if A=2^65 AND B=2^64+2^63.....+2^0
options
a) A is larger than B by 2^64 times
b)B is larger than A by 1
c)A is larger than B by 1
d) None

• Ans) C
  lets say A : 2^4=16 , B: 2^3+2^2+2^1+2^0 = 15 so A is larger than B by 1 always
• 9 years agoHelpfull: Yes(14) No(1)
• ans) c
  B=2^64+2^63+........+2^0 (here makes a GP series)
  so, sum of GP series=a(r^n-1)/(r-1)
  =1(2^64-1)/(2-1)
  =2^64-1
  and, A=2^64 (which is larger than by 1)
  
• 9 years agoHelpfull: Yes(4) No(2)
• multiply B by 2 on both sides by 2 then do A-B u will get A-B=1
• 9 years agoHelpfull: Yes(3) No(0)
• B is a GP with
  a = 2^0 = 1 and r = 2 and n = 65
  therefore B = 2^0 (2^65 - 1) / (2 -1) = 2^65 - 1 = A - 1
  thus ans is C) A is larger than B by 1
• 9 years agoHelpfull: Yes(2) No(0)
• option c a is larger than b by 1
  
• 9 years agoHelpfull: Yes(1) No(0)
• take them as binary no. A=100000000...00(64 0's) and 011111..11(64 1's) so A>B by 1.
  
  eg, 100 in binary =4 in decimal
  011 in binary =3 in decimal
  the same rule applies over here.
  so ,option c.
• 7 years agoHelpfull: Yes(1) No(0)
• Ans: A is Larger than B by 1
• 9 years agoHelpfull: Yes(0) No(0)
• Answer is C
  Since, if we take a small no say
  A= 2^3 and B = 2^2+2^1 + 2^0
  
  then is is clear that "A is larger than B by 1"
• 9 years agoHelpfull: Yes(0) No(0)
• c)A is larger than B by 1
• 9 years agoHelpfull: Yes(0) No(0)
• 2^n-2^n-1=1
  Hence a is larger than b by 1.
• 9 years agoHelpfull: Yes(0) No(1)
• A=2^65
  B=2^65-1(after solve GP)
  so that A is larger than B by 1.
• 9 years agoHelpfull: Yes(0) No(0)
• c option
  coz B= 2^65-1 by gp series summtion
• 8 years agoHelpfull: Yes(0) No(0)