Is it possible for a wooden block in the shape of a rectangular solid

Question

Is it possible for a wooden block in the shape of a rectangular solid measuring l by w by h centimeter to pass through a square hole with sides of length 4 centimeters?

1) The volume of the wooden block is 16 cm3.

(2) L > w > h > 1

Source: Advanced Quant Manhattan Prep 2020

GMATSlayer2021 · Answer

Given: dimension of the square is 4cm x 4cm

Statement 1:
The volume of the block is 16
This could mean the dimensions are:
64 * 1/2 * 1/2 - Possible
4 * 4 * 1 - Possible
8 * 2 * 1 - Possible
Sufficient

Statement 2:
L > w > h > 1
It could be 1.1 * 1.2 * 1.3 that is possible OR 100 * 100 * 100 that is impossible

Thus, answer is A

IanStewart · Answer

As long as two of the three dimensions of the block are less than 4 cm, the block will be able to pass through the square. Using Statement 1, it's certainly possible that two of the dimensions are less than 4 cm - it could measure 2x2x4, say. But it's also possible that only one of the dimensions is less than 4 cm. Maybe the height is 1/1,000,000 cm, and the other two dimensions are both 4000 cm, which would look like an enormous square sheet of paper. Without bending the sheet, you couldn't pass that sheet through a small square hole no matter how you rotate it.

Statement 2 is clearly insufficient alone, but using both Statements, if it were true that two of the block's dimensions were greater than 4, then since the third dimension must be greater than 1, then the volume would automatically be greater than 16 cm^3. So it's impossible for two (or all three) of the dimensions to exceed 4 cm. So at most one dimension exceeds 4 cm, and we know if only one dimension is greater than 4 cm, the block can fit through the square. So the answer is C.

jrk23 · Answer

Don't we have any decimal value greater than 1 but less than 4 that make it true to pass through the sqaure. in that case it will pass, but if have 16,1,1 it will not pass. so have both answers. Please correct me where i am wrong.

Davinder1209 · Answer

Volume is 16
1) it can be 8*2*1 or 4*4*1 so Insufficient
2) L>B>H>1 i.e 4*3*2 or Any integers

Considering both 
If abc=16 and a>b>c then we can get these answer in same ascending of in decimal form.

IanStewart · Answer

If it measures 16 x 1 x 1, you would just rotate it so a 1 x 1 side was facing the square. Then it will easily pass through.

You might imagine a long commuter train and a normal-sized train tunnel. The train might easily pass through the tunnel if the train is traveling normally down the tracks. But if you rotate the train 90 degrees (so the train windows on one side are facing the tunnel entrance) and tried to push it through the tunnel, it won't fit because the train is far too long.

In this question, when two of the dimensions of the block are smaller than the dimensions of the square, we can make the block pass through the square if we rotate the block to the right position.

jrk23 · Answer

Thanks for the explanation. I completely missed out this part while solving. Thanks again

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Is it possible for a wooden block in the shape of a rectangular solid

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