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What is the maximum number of rectangular blocks, each with [#permalink]
18 Jul 2009, 18:16

00:00

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Difficulty:

15% (low)

Question Stats:

74% (01:49) correct
25% (00:35) wrong based on 153 sessions

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

Re: What is the maximum number of retangular blocks, each with [#permalink]
25 Mar 2012, 02:45

2

This post received KUDOS

Expert's post

mymbadreamz wrote:

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.

Re: Data Sufficiency [#permalink]
08 May 2012, 22:50

Clearly (B)

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.

Re: Data Sufficiency [#permalink]
09 May 2012, 01:59

Expert's post

Merging similar topics.

rakp wrote:

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.
_________________

Re: What is the maximum number of rectangular blocks, each with [#permalink]
18 May 2014, 10:07

1

This post received KUDOS

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

gmatclubot

Re: What is the maximum number of rectangular blocks, each with
[#permalink]
18 May 2014, 10:07