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 information about the cans. Not sufficient.
(2) The exterior of each can is 6 inches high and has a diameter of 4 inches. No information about the cartons. Not sufficient.

(1)+(2) If the dimensions of the carton are 1 by 1 by 2,304, then zero cylindrical cans can be packed in the carton but if the dimensions of the carton are 12 by 12 by 16, then more than zero cylindrical cans can be packed in the carton. Not sufficient.

Answer: E.
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If the dimensions had been given instead of volume in 1, it would have been sufficient.
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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 that the volume of a can does not limit its height or diameter, so for any volume we can consider the height to be greater than any of the dimensions of the carton, and this would mean 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)

Bunuel
Hi, I have couple of queries in this question

1) Are we assuming that can is right angled cylinder ?

2) Even if Can is cylinder and we know size and shape of Carton, number of cans in box will be dependent on the arrangement of cans, so answer will be E in any case >

Hi,

Can anybody help me understand graphically.

Thanks in advance.

Hello faizanqazi,

There was a similar question discussed in an Old OG question. In that question the Stem itself has a graphical representation. The responses for other Club users may help you to co-relate this question better

Link to the Old OG question - https://gmatclub.com/forum/the-inside-o ... 38301.html

I hope this helps you.


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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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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
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what is the difference between interior volume and exterior ?

1 by 1 by 2,304 its hard to imagine carton with such dimension The exterior of each can is 6 inches high and has a diameter of 4 inches .... it means 6*4 = 24

and 2,304/24

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 that the volume of a can does not limit its height or diameter, so for any volume we can consider the height to be greater than any of the dimensions of the carton, and this would mean that 0 cans could be placed.[/quote]

If we were given two dimensions of the box along with the volume, could we have answered the question combining (1) and (2)?

Thanks in advance!

Genoa2000
Yes, in that case you can easily calculate the third dimension of the box. And there would have been only one answer either a '0' or '40' or any other value.
Case I: L = 12, B = 12, H = 16
Number of cans = \(\frac{96}{\pi}\) (integer value only)

Case II: L = 48, B = 12, H = 4
Number of cans = 0

Only one value had been possible whatever be it.

HTH..
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Two things are required for answering these types of questions:
1. The dimensions of the container
2. Dimensions of the cylindrical unit.

We can jump straight to C.

Since we don't have the dimensions of the container, then we can't determine how many cans will fit.

E.
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Might be a weird question, but let's say you are given the exterior of the carton as well, would that be enough for answer choice C.

Generally speaking, aren't there multiple ways of packing cans into a carton, which means there are multiple solutions (numbers of cans that fit into the carton)?

Thx in advance!

Answer: Option E

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Such questions are actually mentally disturbing. Why would anyone expect a card board box of 1*2034? Anyway need to be more precautious