Consider the following question and decide whether the statements are sufficient to answer the question.
Question :
In a box, there are packets of three different sizes. How many packets are there in the box ?
Statements :
(1) Half of all the packets are of medium size.
(2) there are six big packets.
(3) There are twice amount of smaller packest than there are large packets.

Options

A. Statements 1 and 3
are sufficuent
B. Statements 1,2 and 3
together are sufficient
C. None of the statements
are sufficient.
D. Statements 1 and 2
are sufficient

Answer

To solve the question, we need to analyze the statements provided and determine whether they are sufficient to find the total number of packets in the box.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( x \) be the number of small packets.
- Let \( y \) be the number of medium packets.
- Let \( z \) be the number of large packets.

2. **Analyze the Statements:**
- **Statement 1:** Half of all the packets are of medium size.
- This implies:
\[ y = \frac{1}{2}(x + y + z) \]
- Rearranging gives:
\[ 2y = x + y + z \implies y = x + z \]

- **Statement 2:** There are 6 big packets.
- This gives us:
\[ z = 6 \]

- **Statement 3:** There are twice as many smaller packets as there are large packets.
- This implies:
\[ x = 2z \]
- Substituting \( z = 6 \) gives:
\[ x = 2 \times 6 = 12 \]

3. **Combine Statements:**
- From Statement 2, we have \( z = 6 \).
- From Statement 3, we have \( x = 12 \).
- Substitute \( x \) and \( z \) into the equation derived from Statement 1:
\[ y = x + z = 12 + 6 = 18 \]

4. **Calculate Total Packets:**
- The total number of packets is:
\[ x + y + z = 12 + 18 + 6 = 36 \]

### Conclusion:
To find the total number of packets, we needed all three statements. Therefore, the answer is that all three statements together are necessary to determine the total number of packets in the box.