if w and x are odd numbers and y and z is even then 1/8[(w^2+x^2)*(y^2+z^2) is
option
1. always even
2. always odd
3. even or odd
4. can be fractional

• 1/8[(w^2+x^2)*(y^2+z^2)]
  =1/8[(odd^2+odd^2)*(even^2+even^2)]
  =1/8[(2*odd)*4(may even or odd)]
  =odd*(even or odd)
  =odd or even
• 11 years agoHelpfull: Yes(15) No(2)
• odd^2=odd(W^2= X^2=odd)
  eve^2=eve(y^2=z^2=eve)
  odd+odd=eve (w^2+x^2=odd+odd=eve)
  eve+eve=eve (y^2+z^2=eve+eve=eve)
  eve*eve=eve {[(w^2+x^2)*(y^2+z^2)]=eve*eve=eve}
  so finally
  eve/8
  let 'n' is any num
  eve=2*n
  2*n/8=n/4
  ans: can be fractional (except 4 multiples) , option 4
• 11 years agoHelpfull: Yes(9) No(13)
• 1/8[(w^2+x^2)*(y^2+z^2)]
  =1/8[(odd^2+odd^2)*(even^2+even^2)]
  now, odd^2+odd^2=even=2*odd(ex 3^2+5^2=34=2*17)
  even^2+even^2=(2m)^2+(2n)^2=4(m^2+n^2),value of m^2 & n^2 may even or odd
  ex 2^2+6^2=40=4*10=4*even
  8^2+10^2=164=4*41=4*odd
  
  =1/8[(2*odd)*4(may even or odd)]
  =odd*(even or odd)
  =odd or even
  
• 11 years agoHelpfull: Yes(9) No(2)
• both even and odd
• 11 years agoHelpfull: Yes(8) No(6)
• for w=5, x=3, y=2, z=4
  the expression = 1/8[(25+9)*(4+16)]= 34*20 / 8 = 85 (odd)
  so ans:- both even and odd..
• 11 years agoHelpfull: Yes(5) No(5)
• ans.4-Can be fractional
  
• 11 years agoHelpfull: Yes(4) No(9)
• let a,b,c,d are any numbers
  odd^2=odd(W^2= X^2=odd)
  eve^2=eve(y^2=z^2=eve, y^2=2*a, z^2=2*b)
  odd+odd=eve (w^2+x^2=odd+odd=eve = 2*c)
  eve+eve=eve (y^2+z^2=eve+eve= (2*a)^2+ (2*b)^2 = 4*(a^2+b^2)= 4*d)
  eve*eve=eve {[(w^2+x^2)*(y^2+z^2)]=eve*eve= 2*c * 4*d= 8*c*d}
  so finally
  8*c*d/8= c*d
  if in c and d any one is eve number, we get eve number
  else we get odd
  so ans : even or odd
• 11 years agoHelpfull: Yes(4) No(4)
• Hi friends all going blindly
  you are correct
  odd+odd =even
  even+even =even
  
  even*even =even
  
  but there is no rule that an even number when divided by a number must be an even number
  
  For example : 120/8 =15
  even number/8 =odd
  
  in the same way
  suppose consider
  
  w=3
  x=9
  
  y=4
  z=6
  
  then 1/8[(w^2+x^2)*(y^2+z^2)]
  1/8[(9+81)*(16+36)]
  1/8[90*52]
  13*45
  
  Final product is odd number it mi8 be even in case of
  w=5
  x=11
  
  y=6
  z=10
  
  so answer is even or odd
  Thank you
• 11 years agoHelpfull: Yes(4) No(1)
• always even
• 11 years agoHelpfull: Yes(2) No(13)
• 3option
  lets supose consider w be 3 x be 5 y=2 z=4
  1/8[(9+25)*(4+16)]=1/8[34*20]=1/8[680]=85 similarly if we consider w,x be 1,1 y,z be 2,2 we wil get 2
• 11 years agoHelpfull: Yes(2) No(5)
• 4.can be fractional
  x1,w3,y2,z4 provides 200/8 ie fraction means not always even,not always odd,and not even or odd
• 11 years agoHelpfull: Yes(2) No(4)
• option 1 always even
  
  w,x are odd so w^2+x^2 = odd+odd = even
  y,z are even so y^2+z^1 = even + even = even
  divided by 8 even/even = even
  Also the result cannot be fractonal as 8=2*2*2, there are more then three 2's in the numerator to cancel out 8
• 11 years agoHelpfull: Yes(1) No(7)
• its 2)
  always odd
• 11 years agoHelpfull: Yes(1) No(2)
• guys its option 4 rite..........how come 1/[680]=85.....its fraction....
• 11 years agoHelpfull: Yes(1) No(3)
• even or odd
• 11 years agoHelpfull: Yes(1) No(1)
• AFTR CALCULTING odd^2+odd^2=even as odd+odd=even
  even^2+even^2=even
  their multiplication wll be even
  ...
  
  we alwys get even value when we multiply a even no to even or odd so in this case revers will also true.
  so answer will be even or odd.
• 11 years agoHelpfull: Yes(1) No(1)
• @ pappu bhai 200/8=25 it is not a fraction
• 11 years agoHelpfull: Yes(0) No(1)
• ? wrong lag raha h
• 11 years agoHelpfull: Yes(0) No(1)
• odd+odd=odd;
  even+even=even;
  odd*even=even;
  &even/even=even;
  then the ans is always even(A)
• 11 years agoHelpfull: Yes(0) No(7)
• even/even can be odd. As in 24/8 equals 3. So it can be a fraction as well coz 44/8 is always a fraction even both are even.
• 11 years agoHelpfull: Yes(0) No(2)
• always even
  
• 11 years agoHelpfull: Yes(0) No(2)
• @harshvardhan how can 44 comes give example..bhai it is not possible ..
• 11 years agoHelpfull: Yes(0) No(1)
• Can be even or odd
  square of odd is odd and square of even is even
  odd+odd = even
  even+even =even
  even*even= even
  even/8 = can be even or odd
  it can't be fractional you can check bg taking any values.
• 11 years agoHelpfull: Yes(0) No(1)
• 3 is the answer.
  
  if w=1 and x=3
  y=2 and z=4
  value we get is 25(odd)
  
  if w=7 and x=9
  y=8 and z=6
  value we get is 2000(even)
  
• 11 years agoHelpfull: Yes(0) No(1)
• both even and odd.....
  
• 11 years agoHelpfull: Yes(0) No(1)
• always odd.
  take w=1, x=3, y=2, z=4
  so,
  [(1^2+3^2)*(2^2+4^4)]/8= 25
  Hence always odd..
  try with any no..
• 11 years agoHelpfull: Yes(0) No(3)
• ans : a= even(n)/8 _ now (if n = 8 then a= 1 which is odd) & (if n=16 then a= 2 which is even) so ans should be """even or odd"""
• 11 years agoHelpfull: Yes(0) No(1)
• always odd..
  because put any number u'll get odd number as a reslut.
  eg. w/x=1,3,5,7,9....
  nd y/z= 2,4,6,8,10...
  reslut = 5 / 0.5 /0.05... in last (i.e 5 is odd)
• 11 years agoHelpfull: Yes(0) No(2)