Data Sufficiency

ardz24 wrote:What is the number of cans that can be packed in a certain carton?

(1) The interior volume of this carton is 2,304 cubic inches.
(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.

What's the best way to determine which statement is sufficient? Can any experts help?

Target question: What is the number of cans that can be packed in a certain carton?

Let's head straight to.....

Statements 1 and 2 combined
Consider these two conflicting cases (that satisfy BOTH statements):
Case a: the dimensions of the box are numbers are 1 x 1 x 2304 (inches), in which case ZERO cans can fit inside the carton
Case b: the dimensions of the box are numbers are 10 x 10 x 23.04 (inches), in which case MORE THAN ZERO cans can fit inside the carton

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

ardz24 wrote:What is the number of cans that can be packed in a certain carton?

(1) The interior volume of this carton is 2,304 cubic inches.
(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.

We need to determine the number of cans that can be packed in a carton. Before moving to the statements, we should recognize that we are not given the shape of the carton. Keep in mind that cartons of different shapes will allow a varying number of cans to be packed into the carton.

Statement One Alone:

The interior volume of this carton is 2,304 cubic inches.

Even though we know the volume of the carton, we still do not know the dimensions of the cans or the shape of the carton. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The exterior of each can is 6 inches high and has a diameter of 4 inches.

Although we have the dimensions of each can, we still do not know the shape or dimensions of the carton. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statements one and two, we know the volume of the carton and the dimensions of each can. However, without knowing the exact shape or dimensions of the carton, we cannot determine how many cans can be packed into the carton.

For example, if the carton were 16 by 16 by 9, we could fit only a single layer of 16 cans, with a lot of space left above the cans. But if the carton were 9 by 128 by 2, we couldn't fit any cans because both the diameter and the height of the cans would exceed the height of the carton.

Answer: E