Cubes - GMAT Quantitative Reasoning

Statement 1: We can use the surface area to find the length of the cube's edge and then determine the length of the diagonal.

where represents the length of the cube's edge

Now that we know the length of the edge, we can find the length of the diagonal: .

Statement 2: Once again, we can use the provided information to find the length of the cube's edge.

Which means the length of the diagonal is .

Thus, each statement alone is sufficient to answer the question.

Statement 1: To find the length of the diagonal of the cube we need to find the length of the cube's edge. We can use the given surface area value to do so:

Now that we know the length of the cube's edge, we can calculate the diagonal:

Statement 2: We're given the volume of the cube which we can also use to solve for the length of the cube's edge.

Knowing the length of the cube's edge allows us to calculate the diagonal:

Each statement alone is sufficient to answer the question.

Statement 1: We need the length of an edge in order to find the diagonal of the cube. Luckily, we can find the length using the information provided:

Now that we know the length of an edge is 11 cm we can find the length of the diagonal.

Statement 2: We're given the information we need to find the diagonal, all we need to do is plug it into the equation

Statement 1: The information provided in the question is only useful if we're given a relationship between cube A and cube B. Since this statement does provide us with the ratio of 1:2,we can answer the question.

where represents the length of the cube's edge

we can easily see the length measures

Remember the ratio of cube A to cube B is 1:2.

Now that we know the length, we can find the diagonal of the cube:

Statement 2: We're given information about cube A so we don't need to worry about cube B. Using this information we can solve for the edge length of cube A and then calculate the diagonal.

Knowing the length of the edge allows us to find the diagonal of the cube

Call the sidelength, surface area, and volume of the cube , , and , respectively.

Then

or, equivalently,

So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be

Also,

or, equivalently,

Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be

Therefore, the answer is that either statement alone is sufficient.

The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula can be used to find the volume of the sphere.

In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.

Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is where is the length of an edge of the cube and is the length of the diagonal we are able to find the length of the edge. Therefore statement 1 alone is sufficient.

Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.

Statement 1 alone is sufficient.

Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.

Statement 1 tells us that the volume of the cube is , from this we can find the length of the side of the cube. Statement 1 alone is sufficient.

Statement 2, tells us that the area of ABCD is , similarily, by taking the square root of this number, we can find the length of the edge of the cube.

Therefore each statement alone is sufficient.

Statement 1: Use the volume formula for a cube to solve for the side length.

where represents the length of the edge

Statement 2: Use the surface area formula for a cube to solve for the side length.

Each statement alone is sufficient to answer the question.

To find the surface area of a cube, we need the length of one side.

Statement I gives the diagonal, we can use this to find the length of one side.

Statement II gives us a clue about the length of one side; we can use that to find the full length of one side.

The following formula gives us the surface area of a cube:

Use Statement I to find the length of the side with the following formula, where is the diagonal and is the side length:

So, using Statement I, we find the surface area to be

Using Statement, we get that the length of one side is two times two:

Again, use the surface area formula to get the following:

The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.

To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is .

Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is .

So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get . Thus, we can solve this problem with just the information from statement 1.

Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.

Therefore, the answer is that either statement alone is sufficient to answer the question.

If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square.

If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.

Therefore either statement alone is sufficient to solve the question.

Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.

Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do:

Now that we have our length, we can calculate the volume.

Recall that the volume of a cube is equal to the cube of its side length, and that the diagonal of a cube is equal to length.

I) Use the following:

II) Gives us the diagonal. Divide by the square root of three, then cube it!

Either statement is sufficient to answer the question.