Quant Question Of The Day: 77
Counting
27 unit cubes are assembled together to form a 3 × 3 × 3 cube. How many sets of 3 cubes can you find such that the centres of the 3 cubes lie in a straight line?
a) 76
b) 32
c) 49
d) 44
e) 50
a1 a2 a3
a4 a5 a6
a7 a8 a9
This is one layer, we have 2 more layers like this just above it (bn and cn)
So, a1. b1, c1 (9 ways)
Similarly for other two dimensions
So, 27 ways
Now, a1, a5, a9 and a3, a5, a7
So, for every layer 2 ways and we have three dimension and every dimension has three layers
So, 2× 9 = 18 more
Now, 4 diagonals of the cube
So, 27 + 18 + 4 = 49 sets
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