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# A wooden cube n units on a side is painted red on all six faces and th

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Math Expert
Joined: 02 Sep 2009
Posts: 59720
A wooden cube n units on a side is painted red on all six faces and th  [#permalink]

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22 Mar 2019, 01:18
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Difficulty:

65% (hard)

Question Stats:

50% (02:32) correct 50% (02:14) wrong based on 20 sessions

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A wooden cube n units on a side is painted red on all six faces and then cut into n^3 unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

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Joined: 27 Sep 2018
Posts: 37
Re: A wooden cube n units on a side is painted red on all six faces and th  [#permalink]

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22 Mar 2019, 03:10
Total no of faces painted by red of unit cube =6n^2

Total no of faces of n^3 unit cubes =6n^3

Now atq,Exactly one-fourth of the total number of faces of the unit cubes are red
Which means
6n^2=1/4(6n^3)

Solving we get n =4

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Math Expert
Joined: 02 Aug 2009
Posts: 8309
Re: A wooden cube n units on a side is painted red on all six faces and th  [#permalink]

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22 Mar 2019, 03:12
Bunuel wrote:
A wooden cube n units on a side is painted red on all six faces and then cut into n^3 unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Visualization is the key..

When you are making n^3 cubes out of a cube with n units, means the side of smaller cube is 1 unit as volume of bigger cube is n*n*n=n^3....just for information
Total faces painted red is equal to surface area of bigger cube =6*(n*n)=6n^2.
Number of faces of n^3 cube is 6*n^3..
It is given that (6n^2/6n^3)=(1/4)...n=4

B
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Re: A wooden cube n units on a side is painted red on all six faces and th  [#permalink]

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22 Mar 2019, 03:19
surface area of cube = 6n^2

now after cuttin it into n^3 unit cubes

total surface area = 6*n^3

now it has exactly 1/4 th faces as red then

total surface area before cut = 1/4( surface area after cut)

6n^2= 1/4(6*n^3)

means n = 4

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Location: India
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Re: A wooden cube n units on a side is painted red on all six faces and th  [#permalink]

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22 Mar 2019, 04:22
Bunuel wrote:
A wooden cube n units on a side is painted red on all six faces and then cut into n^3 unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

total sides of cube - 6*s^3 & painted red = 6*s^2
so
6*s^2/6s^3 = 1/4
s= 4
IMO B
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Re: A wooden cube n units on a side is painted red on all six faces and th  [#permalink]

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24 Mar 2019, 18:29
Bunuel wrote:
A wooden cube n units on a side is painted red on all six faces and then cut into n^3 unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Before the cube is cut, the surface area of the cube is 6n^2. After the cube is cut, the total surface area of the n^3 unit cubes is n^3 x 6 = 6n^3. Thus we can create the equation:

6n^2 = ¼ x 6n^3

1 = ¼ x n

4 = n

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Re: A wooden cube n units on a side is painted red on all six faces and th   [#permalink] 24 Mar 2019, 18:29
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