Latest Infosys Aptitude Question SOLUTION: 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

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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

Asked In Infosys vamsybeera (9 years ago)

Solved Tarun G Joy Read Solution (13)

Is this Puzzle helpful?   (117)   (53) Submit Your Solution Data Interpretation

Read Solution (13) :

Ann  (9 years ago)

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

Is this solution Helpfull? Yes (22) | No (2)  

thrilok chand  (9 years ago)

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

Is this solution Helpfull? Yes (15) | No (4)  

Tarun G Joy  (9 years ago) Best Solution

11- 384
12- 80
13- 216
14- 24
15- 144

Is this solution Helpfull? Yes (13) | No (19)  

  (6 years ago)

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

Is this solution Helpfull? Yes (9) | No (1)  

anand mehta  (7 years ago)

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

Is this solution Helpfull? Yes (5) | No   

annu priya  (9 years ago)

plzz smbody explain

Is this solution Helpfull? Yes (4) | No   

Atul Kumar Mishra  (8 years ago)

11.(C)
12.(d)
13.(c)
14 (a)
15(b)

Is this solution Helpfull? Yes (3) | No   

annad  (9 years ago)

11(c)384
12(b)64
14(a)24
15(a)64

Is this solution Helpfull? Yes (1) | No (7)  

sai prathyusha  (7 years ago)

512 identical cubes means 7 cuts on each face
red cubes =128 therefore no red painted =512-128=384

Is this solution Helpfull? Yes (1) | No   

alekhya gandhi  (9 years ago)

11(c) 384
12(a) 96
13(b) 125
14(a) 24
15(b) 144

Is this solution Helpfull? Yes | No (4)  

Namratha Annapureddy  (9 years ago)

Could somebody explain it in detail....

Is this solution Helpfull? Yes | No (2)  

P KRISHNA  (9 years ago)

Can you explain 11,12 questions?

Is this solution Helpfull? Yes | No (1)  

Ankita Ghosh  (9 years ago)

is calculator allowed in Infosys? like here we need to find cube root...is online calculator provided

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