Page 253 - Services Selection Board (SSB) Interviews

Cubes 249
But here we have removed a cubes of the form of 29. (a) From top face (out of 3 × 3 square face) only one
3 × 3 × 3 and again put it back so out of three cube is with one face painted.
new exposed faces of big cube we will have 4 cubes From 4 vertical faces each face will give us 6 cubes
in each face that is painted with one colour hence hence total number of cubes from vertical faces is
number of cubes from these three surfaces is 3 × 4 6 × 4 = 24.
= 12 From bottom face we will get 3 × 3 = 9 cubes
Now consider out of 3 × 3 × 3 cubes we will have 6
cubes (one in each face) which are painted only one So total number of cubes with one face painted is 1
face. + 24 + 9 = 34
Hence total number of cubes = 48 + 12 + 6 = 66 30. (d) Number of cubes with no face painted is
23. (a) Without any changes number of cubes with no 105 – 34 – 24 – 20 = 27
3
face colour is given by (6 – 2) = 64 Or else all the 3 × 3 × 3 inner cubes will remain
Now because of removal of 3 × 3 × 3 cubes from coloured.
one of the corner from each face that were not Solution for 31–35:
painted earlier got exposed and will get painted, so Here we have following cases:
from 3 × 3 × 3 cubes 4 × 3 = 12 cubes got painted, Case (i): When same colour is on opposite face.
and a similar number from 3 exposed faces of big
cube got painted. Case (ii): When two red colours are on opposite face and
Total number of cubes with no face painted is blue & green on adjacent faces
64 – 12 – 12 = 40 Case (iii): When two green colours are on opposite face
24. (c) Out of 27 small cubes from 3 × 3 × 3, outer 26 and blue &red on adjacent faces.
st
cubes are 1 painted with blue and then it is kept Case (iv): When two blue colours are on opposite face
back with original cube and painted with yellow so and red & green on adjacent faces.
out of 26 cubes only 5 edges will give us cubes with Case (v): When same colours are on adjacent faces.
both the colours and number of such cubes are 12 31. (a) We will evaluate the value of ‘K’ in each and
25. (d) Out of 12 cubes in previous question there are every case:
4 cubes with 2 faces yellow so number of cubes Case (i): In this case number of cubes is given by 4
painted two faces only one with yellow and one with common edges except all 8 corner ones so number
blue is 12 – 4 = 8 of cubes is 5 × 4 = 20
Solution for 26–30: Case (ii): In this case number of cubes is given by 4
26. (d) Number of cubes removed from top face = 16 common edges (From one edge we will get 5 cubes
Number of cubes removed from bottom face = 4 with 2 face painted) except 6 corner ones (2 corner
Number of cubes left = 125 – (16 + 4) = 105 cubes are painted with only red and blue) so number
27. (a) Number of cubes with three coloured face on the of cubes is 5 × 4 + 2 = 22
top side = 4 Case (iii): In this case number of cubes is given by 2
nd
Number of cubes with three coloured face on the 2 common edges (From one edge we will get 5 cubes
from top side = 4 with 2 face painted) so number of cubes is 5 × 2 =
Number of cubes with three coloured face on the 10.
bottom side = 12 Case (iv): In this case number of cubes is given by 4
Total number of such cubes = 12 + 8 = 20 common edges (From one edge we will get 5 cubes
28. (b) Number of cubes with two face painted from the with 2 face painted) except 6 corner ones (2 corner
top side (Which is a square of 3 × 3 = 9 cubes) is 4. cubes are painted with only red and blue) so number
nd
Number of cubes with two face painted from the 2 of cubes is 5 × 4 + 2 = 22
from top side (Which has four edges and each edge Case (v): In this case number of cubes is given by 3
has 3 such cubes) is 4 × 3 = 12. common edges (From one edge we will get 5 cubes
Number of such cubes from vertical edges is 4 × 1 = 4 with 2 face painted) except 6 corner ones (2 corner
cubes are painted with only red and blue) so number
Number of such cubes from bottom face is 4 × 1 = 4 of cubes is 5 × 3 + 2 = 17
Hence total such cubes is 4 + 12 + 4 + 4 = 24 Hence option (A) gives the all possible value of ‘K’