[skarya]

1.What is the probability that events A and B both occur?

P(both A&B)=P(A)*P(B) if two events are dependent
P(both A&B)=P(A)+P(B) id two events are independent

(1) The probability that event A occurs is 0.8.
no info about event B (0, 1.0) - not sufficient

(2) The probability that event B occurs is 0.6.
no info about event A(0,1.0) - not sufficient

(1)+(2) P(A)=0.8 and P(B)=0.6

no info if P(A) and P(B) are dependent or independent
not sufficient

answer= E

2. In the xy-plane, does the point (4, 12) lie on line k ?

y=mx+c

(1) The point (1, 7) lies on line k.
7=m+c
=not sufficient
(2) The point (-2, 2) lies on line k
2=-2m+c
not sufficient

(1)+(2)
7=m+c and 2=-2m+c => 7-2=m+2m=>m=5/3 AND c=7-5/3=16/3
y=mx+c = (5/3)x+(16/3) = (5x+16)/3
if (4,12) lies on line k then it must satisfy above equation
y=12, mx+c=(5*4+16)/3=36/3=12 which is TRUE

sufficient

answer = C

BTW for DS Qs we don't need to see if it really lies on line K or not...all we need to make sure there is enough info to find that out.