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What is the maximum number of rectangular blocks, each with [#permalink]

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18 Jul 2009, 19:16

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What is the maximum number of rectangular blocks, each with dimensions 12 centimeters by 6 centimeters by 4 centimeters, that will fit inside rectangular box X?

(1) When box X is filled with the blocks and rests on a certain side, there are 25 blocks in the bottom layer. (2) The inside dimensions of box X are 60 centimeters by 30 centimeters by 20 centimeters.

What is the maximum number of retangular blocks, each with dimensions 12 centimeters by 6 centimeters by 4 centimeters, that will fit inside rectangular box X?

1. When box X is filled with the blocks and rests on a certain side, there are 25 blocks in the bottom layer. 2. the inside dimensions of Box X are 60 centimeters by 30 centimeters by 20 centimeters.

25 = 25*1 or 5*5 so the only possible arrangement of the boxes is 25 of one row or 5*5 rows with each arrangement we can have differnt dimension for the big box........insuff

from 2

thinking volume 12*6*4 = 288 for each samll box , 36000 = volume of big one thus max number is 36000/288 = 125 boxes..suff

I didn't get this explanation. Can someone explain? Thanks.

What is the maximum number of rectangular blocks, each with dimensions 12 centimeters by 6 centimeters by 4 centimeters, that will fit inside rectangular box X?

(1) When box X is filled with the blocks and rests on a certain side, there are 25 blocks in the bottom layer. Useless info: the maximum # of boxes clearly will be different for the box X with the height of 12 centimeters and for the box X with the height of 12,000 centimeters (for example). Not sufficient.

(2) The inside dimensions of box X are 60 centimeters by 30 centimeters by 20 centimeters --> we have the dimensions of the little boxes as well as the dimensions of box X (basically we have all the info we could possibly knew), hence we can calculate the maximum # of boxes that will fit inside box X, no matter what this # actually is. Sufficient.

What is the maximum number of rectangular blocks, each with dimensions 12cms by 6cms by 4cms, that will fit inside rectangular box X?

1. When box X is filled with the blocks and rests on a certain side, there are 25 blocks in the bottom layer. 2. The inside dimensions of box X are 60cms by 30cms by 20 cms.

Statement 1: This will give us two dimensions of the larger box, but since we do not know the height of the larger box, this is insufficient. Statement 2: We know the dimensions of the larger box so we can calculate. Sufficient.

What is the maximum number of rectangular blocks, each with dimensions 12cms by 6cms by 4cms, that will fit inside rectangular box X?

1. When box X is filled with the blocks and rests on a certain side, there are 25 blocks in the bottom layer. 2. The inside dimensions of box X are 60cms by 30cms by 20 cms.

Please DO NOT reword or shorten the questions.
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Re: What is the maximum number of rectangular blocks, each with [#permalink]

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18 May 2014, 11:07

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statement (1): Now here are 25 blocks in bottom layer but we don't know which face is on the lower layer so we can't calculate the max no of block.

so statement is insufficient.

statement (2): dimension of rectangular box X = 60x30x20 cm3 volume = 60x30x20 = 36000 cm3 so dividing by volume of blocks , no. of max blocks that can be accommodated = 36000/288 = 125.

also area of faces of rectangular box = 60x30, 30x20, 60x20 = 1800,600, 1200 cm3.

now 1800/72 = 25 so 12x6 face exactly fits on 60x30 face. 20/4=5 thus overall 125 blocks sets fully inside it ..which was max capacity. so it is sufficient also if we check for other dimensions like 600/24 = 25, and 60/12=5 ..so it same also if we check 1200/48 = 25, and 30/6 = 5..so it is same.

if we take any other face ... u can't put max. blocks.. Hence B

What is the maximum number of rectangular blocks, each with [#permalink]

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06 Aug 2014, 11:55

Most of you are making a BIG mistake. The correct answer is B but many of you are incorrectly justifying your answer choice.

In this scenario, you can't multiply the dimensions of the box to attain the total volume and then divide that number by the volume of the rectangular box to determine the total number of blocks that could fit. That's wrong.

For example, I could ask what is the total number of rectangular blocks (10x2x1) that fit in a rectangular box of (5x4x1).

Do you see the problem? With the method most of you are using, your answer to this question would be 1 block. However, while both volumes equal 20 cubic units, you can't fit a rectangular block with side length 10 into a box with side length 5 no matter how you try.

The correct way of approaching this problem is demonstrated by Brunel:

Bunuel wrote:

(2) The inside dimensions of box X are 60 centimeters by 30 centimeters by 20 centimeters --> we have the dimensions of the little boxes as well as the dimensions of box X (basically we have all the info we could possibly knew), hence we can calculate the maximum # of boxes that will fit inside box X, no matter what this # actually is. Sufficient.

Re: What is the maximum number of rectangular blocks, each with [#permalink]

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12 Feb 2016, 20:35

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