1. I agree with E for this one. If we combine both statements, we know the rates of each person and their relative starting positions, but we don't know what direction Chris traveled in (so we don't know how far she was from Charlie to begin with).

2. All positive integers will share the common factor 1. Statement (1) tells us that a and b have only one common factor, so we know it must be 1, which makes 1 the greatest common factor of a and b. Statement (2) tells us that a and b are both prime, so the greatest common factor will have to be 1 or a and b could be the same prime number and the gcf would be a (=b). Therefore, (2) alone is not sufficient b/c the possiblity of a=b is not ruled out.

3. Clearly (1) alone does not give us enough info since there are plenty of numbers in addition to 5 that are not factors of 6006. However, (2) tells us that 5 is the largest divisor of a. Since all positive integers have the divisors 1 and themselves, the largest divisor of a positive integer will always be the number itself. So, for 5 to be the largest divisor of a, a must be equal to 5 and statement (2) alone is sufficient.

4. I would do this one by drawing it out on a graph. Put a point at (0,56) to start. Statement (1) tells us another vertex is at the origin, so add a point at (0,0). Then for the area of the triangle to equal 196 we can solve for the x-coordinate of the third point.

196 = (1/2)*56*x
x = 7

So, add a point at (7,0). If we then draw a line connecting A and C, we would be able to count the number of times it intersects the graph grid (where both x and y will be integers). We don't have to actually do this, just know that we could and that (1) is sufficient.

Statement (2) gives us enough info to place point C somewhere on the positive x-axis, but we don't know where and therefore, we can't know how many times the line AC will intersect the grid. For example if we put point C at (0,0.5) the line will never have a point with integer x and y coordinates. On the other hand, if point C is at (56,0), then AC will intersect with lots of points with integer coordinates (55,1) (54,2) ... (1,55)... therefore, (2) alone is not sufficient

outstanding explanation.. thanks a ton