Clarification on Geomtery problem

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Clarification on Geomtery problem

by knight247 » Tue Aug 30, 2011 6:42 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.

This one is from the OG. Problem is pretty simple. OA is [spoiler]B[/spoiler]

Statement one is insufficient because we don't know on which side the rectangular blocks are resting.

About statement two, If I take the following
approach let z be the number of blocks

60*30*20=z*12*6*4
z=125. Is equating their volumes and find the value of z sufficient considering that we know the individual dimensions of both Box X and the blocks? Would this approach work for problems where we only know the volume but not the individual sides. Or when we know some of the dimensions but not all? Hope my questions didn't seem too complicated. Thanks

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by Brian@VeritasPrep » Tue Aug 30, 2011 9:10 am
Hey knight247,

Great question - and particularly in a Data Sufficiency context it's important to know that the answer is "no". So, for example, if statement 2 were not the individual dimensions but instead that "the volume of box X is 36,000 cm^3", it would not be sufficient.

Why not?

We can't assume that the blocks will fit evenly in the box. Maybe the most egregious way to demonstrate this is to imagine a box that has that volume of 36,000, but is 36,000 cm long, 1 cm high, and 1 cm deep. The volume is 36,000 cm, but you wouldn't be able to fit any blocks in it because the height and depth of the box are too small.

Or in another example, say you had a cylinder with that same volume. Because the walls of the cylinder are round but the blocks are rectangular, you have to waste some space in there - you can't get the volumes to match up perfectly.

So your calculation works if the blocks fit evenly, of if you're trying to fit liquid in a container (because it will adhere to the container's shape). But it's important to note that the GMAT can make a volume problem substantially harder just by using dimensions in which the items that fill the container won't fit the container perfectly.
Brian Galvin
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Veritas Prep

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by czarczar » Wed Aug 31, 2011 2:12 pm
Thanks Brain.