If a cube of dimension 4 by 4 by 4 is cut into 1 by 1 by 1 a

[GMATinsight]

If a cube of dimension 4 by 4 by 4 is cut into 1 by 1 by 1 after painting it by red color then which of the following is/are true.

I) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4
II) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.
III) Number of cubes having 2 faces painted is same as number of cubes having one face painted

a) None
b) II and III
c) II only
d) I, II & III
e) I & III only


Answer: Option D

[GMATinsight]

If a cube of dimension 4 by 4 by 4 is cut into 1 by 1 by 1 after painting it by red color then which of the following is/are true.

I) Ratio of number of painted surfaces of resultant cubes to total number of surfaces is 1/4
II) Number of cubes having no faces pointed is equal to number of cubes having three faces painted.
III) Number of cubes having 2 faces painted is same as number of cubes having one face painted

a) None
b) II and III
c) II only
d) I, II & III
e) I & III only


Answer: Option D

Everything about the painted cube problem is calculated as shown in attachment here