Question

Positive integers are written on all the faces of a cube, one on each. At each corner (vertex) of the cube, the product of the numbers on the faces that meet at the corner is written.The sum of the numbers written at all the corners is 572. If N denotes the sum of the numbers on all the faces, the possible value(s) of N is/are

• A. 28
  
• B. 37
  
• C. 41
  
• D. 147

Answer 1

Answer: (A), (B), (D)

The correct options are
A 28

B 37

D 147

Let ABCDPQRS be a cube, the numbers are a,b,c,d,e,f be written on the 6 faces

So,
$ade+abe+abf+adf+cde+bce+bcf+cdf=572$

$\Rightarrow (e+f)(a+c)(b+d)=2^2\times 11\times 13$

So possible combinations are (4, 11, 13), (2,22,13), (2,11,26),(2,2,143)

So $N=a+b+c+d+e+f=28,37,39,147$