Question

Look at this set of 10 numbers:
7931151114
By how much would the range increase if the number 2 replaced one of the 1's in the set?

Answer 1

To find out how the range would change if one of the 1's in the number set is replaced with a 2, we first need to determine the current range of the set of numbers.

1. **Current Numbers**: The numbers in the set are: 7, 9, 3, 1, 1, 5, 1, 1, 4 (which we get by separating the digits of the original number 7931151114).

2. **Current Minimum and Maximum**:
- Minimum (min) = 1
- Maximum (max) = 9

3. **Calculate Current Range**:
- Current Range = max - min = 9 - 1 = 8

4. **Replacing one of the 1's with a 2**: If we replace one of the 1's with a 2, the new set of numbers will be: 7, 9, 3, 2, 1, 5, 1, 1, 4.

5. **New Minimum and Maximum**:
- Minimum remains = 1
- Maximum remains = 9

6. **Calculate New Range**:
- New Range = max - min = 9 - 1 = 8

7. **Change in Range**:
- The increase in the range = New Range - Current Range = 8 - 8 = 0

Thus, the range would **not increase** at all if one of the 1's is replaced by a 2. The range would remain the same.

**Answer**: The range would not increase; it remains 8.