A cube of white chalk

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2sun3: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Mon Jul 07, 2008 6:53 am

by 2sun3 » Wed Aug 27, 2008 9:26 am

A cube of white chalk is painted red, and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids is not painted red?

It's taken from Kaplan GMAT Ed 2005. Please could you try to give me the reasoning behind the steps of calculation. Thanks

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Source: Beat The GMAT — Problem Solving | Wed Aug 27, 2008 9:26 am

pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Wed Aug 27, 2008 9:37 am

Take an easy cube side for example 2.

Let's focus on one rectangle, it is now 2*2*1
The total surface is 2*2 + 2*2 + 1*2 + 1*2 + 1*2 + 1*2=16
The surface which is not painted is 2*2=4
(Draw a cube)
So 4/16=1/4

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rishi235: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Aug 02, 2008 10:05 pm; Thanked: 5 times

by rishi235 » Wed Aug 27, 2008 9:58 am

I agree with pepe.....Ans is 25%...
Did wid the same method

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed Aug 27, 2008 10:57 am

Picking numbers is a great way to solve.

We could also reason it out:

If we cut the cube down the middle, our new shape will also have 6 sides, 5 of which will be red (only the exposed middle will be white).

Two of the 6 sides will be full-sized (the white side and the side opposite) and 4 will be half-sized (the 4 sides "ringing" the white side). Let's call the area of a full side x and the area of a half side .5x; so, the entire surface area will be:

2(x) + 4(.5x) = 2x + 2x = 4x.

The white side has area x, so the proportion of the shape that's white is x/4x = 1/4.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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pre-gmat: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue Jul 15, 2008 7:03 pm; Thanked: 5 times

by pre-gmat » Wed Aug 27, 2008 11:20 am

Can you explain this more to me. I guess I am having a problem envisioning it. I understand thet 2 of teh sides will be full sized but DONT understand other 4 sides.

Two of the 6 sides will be full-sized (the white side and the side opposite) and 4 will be half-sized (the 4 sides "ringing" the white side). Let's call the area of a full side x and the area of a half side .5x; so, the entire surface area will be:

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed Aug 27, 2008 11:28 am

pre-gmat wrote:Can you explain this more to me. I guess I am having a problem envisioning it. I understand thet 2 of teh sides will be full sized but DONT understand other 4 sides.

Two of the 6 sides will be full-sized (the white side and the side opposite) and 4 will be half-sized (the 4 sides "ringing" the white side). Let's call the area of a full side x and the area of a half side .5x; so, the entire surface area will be:

We're making our cut parallel to the sides to create two rectangular boxes with equal volume - in other words, we're cutting the cube in half.

Let's simplify to 2 dimensions. If you cut a square with sides of 1 to create two equally sized rectangles, each rectangle will have dimensions of 1 * 1/2. Now think of that square as the top face of a cube, and you're cutting all the way through instead of just the surface. The top of the shape you've created has dimensions of 1 * 1/2, as do the bottom and 2 of the sides. The surface along which the knife traveled is still a full square, as is the side opposite that one.

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pre-gmat: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue Jul 15, 2008 7:03 pm; Thanked: 5 times

by pre-gmat » Wed Aug 27, 2008 11:32 am

Perfect I got it now:)

I guess I was combining the cut sides of the rectangle.

Thnx a ton:)

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2sun3: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Mon Jul 07, 2008 6:53 am

Still not getting it

by 2sun3 » Thu Aug 28, 2008 6:38 am

Thanks guys,

But still not getting it how is the white side and the side opposite is full sized, and the other 4 are half sized? Please Explain.

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pre-gmat: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue Jul 15, 2008 7:03 pm; Thanked: 5 times

by pre-gmat » Thu Aug 28, 2008 8:21 am

Try taking a cube of Tofu and cut it parallel to sides. You will see that the length of 2 sides is intact and the 4 are cut in Halves)

Stuart's logic is excellent in explaining this. Try reading it 2-3 times.

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