First question:

1. this one is equivalent to x = 2y*k + 4 = y*(2k) + 4. Since y*(2k) is clearly divisible by y, we have to see if 4 is divisible by y. Well, there are several non-zero integers that divide 4: -4, -2, -1, 1, 2, 4, but there is no way of telling if y is a part of this list or not.
2. since the remainder of x+y divided by y is 4, then this is obviously the remainder of x divided by y. This is because (x+y)/y = x/y + y/y = x/y +1, or that y divided by itself gives a remainder of zero. This means that the remainder must come from x/y.

So 2 is sufficient. Answer: B

Second question:

1. is not sufficient since we do not know the average speed of the car for the other 200 km.
2. Let's say that :
s = average speed over the whole trip
t = original time (unknown and required)
s*t = 400
2 is equivalent to: (s+20)(t-1)=st - s + 20t -20 = 400, which means that 20t - s - 20 = 0 (since st=400). Now we have to substitute s with 400/t. The resulting equation will have only one positive answer. So 2 is sufficient.

Answer B

Thanks Dana...you have been very helpful :lol: