Verbal Reasoning - Cube and Cuboid - Discussion

A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.


What is the number of cubes with at least one green face each ?

[A]. 36
[B]. 32
[C]. 38
[D]. 48

Answer: Option C


24 from (I) and 14 from (II)

Viji said: (Sep 12, 2016)  
How comes 14 for 2nd diagram?

Riya said: (Oct 29, 2016)  
It should be 48 32 from (I) and 16 from (ii).

Jaspreet said: (Nov 4, 2016)  
It should be 48.

8 * 4 = 32.
32 + 16 = 48.

Devi Priya said: (Aug 27, 2017)  
In the first cube there are two complete red faces(32 nos) thus no green as any of its adjacent are in the middles ( 4 upper + 4 lower = 8) , therefore ans = 32-8=24.

In the second cube, the red faces that form a 'L' shape i.e 7upper+7 lower =14(red cubes on the top with adj green +red cubes on the bottom with adj green).

Totally, 24+14=32.

Sithara said: (Aug 28, 2017)  
How comes 14 for second peice?

Jairaj Kushwaha said: (Mar 28, 2018)  
In the (I) part, near (I) you can see Greenside (or in the front view) which is divided in 8 section.

If you paint by green colour 4 boxes in the centre appear green only from one side (from the front) but.

Not to any other side but if you consider other 4 boxes, 2 boxes from the right side and other 2 boxes from the left side to you.

Which will paint by green colour from Two sides of the box? So you have to leave 4 boxes on the front (leave corner boxes).

Same apply for the parallel hidden green section in the backside, 4 boxes which you leave from the front and 4 from the back side paint from both the side view.
So finally by the condition, we paint one side green in each box. According to our consideration.
(Front view + parallel hidden view) = 4 + 4 = 8 boxes paint green from the one side. And from the side view 8 + 8 = 16.
8 + 16 = 24 boxes paint green from one side.

In the (II) part, near (II) You can see Greenside (or in the front view) which is divided in 8 section.
If you paint by green colour from the left side 6 boxes paint from one side but in right hand 2 corner boxes.
Are common in adjacent green sides so 2 boxes leave from the front and paint it from the side view.
So, you have total 8 boxes inside view to paint by green colour from the one side.
6 + 8 = 14 boxes from the (II) part.
Total boxes: 24 + 14 => 38 Answer.

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