The inside of a rectangular carton is 48 centimeters long, 32 centimet

SOLUTION


The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?

(1) Each of the cans has a radius of 4 centimeters --> radius=4 means that diameter=8, which implies that along the 48 centimeter length of the carton 48/8=6 cans can be placed and along the 32 centimeter width of the carton 32/8=4 cans can be placed. Thus, k=6*4=24. Sufficient.

(2) Six of the cans fit exactly along the length of the carton --> the diameter of the can is 48/6=8 centimeters. So, we have the same info as above. Sufficient.

Answer: D.
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Since Height of Box and Height of Cans are equal so only one stack of cans is there in the box. No need to bother about height.
So inside dimensions of Box = 48 X 32
St 1: Sufficient: Each can has radius of 4 = Dia is 8 cms. ie (48/8) 6 nos of cans can be in one row. And since cans are identical (32/8) ie 4 cans can fit in colums. So 24 nos of can can fit in box.
St 2: Sufficient: 6 cans can fit along the length. ie dia of each can = 48/6 ie 8 cms. As discussed in St 1.

Hence Answer is D)

I know the measurement of the carton, which is 48*32. Now the can's radius is 4 cm. Although the height of the carton is the same as the height of the cans i.e. 15, which I am ignoring as it will eventually cancel out in the calculation. My question is around the solution that is provided in the O.G. They have simply divided the length of the carton by diameter and width by diameter and then further multiplied the result.

(48/8)*(32/8)
=6*4
=24.

Btw I got the right answer since its a DS problem. I am worried coz had this been a p.s problem, I might have got this one wrong.
Now the way I would have solved this is

1st find the circumference of the circle (eliminating the height as the it is same). 2IIr=2*22/7*4
and then divided it by (48*32)/(176/7). My answer in this case is different from the OA =61.09

Why II (pie) was not considered. Why circumference was not considered instead of diameter. I failed to understand this. Can you please explain this.

Further when I use a formula for rectangle's area =L*B, where both lenght and breadth is present. But in case of circle I don't have a II(pie) anywhere. Why do we use this. What is the significance of II (pie).

Why are you calculating the circumference?
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Straight forward question. You need to get the radius of the cylinders to get the number of cylinders. Both A and B help to calculate r. D wins.

Hi Bunuel,

I am calculating the circumference because I know the area of the rectangular (ignoring the height 15 cm as it is common to both can and carton). Once I know the area, I can divide the area by circumference of the circle to know the no of cans.

It seems that you don't understand the question. You need neither circumference of the cans nor the area.

Simpler example might help:The carton is 16 centimeters long and 16 centimeters wide. If the diameter of the cans is 8 centimeters, how many cans can be placed in the carton?
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We are given that a rectangular carton has a length of 48 cm, a width of 32 cm, and a height of 15 cm. We are also given that there are k identical cylindrical cans standing upright in this carton, and each can has a height of 15 cm. We need to determine the value of k, or the total number of cans in the carton.

Because we have the dimensions of the carton, if we are able to determine the diameter of each can, then we will be able to determine the value of k.

Statement One Alone:

Each of the cans has a radius of 4 centimeters.

Since the diameter is twice the radius we know that the diameter of each can is 8 cm. This is enough information to determine how many cans fit in the carton. Although we do not have to determine the actual value of k (because this is a data sufficiency problem), let’s determine it anyway.

Since the length of the carton is 48 cm we could fit 48/8 = 6 cans along the length of the carton, and since the width of the carton is 32 cm, we could fit 32/8 = 4 cans along the width of the carton.

Thus the carton could hold a total of 6 x 4 = 24 cans. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E.

Statement Two Alone:

Six of the cans fit exactly along the length of the carton.

In a similar fashion to the process used in statement one, we can use the information in statement two to determine the diameter of each can.

(Length of carton)/(diameter of each can) = number of cans that fit along the length of the carton

48/d = 6

48 = 6d

d = 8

Since we have the diameter of each can, we have enough information to determine how many total cans fit in the carton. Statement two alone is also sufficient to answer the question.

The answer is D.

Note that because we have the length of the carton as 48 centimeters, statements 1 and 2 are giving us the same information – the length of the diameter or radius of each can. Whenever the two statements give the same information, the answer has to be D or E. It can’t be A or B because if one statement is sufficient (or insufficient), the other is too. It can’t be C because neither statement is adding information to the other. So as soon as we realized that A was sufficient in this question, we would know the answer is D.
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in statement B, its no where mentioned that radius is integer hence ans cant be D

Hello

Yes its not mentioned in statement 2 that radius is an integer. But thats not an issue. Applying the logic in statement 2, gives us the radius, which is in fact an integer only (4 cm, which is same as that mentioned in statement 1). So there is no problem.

Hi Bunuel, I have a question, because it is mentioned in the question as "filled to capacity", we are considering the cans are standing upright against the surface with dimensions 48 * 32 (as the height exactly matches height of the carton to fill it completely), and find the answer as D.

Had the question not given as "filled to capacity", we could also consider the cans standing upright against surfaces 48 * 15 or 32 * 15, in which cases, we will get different values of k and answer will be E. Is my understanding correct?

Please help.

Thanks

The dimensions of the carton are 48 centimeters long, 32 centimeters wide, and 15 centimeters high. This implies that the carton is standing on 48*32 face. In addition we are told that the cans of stand upright in rows and columns, so they stand on circular base.
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we have computer the number of barrels along height too. Here height of both cans and box is same, is that the reason we have not done so? Because it will be 1.