To determine whether the median of the set `{a, b, c, 51, 85, 72}` is greater than 70, we will analyze the two statements provided.
### Step 1: Understanding the Median
The median is the middle value of a sorted list of numbers. If there are an even number of values, the median is the average of the two middle numbers.
In our case, we have six numbers: `{a, b, c, 51, 85, 72}`. The median will be the average of the 3rd and 4th numbers when sorted.
### Step 2: Analyze Statement 1
**Statement 1:** `b > c > 69`
From this statement, we know:
- Both `b` and `c` are greater than 69.
- Since `b > c`, we can assign minimum values to `c` and `b` as follows:
- Let `c = 70` (the smallest integer greater than 69).
- Then `b` must be at least `71`.
Now we can consider the possible values of `a`:
- The set becomes `{a, 51, 70, 71, 72, 85}`.
#### Sorting the Set
1. If `a < 51`: The sorted set is `{a, 51, 70, 71, 72, 85}`. The median is `(70 + 71) / 2 = 70.5`, which is greater than 70.
2. If `51 < a < 70`: The sorted set is `{51, a, 70, 71, 72, 85}`. The median is still `(70 + 71) / 2 = 70.5`, which is greater than 70.
3. If `70 < a < 71`: The sorted set is `{51, 70, a, 71, 72, 85}`. The median is `(70 + 71) / 2 = 70.5`, which is greater than 70.
4. If `a >= 71`: The sorted set is `{51, 70, 71, 72, 85, a}`. The median is `(71 + 72) / 2 = 71.5`, which is greater than 70.
In all cases, the median is greater than 70. Thus, **Statement 1 is sufficient**.
### Step 3: Analyze Statement 2
**Statement 2:** `a < c < 71`
From this statement, we know:
- `c` must be less than 71.
- Since `c` is an integer, the maximum value for `c` can be `70`.
- Thus, `a` must be less than `70`.
#### Possible Values
If we take the maximum value for `c`:
- Let `c = 70` and `a` can be at most `69`.
Now we can consider the possible values of `b`:
- The set becomes `{a, b, 70, 51, 72, 85}`.
#### Sorting the Set
1. If `b` is the smallest: The sorted set is `{a, 51, 70, 72, 85, b}`. The median is `(70 + 72) / 2 = 71`, which is greater than 70.
2. If `b` is the largest: The sorted set is `{51, 70, 72, 85, a, b}`. The median will depend on the value of `b` and could be less than or greater than 70.
Since the value of `b` can vary and influence the median, **Statement 2 is not sufficient**.
### Conclusion
- **Statement 1 is sufficient** to determine that the median is greater than 70.
- **Statement 2 is not sufficient**.
### Final Answer
The answer is that **only Statement 1 is sufficient** to conclude that the median is greater than 70.
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