if v,w,x,y,z are non negative intergers each leass than 11,then how many distinct
combinations are possible of(v,w,x,y,z) satisfy v(11^4) +w(11^3)+ x(11^2)+ y(11)
+z=151001

• Dividing 151001 by 11^4 give quotient 10 and remainder 4591
  So 151001 = 10*11^4 + 4591
  Dividing 4591 by 11^3 gives quotient 3 and remainder 598
  So 151001 = 10*11^4 + 3*11^3 + 598
  Dividing 598 by 11^2 gives quotient 4 and remainder 114
  So 151001 = 10*11^4 + 3*11^3 + 4*11^2 + 114
  Dividing 114 by 11 gives quotient 10 and remainder 4
  So 151001 = 10*11^4 + 3*11^3 + 4*11^2 + 10*11 + 4
  So v=10, w=3, x=4, y=10, z=4
• 5 years agoHelpfull: Yes(8) No(0)
• v=10,w=3,x=4,y=10,z=4
• 5 years agoHelpfull: Yes(1) No(6)
• 151001 / 11^4 = 10 with remainder = 4591
  
  4591 / 11^3 = 3 with remainder = 598
  
  598 / 11^2 = 4 with remainder = 114
  
  114 / 11^1 = 10 with remainder = 4
  
  Therefore
  151001 = 10 (11^4) + 3 (11^3) + 4 (11^2) + 10 (11^1) + 4 (11^0)
  
  i.e., (v,w,x,y,z) is (10,3,4,10,4). These values satisfies given conditions and is one valid option.
  
  Let's analyze if further option available satisfying the given condition. v,w,x,y,z should be less than 11 and greater than zero. The solution we got have v as 10. Suppose v=9. With this, the maximum value possible under the given constraints is
  9 (11^4) + 10 (11^3) + 10 (11^2) + 10 (11^1) + 10 (11^0) = 146409 < 151001
  
  i.e., when v < 10, the sum will be always less than 151001. Clearly. no further options are available.
  
  Therefore answer is 1
• 3 years agoHelpfull: Yes(1) No(0)
• The question asks no. of possible ways :
  thus the ways can be (v,w,x,y,z) have some value explained by @tushar
  Another possible value can be v=some value and z has correspondingly some value
  So the answer to the problem is like every variable has two possible values either yes/no(0/1)
  Thus,total possible ways = 2^5
  But as we know 11 is not divisible by 151001
  Thus we will remove the possibility that all the values are present but z is not present
  Note:z plays a very important roll here as if all values are 0 z can become 151001 and as follows satisfy a lot of possibilities
  Thus the answer is =2^5-2=30.
  Thank You
• 4 years agoHelpfull: Yes(0) No(3)