Leela has 10 hair clips of 4 different colours . Find how many blue clips she has ?
Statements :
1. There are 2 red clips
2 . The number of yellow clips are twice that of red clips
3. Green clips constitute one-third of the total number of red and yellow clips . which Statement (s) is/are sufficient to answer the above question ?

Options

A. Statement 1 alone
is sufficient
B. Statements 1 , 2 and 3
together are sufficient
C. Statement 1 and 2
together are sufficient
D. Statement 2 alone
is sufficient

Answer

To solve the problem of how many blue clips Leela has, we need to analyze the statements provided and determine which ones are sufficient to answer the question.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Leela has a total of 10 hair clips of 4 different colors: red, yellow, green, and blue.
- We need to find out how many blue clips she has.

2. **Analyzing Statement 1**:
- **Statement 1**: There are 2 red clips.
- This gives us the number of red clips (R = 2) but does not provide any information about the yellow (Y), green (G), or blue (B) clips.
- **Conclusion**: This statement alone is **not sufficient**.

3. **Analyzing Statement 2**:
- **Statement 2**: The number of yellow clips is twice that of red clips.
- If R = 2 (from Statement 1), then Y = 2 * R = 4. However, we still do not know the number of green (G) or blue (B) clips.
- **Conclusion**: This statement alone is **not sufficient**.

4. **Analyzing Statement 3**:
- **Statement 3**: Green clips constitute one-third of the total number of red and yellow clips.
- From Statements 1 and 2, we have R = 2 and Y = 4. Therefore, the total number of red and yellow clips is R + Y = 2 + 4 = 6.
- G = (1/3) * (R + Y) = (1/3) * 6 = 2.
- We now have R = 2, Y = 4, and G = 2, but we still do not know the number of blue clips (B).
- **Conclusion**: This statement alone is **not sufficient**.

5. **Combining All Statements**:
- From Statement 1: R = 2.
- From Statement 2: Y = 4.
- From Statement 3: G = 2.
- Now we can find the number of blue clips (B):
- Total clips = 10
- B = Total - (R + Y + G) = 10 - (2 + 4 + 2) = 10 - 8 = 2.
- **Conclusion**: All three statements together are **sufficient** to determine that Leela has 2 blue clips.

### Final Answer:
- The answer is that Leela has **2 blue clips**.
- The statements that are sufficient to answer the question are **1, 2, and 3 together**.