crackthegmat2011 wrote:Is x^2 - 14x + (50 + c) always positive, provided x being real ?
1) c is a natural number
2) c is an integer
x^2 -14x +50 +c = x^2-14x + 49 + 1 + c =
(x-7)^2 +1+c
(x-7)^2 is always positive, if x is real. [it can be negative if x is imaginary; for example if x = 7+2i]
Thus for the above expression to be always positive (1+c) must be greater than zero.
(i) natural number is referred to as either a set of positive integers (1,2,3....) or a set of non negative integers (0,1,2....). By either definition (1+c) > 0. => Sufficient
(ii) c is an integer => c could either be positive or negative. Thus (1+c) can either be negative or positive. => not sufficient
Answer -> A
