In which quadrant of the coordinate plane does the point (x,y) lie?

Stmt 1: xy = 7

Since the product of x and y coordinates is +7, x and y must be both positive or both negative.
So point (x, y) will be either in the first quadrant(where x and y are both positive)or third quadrant (where x and y both are negative)
Not suff

Stmt 2: 5x + 7y < -1/2
Either x or y or both has to be negative to satisfy the above equation which means point (x,y) can be in any quadrant other than quadrant I.
Three cases can happen
x is negative y is positive. (Eg: x =-5 and y =1) In this case (x,y) will be in quadrant II
x is negative y is negative. (Eg: x =-1 and y = -1) In this case (x,y) will be in quadrant III
x is positive y is negative. (Eg: x = 1 and y = -1) In this case (x,y) will be in quadrant IV.

Not suff

Combining stmt 1 and 2:
From 1: Point (x, y) will be either in the first quadrant(where x and y are both positive)or third quadrant (where x and y both are negative)
From 2: When x and y are both positive 5x + 7y is always positive (So it does not satisfy 5x + 7y < -1/2) So (x,y) can never be in quadrant I.
It has to be in quadrant III.
Suff


Answer C