GMAT Math

Maybe this will help - whenever you're testing values on DS, have this goal in mind: "let me pick some values that will give me a YES answer, then some that will give me a NO answer." This way, you're thinking about extremes, and not just testing randomly.

(1) b > c > 69

So let's think about extremes - what are the smallest possible values of b and c? 71 and 70. If that's the case, our set is (rearranged in order except for a): [a, 51, 70, 71, 72, 85]. Here, it doesn't matter what a is; the median has to be between 70 and 72. This would give us a NO answer.

So can we come up with a YES answer? What would the opposite extreme be? We just know that b and c are greater than 69, so there's no limit to how big they could be! We could say c = 1000, b = 1001, and a = 1002. In that case, our set would be: [51, 72, 85, 1000, 1001, 1002]. Clearly the median is way bigger than 80, so we get a YES answer.

If we have a YES and a NO, it's insufficient.

(2) a < c < 71

Let's think of extremes again. What are the smallest possible values? Let's say a = 1, b = 2, and c = 3. Our set is [1, 2, 3, 51, 72, 85]. Clearly the median is less than 80, so we get a NO.

What are the largest possible values? The largest that c can be is 70, and the largest 1 can be is 69. There are no restrictions on b, so we can say b = 1000. Our set is [51, 69, 70, 72, 85, 1000]. Here, even with a and c at their highest, the median is still only 71. We can't find any values where the median is greater than 80. This is SUFFICIENT.