one boy has all the 2 digit even n0. and other has all the 2 digit odd n0.Both square their no.and add up .what is the difference of these two addition???
a) 0
b) 4905
c) other two options i forgot...

• The total 2 digits no.=90
  As per questn ,we have 2 find
  ((11^2)+(13^2)+(15^2)+(17^2)+...+(99^2))-((10^2)+(12^2)+(14^2)+(16^2)+...+(98^2))
  now it can be written as
  (11^2)-(10^2)+(13^2)-(12^2)+(15^2)-(14^2).........+(99^2)-(98^2)
  =(121-100)+(169-144)+(225-196)+......+(9801-9604)
  =21+25+29+.......+197
  now these terms are in A.P. where a=21, d=4,
  n=45(because 1 odd and 1 even term is used to make 1 A.P. terms)
  so total difference =
  (45/2)*(2*21+(45-1)*4)
  =4905
  
• 11 years agoHelpfull: Yes(67) No(0)
• for AP series with same common difference,sum of the two series=difference of sum of squares of those 2 series.
  for example,
  take 2 AP series as follows:
  odd series 1=1+3+5+7
  even series 2=2+4+6+8
  sum1={n/2(a+l)}={4/2(1+7)}=16 //l=last term,a=first term,n=no of terms
  sum2={n/2(a+l)}={4/2(2+8)}=20
  sum of squares 1=1+9+25+49=84
  sum of squares 2=4+16+36+64=120
  difference of these additions=120-84=36
  sum of these two series=20+16=36
  hence to find answer to the given question,
  its simply addition of these 2 series with
  series 1 in AP with a=10,n=45,and l=98
  series 2 in AP with a=11,n=45 and l=99
  sum1={45/2(10+98)}=2430
  sum2={45/2(11+99)}=2475
  as proved.
  difference=sum of above 2=2430+2475=4905
  hence ,ans=(b)
• 11 years agoHelpfull: Yes(7) No(0)
• other option are 1none of these 2)11...
• 11 years agoHelpfull: Yes(2) No(1)
• 3rd OPTION 1105
• 11 years agoHelpfull: Yes(1) No(4)
• series 1 in AP with a=10,n=45,and l=98
  series 2 in AP with a=11,n=45 and l=99
  sum1={45/2(10+98)}=2430
  sum2={45/2(11+99)}=2475
  as proved.
  difference=sum of above 2=2430+2475=4905
  hence ,ans=(b)
• 11 years agoHelpfull: Yes(1) No(0)
• there is no option like 11...
• 11 years agoHelpfull: Yes(0) No(1)
• Its 4905.just try to solve it. the difference will become the addition of all two digit no.s.
• 11 years agoHelpfull: Yes(0) No(0)
• it can be written as
  (11^2 - 10^2) + (13^2 - 12^2) + ........ + (99^2 - 98^2)
  = 21 + 25 + 29 ....... upto 45 terms
  = (45/2)[2*21 + (45 - 1)*4] = 4905
• 11 years agoHelpfull: Yes(0) No(1)