Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?
x-intercepts of the graph y=(x-p)(x-q) is the values of x for which (x-p)(x-q)=0. So, the x-intercepts are (p, 0) and (q, 0). The question basically asks whether either p or q equals 2.
(1) pq = -8. Not sufficient to say whether p or q equals 2.
(2) -2 – p = q. Not sufficient to say whether p or q equals 2.
(1)+(2) Solving pq=-8 and -2-p=q gives us that either p=-4 and q=2 OR p=2 and q=-4. In ether case one of the unknowns is 2, so y=(x-p)(x-q) intercepts the x-axis at the point (2,0). Sufficient.
Hope it's clear.
Damn, you're good! Was my approach right at all? Sometimes I wish a had an identical twin who could just get a 50 on my Quant section for me while I do the Verbal section, haha.