GMAT QUESTION 58-60

58.In the xy-plane, at what two points does the graph of y = (x+a)(x+b) intersect the x-axis?  1) a+b = -1  2) The graph intersects the y-axis at (0,-6)

Solution:
1. Insufficient. All we have it x^2 -x + ab = 0. Cannot solve for x  2. insufficient. y = x^2 + (a+b)x + ab implies ab = -6. Cannot solve for x  Using 1 and 2, x^2 - x - 6 = 0  x = 3 & -2  So, C is the correct answer

59.If k#0, 1, or -1, is 1/k>0?  1. 1/(k-1)>0  2. 1/(k+1)>0

Solution:
1 - If 1/(k-1) > 0, then k > 1 and hence positive. So, 1/k > 0.Sufficient  2 - If 1/(k+1) > 0, then k > -1. K is not given to be an integer and can take values -0.5, 0.5, 2 etc. So, 1/k can be positive or negative. Insufficient.  Hence A

60.If q is a positive integer less than 17 and r is the remainder when 17 is divided by q, what is the value of r?  1. q>10  2. q=2^k, where k is a positive integer

Solution:
1 - Insufficient. q Can be 11...16 and each yields a different value for r  2 - sufficient. Values for q are 2, 4, 8 and 16  17 / 2 remainder is 1  17 / 4 remainder is 1  17 / 8 remainder is 1  17 / 16 remainder is 1  Hence B