A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21. What is the remainder left, when twice the number is divided by 3D?
a) 13
b) cannot be determined
c) 3
d) 42

• let's number is n
  so n=Dx+8------->1
  n=3Dy+21--------->2
  from 1 & 2 D(x-3y)=13
  here 13 is prime number so it has factors 1 and 13 only
  x-3y must be 1
  let x=4 and y=1
  then n=60
  so 2n is divided that is 120 by 3D that is by 39 we get
  the remainder as 3
• 13 years agoHelpfull: Yes(178) No(16)
• Let the number be n
  
  Given its divided by D and leaves remainder 8. Lets assume the quotient be x. So that
  
  n=Dx+8
  
  Similarly n when divided by 3D leaved remainder 21. Lets assume the quotient be y. So that
  
  n=3Dy+21
  
  Equating the above 2, we get
  
  Dx+8 = 3Dy+21
  
  Dx-3Dy=21-8
  
  D(x-3y) = 13
  
  Since 13 is a prime number and according to the above equation, D and x-3y when multiplied should give me 13
  
  The only two factors of 13 are 1 and 13
  
  So if D is 1, x-3y is 13
  If D is 13, x-3y is 1
  
  D can never be 1 because given the number leaves remainder when divided by D. No number can leave remainder whe
• 13 years agoHelpfull: Yes(65) No(21)
• i think ans must be b) cant be determind. bcz D(x-3y)=13 and d must be 13. it cant be 1. now (x-3y)=1 and in order to satisfy this result it is possible to choose any arbitay value of x & y.(eg. x=4 y=1,x=7 y=2,x=9 y=3 and so on)and for each time we get a new value of reminder. therefore ans must be (b).
• 13 years agoHelpfull: Yes(14) No(27)
• let the number be N.
  
  From the Given that, it is understood that
  (N/D) + 8 = (N/3D)+27
  => N/D - N/3D =27-8
  =>2N/3D =13, hence the answer is 13.
• 9 years agoHelpfull: Yes(9) No(5)
• by using division rule, x=dp+r, where d is +ve integer, p is quotient and integer,and r is reminder and 0(1),
  x=3Dq+21 -------->(2), where p and q are Quotients.
  From (1) & (2), D(p-3q)=13,
  we know that 13 is prime number.
  so, factors of 13 are only 1 & 13.
  therefore D=13 & p-3q=1 ( From (A), 8
• 13 years agoHelpfull: Yes(5) No(37)
• acc to given (n-8)/d and (n-21)/3d will nt leave any remainder...
  
  So, multiply 1st by 3 and devide by 3 and then subtract 2nd from 1st.
  
  we get
  3(n-8)/3d - (n-21)/3d = (2n-3)/3d....from the ans. we get remainder ==3 when 2n is devided by 3d
  
• 11 years agoHelpfull: Yes(4) No(1)
• pls check calculation @ mithila nand jha ...when we divide 120/39 then we get remainder as 1.
  your process is correct.
  
• 8 years agoHelpfull: Yes(0) No(1)
• #jyoti 120/39 gives rem as 3 not 1
• 7 years agoHelpfull: Yes(0) No(0)
• my ans is = 13
• 4 years agoHelpfull: Yes(0) No(0)