males and females.

### Final Conclusion:
The data given in both statements are **not sufficient** to determine the exact number of males and females in the party.