Data Sufficiency

What is the total surface area of rectangular solid R ?

(1) The surface area of one of the faces of R is 48

(2) The length of one of the edges is 3

Ans E

I chose A

Doubt : If we know the area of one of the faces of R, isnt that sufficient to calculate the total surface area which will be the surface area of one face*no.of faces

And rectangular solid has 6 faces

Where did I go wrong ?

moneyman wrote:What is the total surface area of rectangular solid R ?

(1) The surface area of one of the faces of R is 48

(2) The length of one of the edges is 3

Ans E

I chose A

Doubt : If we know the area of one of the faces of R, isnt that sufficient to calculate the total surface area which will be the surface area of one face*no.of faces

And rectangular solid has 6 faces

Where did I go wrong ?

What you did is true only for cubes, in which each of the six faces are equal. This is a rectangular solid . In a rectangular solid the opposite faces are equal. The surface area of a rectangular solid is found out by adding the area of each of the six faces. For finding out the surface area we need to know the width (w), height (h), and length (l) (Note that in case of a cube w,l,h are equal). The surface area is given as 2(w*h+h*l+w*l)

In the first statement we have that the area of one of the faces is 48. Then the area opposite to this face will also have an area of 48. But this gives us the area of only 2 of the faces (or one pair of equal faces, where as a rectangular solid has 3 pairs of equal faces) and we have no clue about the other 4 faces. So this statement is not sufficient.

The second statement says that the length of one of the edges is 3. This could be the value of w,h,l. But to find out the value of the surface area we need all the 3 values hence this statement is also insufficient.

Now, even when we combine the 2 statements we see that though we know the surface area of one of the faces and one of the lengths, we still dont know whether the length is the length of w,h,l . With the help of the given information we can find the length of one more length as 48 =3 * w or 3*h or 3*l. We still wont get the value of all the length and hence wont be able to find out the surface area. Hence the answer is E.

Note: - Thing to learn is that a cube and rectangular solid are not the same thing. Read more about the rectangular solid here. Also google rectangular solid to find more

well explained!

thanks gabriel

gabriel wrote:

moneyman wrote:What is the total surface area of rectangular solid R ?

(1) The surface area of one of the faces of R is 48

(2) The length of one of the edges is 3

Ans E

I chose A

Doubt : If we know the area of one of the faces of R, isnt that sufficient to calculate the total surface area which will be the surface area of one face*no.of faces

And rectangular solid has 6 faces

Where did I go wrong ?

What you did is true only for cubes, in which each of the six faces are equal. This is a rectangular solid . In a rectangular solid the opposite faces are equal. The surface area of a rectangular solid is found out by adding the area of each of the six faces. For finding out the surface area we need to know the width (w), height (h), and length (l) (Note that in case of a cube w,l,h are equal). The surface area is given as 2(w*h+h*l+w*l)

In the first statement we have that the area of one of the faces is 48. Then the area opposite to this face will also have an area of 48. But this gives us the area of only 2 of the faces (or one pair of equal faces, where as a rectangular solid has 3 pairs of equal faces) and we have no clue about the other 4 faces. So this statement is not sufficient.

The second statement says that the length of one of the edges is 3. This could be the value of w,h,l. But to find out the value of the surface area we need all the 3 values hence this statement is also insufficient.

Now, even when we combine the 2 statements we see that though we know the surface area of one of the faces and one of the lengths, we still dont know whether the length is the length of w,h,l . With the help of the given information we can find the length of one more length as 48 =3 * w or 3*h or 3*l. We still wont get the value of all the length and hence wont be able to find out the surface area. Hence the answer is E.

Note: - Thing to learn is that a cube and rectangular solid are not the same thing. Read more about the rectangular solid here. Also google rectangular solid to find more

Gabriel, so in order for the answer to be C, what additional information do we need?Thank you!