Question

A positive integer is written on each face of a cube. Each vertex is then assigned the product of the numbers written on the three faces intersecting the vertex. The sum of the numbers assigned to all the vertices is equal to 1001. Find the sum of the numbers written on the faces of the cube.

Options

• 24

• 62

• 31

• 18

Answer 1

Reqd. expression will become

abf + adf + abe + ade + cbf + cdf + cbe + cde
= (a+c) (b+d) (e+f) = 1001
= 13 x 11 x 7
So, a + b + c + d + e + f = 13 + 11 + 7 = 31.
Hence, option 31 is the correct option.