Bunuel wrote:

Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.

(2) There are two red spheres in the box.

We are given that we have red or green spheres or cubes in a box. We need to determine the total number of objects.

Statement One Alone:

There are six cubes and 5 green objects in the box.

Although we know the number of cubes in the box, we do not know the number of spheres, and thus we cannot determine the total number of objects in the box. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

There are two red spheres in the box.

Since we do not know how many spheres or cubes are in the box, we cannot determine the total number of objects. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two together, although we know there are 6 cubes and 2 red spheres, we do not know the shapes of the green objects and thus cannot determine the total number of cubes and spheres. For example, if there is only one green sphere, then there are 5 - 1 = 4 green cubes, and thus 6 - 4 = 2 red cubes. In this case, there are 2 + 2 = 4 red objects and 5 green objects; thus, the total number of objects is 9. On the other hand, if there are two green spheres, then there are 5 - 2 = 3 green cubes, and thus 6 - 3 = 3 red cubes. In this case, there are 3 + 2 = 5 red objects and 5 green objects; thus, the total number of objects is 10. So, we cannot determine with certainty the total number of objects in the box.

Answer: E

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