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Logical Reasoning Problem 10

A wooden cuboid of dimensions 9 x 7 x 5 unit is painted in a fixed pattern.
(i) The two opposite faces in the front and back are painted in red with 9 x 7 cuts.
(ii) The other two opposite faces on the sides are painted in green with 7 x 5 cuts.
(iii) The remaining top and bottom faces are painted in blue.
The cuboid is cut into 315 small cubes.
1. How many cubes have all the three faces coloured ?
   (a) 8  (b) 32
 (c) 24  (d) None of these
2. How many cubes have two faces coloured ?
   (a) 60  (b) 142
 (c) 105  (d) None of these
3. How many cubes have one face coloured ?
  (a) 142  (b) 105
(c) 71  (d) None of these
4. How many cubes have no face coloured ?
   (a) 142  (b) 60
 (c) 105  (d) None of these
5. How many cubes have two faces coloured, that too Red and Green ?
   (a) 14  (b) 20
 (c) 32  (d) None of these

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1 comment

  1. Nishant Dhote

    Ans
    1) A
    2) A
    3) A
    4) C
    5) B
    .
    Solution: 1) 8 Corner (With 3 Clr)

    2) (7+5+3)*4=60
    (L+B+H)*Sides
    L=9-2Clr
    B=7-2clr
    H=5-2clr
    Cube Side=4

    3) (15+35+21)*2=142
    First Draw Cube Sketch then Solve

    4) 7*5*3=105
    l*b*h
    L=9-2Clr
    B=7-2clr
    H=5-2clr

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