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Square cardboard

by manik11 » Mon May 30, 2016 11:40 pm
A flat square piece of cardboard is to be made into a cubic open box by cutting 4 equal squares from its edges. What is the volume of the box created?

(1) The area of the cardboard piece is 144 square inches.
(2) Each of the squares that are cut from the cardboard has an area of 16 square inches.

OA : D

Experts,could you please show how statement 1 can be sufficient?
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Source: — Data Sufficiency |
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by MartyMurray » Tue May 31, 2016 4:15 am
manik11 wrote:Experts,could you please show how statement 1 can be sufficient?
Statement 1: The area of the cardboard piece is 144 square inches.

Given that the piece of cardboard is a square, if its area is 144, the length of each of its sides is 12.

In order to create a cubic open box in the way described, you have to create 4 sides and a bottom, each of which has the same dimensions.

The four sides are attached to the bottom, two on each side of the bottom. So the length of the edges of the four sides and of the bottom will be 1/3 of the length of the original piece of cardboard.

12/3 = 4 = the length of the edges of the cube

4 x 4 x 4 = 64 = the volume of the cube

Sufficient.
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by manik11 » Tue May 31, 2016 4:29 am
Marty Murray wrote: So the length of the edges of the four sides and of the bottom will be 1/3 of the length of the original piece of cardboard.
Marty, Could you please explain this part of the solution again. I just can't get how the sides of the cube would be 1/3rd of the side of the original cardboard.

Thanks!
Manik
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by MartyMurray » Tue May 31, 2016 4:39 am
manik11 wrote:
Marty Murray wrote: So the length of the edges of the four sides and of the bottom will be 1/3 of the length of the original piece of cardboard.
Marty, Could you please explain this part of the solution again. I just can't get how the sides of the cube would be 1/3rd of the side of the original cardboard.

Thanks!
Manik
Image

To make the box, fold the four outer squares up, leaving the top open.
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by Matt@VeritasPrep » Tue Jun 07, 2016 11:38 pm
manik11 wrote:
Marty Murray wrote: So the length of the edges of the four sides and of the bottom will be 1/3 of the length of the original piece of cardboard.
Marty, Could you please explain this part of the solution again. I just can't get how the sides of the cube would be 1/3rd of the side of the original cardboard.

Thanks!
Manik
This is useful to learn, but one last testday tip: since this is DS, you don't even need to visualize how to do it - you just need to recognize that there is only one way.
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