If w and x odd numbers,y and z even numbers then
1/8[(w^2+x^2)*(y^2+z^2)]
A.always odd
B.always even
C.may be both
D.not an interger

• Let,
  w = 1(odd), x = 3(odd)
  y = 2(even), z=4(even)
  we get
  1/8* { ( 1 + 9 ) ( 4 +16 ) }
  1/8 * { 10 * 20 } = 25 [which is odd]
  
  now,
  If we take
  w = 1(odd), x = 3(odd)
  y = 12(even), z = 20(even)
  we get,
  1/8 * { ( 1 + 9 ) ( 144 + 400 ) }
  1/8 * { (10) (544) } = 680 [which is even]
  
  The value can be even and can be odd.
  So, the ans is C.
• 10 years agoHelpfull: Yes(48) No(1)
• Let w=3, x=5
  y= 2, z=4
  Solve for the given equ-
  1/8* [(w^2+x^2)*(y^2+z^2)]
  You will get odd no. not a fraction. (Always)
  So, A is correct option.
• 10 years agoHelpfull: Yes(3) No(9)
• This is correct that product of two term always gives even but after dividing 8 it is not sure that the out put will be even only or odd only so,
  after checking all the possibility Option C is correct.
• 10 years agoHelpfull: Yes(3) No(0)
• odd*odd=odd => w^2 & x^2 are odd
  odd+odd= even => w^2 + x^2 is even-----1
  even*even=even => y^2 & z^2 are even
  even+even=even => y^2 + z^2 is even-----2
  
  now 1+2 i.e even +even = even
  
  Now even/8 = even or odd
  u can check by putting values like
  8/8=1
• 9 years agoHelpfull: Yes(3) No(0)
• D) not an integer because it will always be a fraction
• 10 years agoHelpfull: Yes(2) No(6)
• Option should be C.
  When I cheked by putting the values, then I got it may be both an even number or an odd number.
• 10 years agoHelpfull: Yes(2) No(0)
• A) Always odd
• 10 years agoHelpfull: Yes(1) No(2)
• a is correct answer.
• 10 years agoHelpfull: Yes(1) No(2)
• Always odd answer a) is correct
• 10 years agoHelpfull: Yes(1) No(2)
• may be both...
• 9 years agoHelpfull: Yes(1) No(0)
• how shruti
• 10 years agoHelpfull: Yes(0) No(0)
• B will be the right option check by putting the value in the position.
• 10 years agoHelpfull: Yes(0) No(2)
• try with these,
  13, 17 and 56, 2
  u will get a fraction... so D is right option....
• 10 years agoHelpfull: Yes(0) No(7)
• Shruti can u explain ur answer??
• 10 years agoHelpfull: Yes(0) No(0)
• Always even
• 10 years agoHelpfull: Yes(0) No(1)
• guys this kind of question quite easy to solve just consider different values odd and even and u can verify it it will always be odd;
  
• 9 years agoHelpfull: Yes(0) No(2)
• If this equation is under the 1 ,then always be a fraction number it is. then option D is perfect. am agree with shruti.
• 9 years agoHelpfull: Yes(0) No(0)
• option d is correct when 1 is divided by any no it gives ans in decimal or fraction so in this ques 1/8[......] not a integer.
• 9 years agoHelpfull: Yes(0) No(0)
• since , even * even=even;
  odd * odd=odd;
  
  even + even= even;
  odd+ odd=even;
  
  but even/even or even/odd or odd/even or odd/odd may be even may be odd and may be its not an integer.
  
  these concept is applied here;
  now you can find result..Answer : (D)
• 9 years agoHelpfull: Yes(0) No(0)
• putting different values of w,x, y,z answer is may be even ,odd or for some values it is not a integer it comes out fraction
• 9 years agoHelpfull: Yes(0) No(0)
• (Odd+odd)*(even+even)/8
  Even *even /8
  Always even
• 9 years agoHelpfull: Yes(0) No(0)
• (Odd+odd)*(even+even)/8
  Even *even /8=even/8
  so it may be odd or even=option c
• 8 years agoHelpfull: Yes(0) No(0)