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705-805 Level|   Geometry|      
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damham17
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How many cylindrical cans with a radius of 2 inches and a height of 6 Updated on: 22 Nov 2018, 04:01
Originally posted by damham17 on 15 Mar 2012, 19:20.
Last edited by Bunuel on 22 Nov 2018, 04:01, edited 2 times in total.
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32% (01:24) correct 68% (01:19) wrong based on 451 sessions

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How many cylindrical cans with a radius of 2 inches and a height of 6 inches can fit into a rectangular box?

(1) The volume of the box is 240 cubic inches.

(2) The length of the box is 3 inches.
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How many cylindrical cans with a radius of 2 inches and a height of 6 16 Mar 2012, 01:37
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How many cylindrical cans with a radius of 2 inches and a height of 6 inches can fit into a rectangular box?

Notice that the radius of 2 inches means the diameter of 4 inches.

(1) The volume of the box is 240 cubic inches --> if the dimensions are 1*1*240 then we can fit zero cans but if the dimensions are 4*6*10 then we can fit more than zero cans. Not sufficient.

(2) The length of the box is 3 inches --> since both the diameter (4) and height (6) of the cans are greater than the length of the box (3) then zero cans can be fit into the box. Sufficient.

Answer: B.
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How many cylindrical cans with a radius of 2 inches and a height of 6 25 Sep 2014, 07:22
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Good question. It is easy to miss radius.... dia =4 >3
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How many cylindrical cans with a radius of 2 inches and a height of 6 13 Oct 2015, 01:01
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damham17
How many cylindrical cans with a radius of 2 inches and a height of 6 inches can fit into a rectangular box?

(1) The volume of the box is 240 cubic inches.

(2) The length of the box is 3 inches.

Would someone please clarify this answer for me? Thanks.
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good question for testing the common sense

only have to see that that there can fit no can of dia 4 inches in the box of length 3 inches ( what ever the other sides be)
so (2) is sufficient

and form one we don't get any idea about the fitting of cans or not
i.e. there can be cans or as in (2) there can be no one

so (1) is not sufficient
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How many cylindrical cans with a radius of 2 inches and a height of 6 14 Oct 2015, 06:31
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

How many cylindrical cans with a radius of 2 inches and a height of 6 inches can fit into a rectangular box?

(1) The volume of the box is 240 cubic inches.

(2) The length of the box is 3 inches.

For this question, the radius of the can is given to be 2 inches and the height is 6 inches. From condition 2, the box with length 3 inches cannot fit the cylindrical can, so the answer is 0 and (B), but the question does not come out this way.
Originally, this question has 3 variables (length, width, height) of the box, and we need 3 equations when only 2 equations are given from the conditions provided, so the answer becomes (E) as they are insufficient.

For cases where we need 3 more equation, 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, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. 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 using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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How many cylindrical cans with a radius of 2 inches and a height of 6 23 Jul 2025, 03:51
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Bunuel
How many cylindrical cans with a radius of 2 inches and a height of 6 inches can fit into a rectangular box?

Notice that the radius of 2 inches means the diameter of 4 inches.

(1) The volume of the box is 240 cubic inches --> if the dimensions are 1*1*240 then we can fit zero cans but if the dimensions are 4*6*10 then we can fit more than zero cans. Not sufficient.

(2) The length of the box is 3 inches --> since both the diameter (4) and height (6) of the cans are greater than the length of the box (3) then zero cans can be fit into the box. Sufficient.

Answer: B.
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You said the box isn’t suitable because its height is 3 inches while the cylinder is 6 inches tall — but can’t we just lay the cylinder on its side and place it inside the box?
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How many cylindrical cans with a radius of 2 inches and a height of 6 23 Jul 2025, 14:23
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Bunuel
How many cylindrical cans with a radius of 2 inches and a height of 6 inches can fit into a rectangular box?

Notice that the radius of 2 inches means the diameter of 4 inches.

(1) The volume of the box is 240 cubic inches --> if the dimensions are 1*1*240 then we can fit zero cans but if the dimensions are 4*6*10 then we can fit more than zero cans. Not sufficient.

(2) The length of the box is 3 inches --> since both the diameter (4) and height (6) of the cans are greater than the length of the box (3) then zero cans can be fit into the box. Sufficient.

Answer: B.
You said the box isn’t suitable because its height is 3 inches while the cylinder is 6 inches tall — but can’t we just lay the cylinder on its side and place it inside the box?
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No, you can’t. The diameter of the cylinder is 4 inches, which is also more than the box’s length of 3 inches. So even if you lay the cylinder down, it still won’t fit in any orientation.
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