There is a cube in which one pair of opposite faces is painted red ; the second pair of opposite faces is painted blue and the third pair of opposite
faces is painted green. This cube is now cut into 512 smaller but identical cubes.
11. How many small cubes are there with no red paint at all ?
a)256 b)144 c)384 d)400 e)220
12. How many small cubes are there with at least two different colours on their faces?
a)96 b)64 c)120 d)80 e)60
13. How many small cubes are there without any face painted ?
a)64 b)125 c)216 d)343 e)120
14. How many small cubes are there with only red and green on their faces ?
a)24 b)12 c)27 d)16 e)12
15. How many small cubes are there showing only green or only blue on their faces ?
a)64 b)144 c)125 d)169 e)122

• For any cube,
  let x denote number of cuts.Then
  No: of cubes with 3 faces colored = 8
  No: of cubes with 2 faces colored = 12* (x-2) where 12 is the number of edges
  No: of cubes with 1 faces colored = 6* (x-2)^2 where 6 is the number of faces
  No: of cubes with 0 faces colored = (x-2)^3
  Total cubes= x^3
  Total inner cubes =(x-2)^2
  
  Comming to the question..........
  given 512 smaller cubes.so number of cuts=x=8 {cuberoot of 512)
  
  Q1. No red = Total cubes - Cubes with red color
  According to formula all colors are present on 8 cubes.
  Now cubes with 2 colors = 12(x-2)... But here only 2 sides have red ,so number of satisfying edges is 4 out of 12.
  hence eq. becomes 8(x-2)=8(8-2)=48
  Now 1 face = 6(x-2)^2
  here only 2 faces in red
  So eq. becomes 2(x-2)^2=72
  Adding all three , we get 8+48+72=128..
  So without red =512-128=384
  
• 9 years agoHelpfull: Yes(22) No(2)
• divide the cube into 512 identical pieces,
  i.e, in 1 side of original cube contains 64 small cubes,
  for question 1:: they were 128(64*2) cubes contain red faces. just subtract 128 from 512, then u will get 384.
  for question 2:: there will be 10 corners in a cube and each corner contains 8 small cubes, 10*8=80 will be the ans
  for question 3:: 512 - 128(2 faces) + 96(2 faces) + 72(2 faces) = 216.
  for question 4:: only 4 corners contains green and red, by excluding other color cubes, 6 cubes contain only green and red, so ans will be 24.
  for question 5:: by excluding corner cubes, there were 36 cubes, and we have to count only green or or only red, 36 * 4(2 red +2 green) = 144
• 9 years agoHelpfull: Yes(15) No(4)
• 11- 384
  12- 80
  13- 216
  14- 24
  15- 144
• 9 years agoHelpfull: Yes(13) No(19)
• First of all, calculate the length of the parent cube,
  We have 512 cubes each have 1 unit length. So 512 cubes =8*8*8
  The side of the big cube=8 unit.
  
  1. Calculate the no. of cubes without having red colour at all. So first calculate the cubes with red colour
  No of red= 2*(No of cubes on one face)= 2*(8*8)=128
  No of cubes without red=512-128=384 so option c is correct.
  2. No of cubes with at least 2 different colours on faces= No of the cubes with 2 colours + No of Cubes
  with 3 colour faces
  
  No of cubes with 2 faces coloured= (X-2)*No of Edges
  X=Length of big cube/length of small cube=8/1=8
  No of edges on big cube=12
  No of cubes with 2 faces coloured=(8-1)*12=72
  
  No of cubes with 3 faces coloured= No of cubes corners in big cube=8
  
  No of cubes with at least 2 different colours on faces=72+8=80 so option d is correct.
  
  3. small cubes are there without any face painted =(X-2)^3=(8-2)^3=216 so the option c is correct.
  
  4. How many small cubes are there with only red and green on their faces= No of cubes with only
  red+No of cubes with only green
  
  No of cubes with only green=2*(6) (Not including the edges and corner cubes and 2 is multiplied
  for two faces )
  No of cubes with only red=2*(6) (Not including the edges and corner cubes and 2 is multiplied
  for two faces )
  How many small cubes are there with only red and green on their faces=12+12=24
  5. How many small cubes are there showing only green or only blue on their faces= Left the corner and
  edge touched cubes for both the side i. 6*6 on one side and 2*6*6 for one type colour
  
  How many small cubes are there showing only green or only blue on their faces=2*(2*6*6)=144 so
  option b is correct
• 6 years agoHelpfull: Yes(9) No(1)
• 11. C no red=total-red side=(512-(64+64))=384
  12. D at least two different color=72(two side painted=12*(8-2))+8(3-side painted)=at corners.
  13. C (8-2)^3=216
  14. A only red+green(4*(8-2))=24
  15. C only green or only blue=(72+72) =144
• 7 years agoHelpfull: Yes(5) No(0)
• plzz smbody explain
  
• 9 years agoHelpfull: Yes(4) No(0)
• 11.(C)
  12.(d)
  13.(c)
  14 (a)
  15(b)
• 8 years agoHelpfull: Yes(3) No(0)
• 11(c)384
  12(b)64
  14(a)24
  15(a)64
• 9 years agoHelpfull: Yes(1) No(7)
• 512 identical cubes means 7 cuts on each face
  red cubes =128 therefore no red painted =512-128=384
  
• 7 years agoHelpfull: Yes(1) No(0)
• 11(c) 384
  12(a) 96
  13(b) 125
  14(a) 24
  15(b) 144
• 9 years agoHelpfull: Yes(0) No(4)
• Could somebody explain it in detail....
• 9 years agoHelpfull: Yes(0) No(2)
• Can you explain 11,12 questions?
  
• 9 years agoHelpfull: Yes(0) No(1)
• is calculator allowed in Infosys? like here we need to find cube root...is online calculator provided
• 9 years agoHelpfull: Yes(0) No(4)