A cube is painted with blue and red color such that each color is pain

Question

A cube is painted with blue and red color such that each color is painted on three faces.The cube is now cut into 27 smaller and identical cubes. How many smaller cubes have only two faces painted in two different colors?

(1) Two opposite faces have red paint on them.
(2) Each face with blue paint is adjacent to every other face with blue paint.

eshan429 · Answer

a) If two opposite faces have red paint on them, no matter which face we paint red, the other three faces will be blue in color. Now, three adjacent faces have the color red and the other three adjacent faces will have the color blue.

Also, as the cube is being cut into 27 different pieces, this means that we are making 6 cuts (two each across the two opposite faces). Only the center part of each edge will have colours on two faces as each edge is getting cut into 3 pieces. Once we know how this cube is painted and how it's being cut, we can count the number of small cubes with only two faces painted in two different colors. ----> Sufficient

b) Gives the same info as (a). ----> Sufficient

Since, both a & b are sufficient, the answer is D.

Hope that makes it clear.

Bunuel · Answer

A cube is painted with blue and red color such that each color is painted on three faces.The cube is now cut into 27 smaller and identical cubes. How many smaller cubes have only two faces painted in two different colors?

Painting a cube in such a way can only be done in two ways:
(i) Three adjacent faces are of the same color (bottom and two adjacent side faces).
(ii) Two opposite faces and a face joining them are of the same color (bottom, top and one of the side faces).

So, basically we need to know which case we have (we'll have all the information possible so would be able to answer the question no matter what the actual answer would be).

(1) Two opposite faces have red paint on them. We have the second case. Sufficient.

(2) Each face with blue paint is adjacent to every other face with blue paint. We have the second case. Sufficient.

Answer: D.

Bunuel · Answer

Similar questions to practice: the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html 64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html if-a-4-cm-cube-is-cut-into-1-cm-cubes-then-what-is-the-107843.html a-large-cube-consists-of-125-identical-small-cubes-how-110256.html a-cube-of-side-5cm-is-painted-on-all-its-side-if-it-is-sliced-into-48513.html 3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html

Arro44 · Answer

Could someone represent the solution graphically? I thing this would go a long way towards making understanding easier.

sananoor · Answer

Both the statement gives u same info so its either D or E
rule out A, B and C
without going into details, one can see that it gives clear picture of cube and by dividing it into 27 small pieces, one can see that its central part that gives two colors...answer is D

bumpbot · Answer

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A cube is painted with blue and red color such that each color is pain

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