How many of the cubes have 2 faces painted? 48 44 45 None of these Let us see th

CuriousTab

Discussion

Home ‣ Non Verbal Reasoning ‣ Cubes and Dice See What Others Are Saying!

Question
How many of the cubes have 2 faces painted?
Options
A. 48
B. 44
C. 45
D. None of these

Correct Answer

45

Explanation

Let us see the changes due to removal of cube from corner-
Number of vertices with three faces exposed (Painted) is 7 + 3 = 10
Number of Cubes with 2 sides exposed (Painted): In general one edge gives us 4 (n - 2 in general case) cubes with two face painted but in this case out of 12 edges only 9 edges will give us 4 cubes in one edge and remaining 3 edges will give us 3 cubes from one edge, hence total number of edge is 9 x 4 + 3 x 3 = 45
Number of Cubes with 1 side exposed (Painted): It will remain same as normal case i.e. 6(4²) = 96
Number of Cubes with no sides exposed (Painted) is 4³ = 64
From the above observation:
From the above explanation number of the cubes with 2 faces painted is 45.