text: which one is false ? let x<0,0<y1 which of the following is false ?  a)(x^2-z^2) has to be positive b)yz can be less than one c)xy can never be zero d)(y^2-z^2) is always negative  question:  my question is, should i assume numbers  x,y,z which satisfy those conditions {x<0,0<y1} and start testing  each of the answer ?  say, i took x=-1  , y=.5 , z=2  but , you know the problem could be, if i choose badly  then everythin would be messed up.  and if i try to solve this problem algebrically, then it would be difficult and time consuming.   how do i solve this problem quickly and correctly ? can you give some tips ?  thank you i would try to pull out the inherent properties in the problem as they relate to the possible choices.  for example, in this one, we have:  x < 0 0 < y  1  for (a), we are told that x^2 - z^2 is always negative.  in this case, we want to either note that x^2 - z^2 factors into (x+z)(x-z) or that x^2 = (-x)^2.  both would suggest that we can make x^2 - z^2 zero by choosing any x = -z (e.g. z = 2, x = -2) so (a) is immediately shown false.  for (b), we note that if z > 1, 0 < 1/z  0 and x^2 > 0 are both possibilities, we can eliminate both since they are equivalent conditions. and they can't both be true/false when we are only allowed to pick one or the other.