1. B

(1) Insufficient. It may look like the two are equal, but not necessarily. All the statement tells us is that x2 is equal to y2. That doesn't mean that x equals y, because one could be negative and the other positive.

(2) Sufficient. This tells us that (x - y) (x - y) = 0. So, (x - y) = 0. The only way the difference between the two variables can be 0 is if they are the same.

2. A.

(1) Sufficient. Since the quantity 2R is divisible by 3, one of those two factors must be divisible by 3. Since 1 isn't; R must be.

(2) Insufficient. We know that quantity 3R is evenly divisible by 3, which means that at least one of the factors must be divisible by 3. The problem, though, is that 3 is evenly divisible by 3, making it impossible for us to determine if R is.

3. D

(1) Sufficient. With the distance known, we could plug it into the rate formula and computer Bill's rate.

(2) Sufficient. If he covered the same distance at 30 mph as he did at 60 mph, he must have been traveling at 30 mph for twice as long as he was at 60 mph. Given that he traveled for 3 hours, he traveled at 30 mph for 2 hours and 60 mph for 1 hour. That comes to 120 miles total distance, and again we solve for the rate.

4. E

(1) Insufficient. Pick 10 for x and 5 for y. This satisfies the statement and would allow us to answer "yes" to the question. We can't stop here though; we have to try different values to see if we can answer the question, "no." Try 5 for x and -10 for y. These values satisfy statement (1) but allow us to answer the question "no."

(2) Insufficient. Try the same values. Those values allow us to answer "no" to the question. But we need to consider other values. If we set y equal to -5 and x equal to 10, we can answer "yes" to the question.

You could guess between (C) and (E) or you could plug in some more numbers. As it turns out the two statements are equivalent. So they are just as insufficient together as they are separate.

5. E

(1) Insufficient. Only information about the tie is given. We know nothing about the belt.

(2) Insufficient. Only information about the belt is given. We know nothing about the tie.

All we can determine is that a greater percentage discount was obtained on the belt. Whether this translates into a greater dollar discount cannot be determined.