A pair of opposite faces of a cube is painted yellow another pair of opposite faces orange and the remaining faces white. The cube is then cut in to 343 smaller but identical cubes.How many of the smaller cubes have exactly two colors on them?a.60             b.50             c.25             d.30

To solve this problem, we need to understand the pattern of colors on the larger cube and then determine how many smaller cubes have exactly two colors on them.

From the given information, we know that a pair of opposite faces of the cube is painted yellow, another pair is painted orange, and the remaining faces are painted white.

Now, let's consider the smaller cubes. Since the larger cube is cut into 343 smaller but identical cubes, we know that it is a 7x7x7 cube. Each face of this cube is divided into 49 smaller squares (7x7).

To find the number of smaller cubes with exactly two colors, we need to determine how many smaller squares have two different colors on them.

Let's analyze each color combination:

1. Yellow and orange: There are 2 faces painted yellow and 2 faces painted orange. Each face has 7x7 = 49 smaller squares. So, the total number of smaller squares with yellow and orange colors is 2x49 = 98.

2. Yellow and white: There are 2 faces painted yellow and the remaining 3 faces are painted white. Each face has 7x7 = 49 smaller squares. So, the total number of smaller squares with yellow and white colors is 2x49 = 98.

3. Orange and white: There are 2 faces painted orange and the remaining 3 faces are painted white. Each face has 7x7 = 49 smaller squares. So, the total number of smaller squares with orange and white colors is 2x49 = 98.

Now, let's add up the number of smaller squares with two different colors: 98 + 98 + 98 = 294.

Since each smaller cube is made up of one smaller square, the number of smaller cubes with exactly two colors on them is also 294.

Therefore, the correct answer is d. 30.