**Given information:**
- The ratio of the number of sides of polygons A and B is 1:2.
- The ratio of the interior angles of polygons A and B is 3:4.

**Let's solve the problem step by step:**

**Step 1: Understanding the concept**
- The number of sides of a polygon determines the number of interior angles it has.
- The sum of the interior angles of a polygon can be calculated using the formula: (n-2) * 180, where n is the number of sides.
- The interior angles of a regular polygon are equal.

**Step 2: Ratio of the interior angles**
- Let the interior angles of polygon A be 3x and the interior angles of polygon B be 4x (since the ratio of the interior angles is given as 3:4).
- The sum of the interior angles of polygon A is (1 * 3x) = 3x.
- The sum of the interior angles of polygon B is (2 * 4x) = 8x.

**Step 3: Finding the number of sides of polygons A and B**
- We know that the sum of the interior angles of a polygon can be calculated using the formula (n-2) * 180.
- Using this formula for polygon A, we can write the equation: (1 * 3x) = (n-2) * 180.
- Simplifying this equation, we get: 3x = 180n - 360.
- Similarly, for polygon B, we can write the equation: (2 * 4x) = (n-2) * 180.
- Simplifying this equation, we get: 8x = 180n - 360.

**Step 4: Solving the equations**
- We have two equations:
- 3x = 180n - 360 (equation 1)
- 8x = 180n - 360 (equation 2)
- By equating the right-hand sides of the equations, we get: 180n - 360 = 180n - 360.
- This implies that the left-hand sides of the equations are also equal: 3x = 8x.
- Solving this equation, we get: 5x = 0.
- This implies that x = 0, which is not possible.

**Step 5: Conclusion**
- Since we cannot find a valid value for x, it means that the given ratios of the interior angles cannot be satisfied.
- Therefore, it is not possible to determine the number of sides of polygon B based on the given information.
- The correct answer cannot be determined.