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# A cube of white chalk is painted red and then cut parallel to the side

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Manager
Joined: 25 Dec 2011
Posts: 54
GMAT Date: 05-31-2012
A cube of white chalk is painted red and then cut parallel to the side  [#permalink]

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02 Jan 2012, 04:33
5
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:21) correct 46% (01:20) wrong based on 83 sessions

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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.

a. 15%
b. 16.67 %
c. 20%
d. 25%
e. 33.33%

As per me the quetsion says new solids - so even a new solid will have 6 surfaces out of which one is not painted red.
So shudnt the answer be b = 16.67 %

Could someone please explain and clarify.

Manager
Status: Enjoying the MBA journey :)
Joined: 09 Sep 2011
Posts: 135
Location: United States (DC)
Concentration: General Management, Entrepreneurship
GMAT 1: 710 Q49 V38
WE: Corporate Finance (Other)
Re: A cube of white chalk is painted red and then cut parallel to the side  [#permalink]

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02 Jan 2012, 05:53
Hi morya003

This problem could be solved easily if we pick some smart numbers (as no numbers are given in the question).

Let's say that the original cube of white chalk had a side of length 2 cm.
The area of a side of the cube will then be 2 x 2 = 4 sq. cm.
The total surface area of the cube will be given by 6 x area of 1 side
i.e. 6 x 4 = 24 sq. cm.

Now, the total surface area represents the area of the cube that has been painted red.

The cube is now cut into half. This means that one of the sides of the newly formed rectangular solid is not painted at all. This area will be equal to the area of the side of the original cube i.e. 4 sq. cm. ---> (1)

Since the newly formed rectangular solid is half of the cube, the area that is painted red is given be (area of 1 side of the cube + half of sum of areas of four other sides of the cube)
i.e. 4 + 1/2 * (4 + 4 + 4 + 4) = 4 + 1/2 (16) = 4 + 8 = 12 sq. cm.

The total surface area of the newly formed rectangular solid will be given by the sum of areas of the sides painted red + the area of the side which is not painted
i.e. 4 + 12 = 16 sq. cm ---> (2)

Now, we are asked to find the percent of the surface area of each of the new solids which is not painted red.
This will be given by the ratio of the area of the surface not painted red to the total surface area of the new solid i.e. from (1) and (2)
i.e. 4 / 16 = 25%

Hence the correct answer is option D

Hope this helps

Cheers!
Sudish
_________________

MBA Candidate 2015 | Georgetown University

Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: A cube of white chalk is painted red and then cut parallel to the side  [#permalink]

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27 Sep 2017, 07:38
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.

Let cube of length = 2a
Now the cube is cut from center to form 2 rectangular cuboids => measurement of cuboid will be 2a , 2a, a ( As only height will be cut short to half of cube =a )

Now all the portions of cuboid is painted red except the cut part which will have measurement equal to area of 1 side of cube = 2a *2a = 4a^2

Total surface area of cuboid = 2(lb+bh+lh) = $$2(2a*2a+2a*a+2a*a) = 2* 8a^2 = 16a^2$$

=> % of cuboid not painted red =$$\frac{4a^2}{16a^2}*100$$= 25%

Re: A cube of white chalk is painted red and then cut parallel to the side &nbs [#permalink] 27 Sep 2017, 07:38
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