Latest CAT Aptitude Question SOLUTION: In a cube, one pair of opposite faces is painted in Red, the second pair of opposite faces is painted Greeen and the third pair is in Blue. This cube is now cut into 729 smaller bu

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(#M40029067) CAT question Keep an EYE

In a cube, one pair of opposite faces is painted in Red, the second pair of opposite faces is painted Greeen and the third pair is in Blue. This cube is now cut into 729 smaller but identical cubes.
(i) How many small cubes are there with at least two different colors on their faces??
(Ans. 92)
(ii). How many small cubes are there with exactly one face painted red???
(Ans. 98)

please explain in detail.

Asked In CAT Divya Srivastava (10 years ago)

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RAKESH  (10 years ago)

let a cube of dimension 9*9*9 is cut into 729 smaller cubes of dimension 1*1*1
1) consider a face of cube
there is a 9*9 square sheet in which 9+8+8+7=32 cubes are painted with at least two different colors (4 cubes are painted with 3 colors,28 are painted with 3 colors).
now cosider opposite face of this face
there also 32 cubes are painted with at least two different colors
now consider 4 corners,not included in these two faces
there are 7 cubes at each corner painted with two colors
so no. of cubes painted with at least two different colors on their faces = 32+32+4*7=92
2)consider a red painted face of cube there is a 9*9 square sheet in which
7*7 cubes are there with exactly one face painted red
there also 7*7 cubes are exactly one face painted red
so total no. of cubes exactly one face painted red=7*7+7*7=98

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