Data Sufficiency

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.

If Statement (1) stated that the carton was shaped as a cube, would the answer then be C?

infiniti007 wrote:If Statement (1) stated that the carton was shaped as a cube, would the answer then be C?

The trick to getting this question right is realizing that a carton with a certain volume can be in various shapes. It could be shaped in such a way as to hold large number of cans, shaped in such a way as to hold only a few cans, or even shaped so that it is so flat or narrow that even though is has a large volume it can hold no cans at all.

So even though the volume of the carton is given, one cannot determine how many cans fit in the carton.

If Statement 1 included not just the volume of the carton but also information defining the shape or interior dimensions of the carton, then one would have sufficient information to determine the number of cans that would fit in the carton. Because all the interior dimensions a cube of a certain volume can be calculated from the volume, if Statement 1 included the information that the carton is in the shape of a cube, one could determine the number of cans that the carton could hold, and the answer to this question would be C.

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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 have 5 variables from the original condition (2 cans (radius, height) 3 carton :length, width, height) therefore we need 5 equations. Since there is only 1 each in 1) and 2), there is high probability that E is the answer, and it turns out that E actually is the answer.

Normally for cases where we need 3 or more equations, such as original conditions with 3 variables, or 4 variables and 1 equation, or 5 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore E has a high chance of being the answer (especially about 90% of 2by2 questions where there are more than 3 variables), which is why we attempt to solve the question using 1) and 2) together. Here, there is 80% chance that E is the answer, while C has 15% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer according to DS definition, we solve the question assuming E would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

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Basically:
1. Having volume is not enough, must know internal dimensions of the carton
2. Also must know the outer dimensions of the can

From (1) + (2) - we still do not know the internal dimensions of the carton. Hence this is insufficient.

(E)