The remainder when the positive integer m is divided by n is r. What is the remainder when 2m is
divided by 2n ?
(A) r
(B) 2r
(C) 2n
(D) m - nr
(E) 2(m - nr)

• Answer is B.
  
  Explanation: Since the remainder when m is divided by n is r, we can represent m as m = kn + r, where k is some integer.Now, 2m equals 2kn + 2r. Hence, dividing 2m by 2n yields 2m/2n = (2kn + 2 r)/2n = k + 2r/2n. Since we are dividing by 2n (not by n), the remainder when divided by 2n is 2r.
• 11 years agoHelpfull: Yes(67) No(4)
• @Sanket By dividing the divisor would be same not the remainder
  
  2m/2n =m/n=k(divisor)
  
  take example 3/2 remainder 1
  But 6/4 remainder 2
• 11 years agoHelpfull: Yes(5) No(2)
• Cant it be like - 2m/2n = m/n = r itself ??
  Correct me if am wrong.
  Thanks :)
• 11 years agoHelpfull: Yes(4) No(11)
• correction
  d) m-nr
  e)2(m-nr)
  
• 11 years agoHelpfull: Yes(3) No(4)
• 2r is ans..
• 11 years agoHelpfull: Yes(3) No(0)
• ans=b)2r
  taking value of m as 8,10 and n as 3,5...nd solve it to find d pattern of ans
• 11 years agoHelpfull: Yes(1) No(0)
• @Aditya Gaurav Please explain how we can say that 2r will be the remainder in the term k +2r/2n ??
• 11 years agoHelpfull: Yes(0) No(3)
• ans is 2r..........................
• 11 years agoHelpfull: Yes(0) No(0)
• n=mk+r(given)...............(i)
  by question, 2n=2mk+z(assume)
  now, z=2(n-mk)
  z=2r...using equation (i)
• 10 years agoHelpfull: Yes(0) No(0)