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OG 12, Q 18 (Solid Geometry)

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OG 12, Q 18 (Solid Geometry)

by rahul.s » Sat Feb 06, 2010 6:22 am
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.

OA: B

please elaborate.
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by shashank.ism » Sat Feb 06, 2010 6:45 am
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.

OA: B

please elaborate.
The answer is B..i.e.B is itself sufficient.

Volume of each rectangular block = 12x6x4 = 288 cm3.
area of faces of rectangular block = 12x6, 6x4, 12x4 =72, 24,48 cm3.


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 option B would be correct.
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by sivsrinivas » Sat Sep 25, 2010 3:42 am
The best way to answer such question is imagining or picturising in the mind. These questions are meant to test our IQ power. So, imagine as if you are doing at home. you will do well. There are questions that we need to take easily. Try to reason than doing calculations. Thats the whole point. We are not expected to do any calculations.
Hope this helps you.
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