What is the number of cans that can be packed in a certain

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.

No info about the cans, so this is not sufficient.

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

No info about the carton, so this is not sufficient.

(1)+(2) If the dimensions of the carton are 1 by 1 by 2,304, then no cylindrical cans can be packed in the carton. However, if the dimensions of the carton are 12 by 12 by 16, then more than zero cylindrical cans can be packed in the carton. Insufficient.

Answer: E.
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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
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It requires dimensions of the carton and dimenions of the cans in order to determine the number of cans that can be packed into the carton. Since both A and B together doesn't give all of these required dimensions, the answer is E.

For those who like the approach of proving that more than one answer is possible, here is that approach:
Stm A)
Volume of carton is given as 2304.
So sides can be 1*1*2304 or 2*1*1152 leading to more than one answer. Hence insufficient.
Stm B)
Volume of carton can be 1 or 10 or 100. In each case it can accomodate different number of cans leading to more than one answer. Hence insufficient.
Stms A and B Together:
Same explanation given under Stm A holds good. Hence insufficient.
Answer is E.

Got the point!
But in a reversal case where dimension of carton is given, along with the volume of can. Then, can we get to the answer as above??Bunuel

No, the answer would still be E. (Well, if the volume of the carton is less than the volume of the cans, then we could say that 0 cans could be placed.) The point is, the volume of a can does not limit its height or diameter. Therefore, for any given volume, we could consider the height to be greater than any of the dimensions of the carton, meaning that 0 cans could be placed.
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To solve this one we need a height of the carton. Neither St1 nor St2 gives us this information even combiden --> (E)
1) l*w*h=2304 what is the Height of the carton? Not Sufficient
2) Can H=6, D=4, we need a height of the carton - If the height is 5 then a can fit there, if the height of the carton is 4 - the answer is NO, the cans don't fit there. Not Sufficient
1+2) We need the height of the carton - Not sufficient (E)

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

Answer: Option E

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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)

Hi Experts,
Bunuel KarishmaB

Even when dimensions are given, we can't answer this question without knowing the shape of both cans and carton.
Am I right?

Thank you!

The word 'can' usually means a right cylindrical object (dimensions given are height and diameter) and carton usually means a box/cuboid so given the dimensions I would think that the data should be sufficient to answer.
In any case, if GMAT intends to give you complete data to make it sufficient in the question, you will likely be given "right cylindrical can" and "cuboidal carton" too.
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Bunuel - 'No, the answer would still be E. (Well, if the volume of the carton is less than the volume of the cans, then we could say that 0 cans could be placed.) The point is, the volume of a can does not limit its height or diameter. Therefore, for any given volume, we could consider the height to be greater than any of the dimensions of the carton, meaning that 0 cans could be placed.'

As you explained, I understand that if height of carton is less than that of can, then it couldnt be placed, but you mentioned if height of Can is greater than 'any' of the dimensions of the carton then 0 can could be placed - how it is possible ? for eg. If can's dimensions are radius - 3 and height - 6 and Carton's dimension are 5*5*7 (l*b*h), then 'Can' can be placed in Carton even if Carton's L and B are less than can's height.

Am i understanding it correctly ? pls help