If v, w, x, y and z are non negative integers, each less than 11, then how many distinct combination of (v,w,x,y,z) satisfy
v(11^4)+w(11^3)+x(11^2)+y(11)+z = 151001
Option
a) 0
b) 1
c) 2
d) 3

• v(11^4)+w(11^3)+x(11^2)+y(11)+z= 151001
  
  => 11*( v*11^3 + w*11^2+ x*11 + y ) + z = 11*13727 + 4
  
  => ( v*11^3 + w*11^2+ x*11 + y )= 13727 & z = 4
  
  => 11*( v*11^2 + w*11 + x ) + y = 11*1247 + 10
  
  => ( v*11^2 + w*11 + x )= 1247 & y = 10
  
  => 11*( v*11 + w ) + x = 11*113 + 4
  
  => ( v*11 + w )= 113 & x = 4
  
  => ( v*11 + w ) = 11*10 + 3
  
  => v = 10 & w = 3
  
  so, v=10, w=3, x=4, y=10 ,z=4
  
  (v,w,x,y,z)=(10,3,4,10,4) => only one soln
  
  so, only one distinct combination of (v,w,x,y,z)
  
  b) 1
• 10 years agoHelpfull: Yes(6) No(0)