X, Y, X and W are integers. The expression X - Y - Z is even and the expression Y - Z - W is odd. If X is even what must be true?
A. W must be odd
B. Y - Z must be odd
C. W must be odd
D. Z must be odd

• ans::W is odd
  X-Y-Z=2a
  X=2b ==>2b-Y-Z=2a ==>Y+Z=2(b-a) ==>both Y and Z are odd or both are even
  Y-Z-W=2c+1 ==>2d-W=2c+1 (bcoz difference of 2 even numbers or 2 odd numbers is always even)
  W=2d-2c-1 ==>W=2(d-c)-1 ==>W is odd
• 11 years agoHelpfull: Yes(45) No(1)
• given X is even
  x-y-z=even if and only if y & z is even
  y-z-w=odd if and only if w is odd since y & z is even
  hence ans is w must be odd
• 11 years agoHelpfull: Yes(4) No(3)
• C. w must be odd!
• 11 years agoHelpfull: Yes(1) No(2)
• ans:w is od
• 11 years agoHelpfull: Yes(0) No(1)
• ans-->w must be odd.
  given X is even
  x-y-z=even if and only if y & z is even
  y-z-w=odd if and only if w is odd since y & z is even
  hence ans is w must be odd
• 11 years agoHelpfull: Yes(0) No(0)
• X-(Y+Z) IS even & X is even so (Y+Z)is even
  if Y+Z is even then Y-Z is even bcs Y-Z =( Y+Z-2*Z) which is even so,
  if (Y-Z)-W is odd then W must be odd
  ANS-A
• 11 years agoHelpfull: Yes(0) No(0)
• w must be odd. option c
• 11 years agoHelpfull: Yes(0) No(0)
• w must be odd
• 11 years agoHelpfull: Yes(0) No(0)
• B because of even - odd=odd
• 11 years agoHelpfull: Yes(0) No(1)
• W must be odd
  
• 11 years agoHelpfull: Yes(0) No(0)
• ans is w must be odd ...
• 11 years agoHelpfull: Yes(0) No(0)
• w must be odd !!!
• 11 years agoHelpfull: Yes(0) No(0)