Question
Janelle has the following data:
b758
If the range is 3, which number could b be?
b758
If the range is 3, which number could b be?
Answers
Answered by
GPT-4o mini
To find the possible value of \( b \) given the data "b758" and that the range is 3, we start by using the definition of range:
The range of a set of numbers is calculated as the difference between the maximum and minimum values of the set.
Given the number "b758," the digits are composed of \( b, 7, 5, \) and \( 8 \). To find the range, we need to identify the maximum and minimum values in this set.
1. Identify the minimum and maximum possibility of \( b \):
- If \( b \) is the smallest digit (minimum), then it would be less than all other digits (5, 7, and 8).
- If \( b \) is the largest digit (maximum), then it should be greater than all other digits.
To satisfy the condition that the range is 3, we can set up the following scenarios:
- **Case 1**: If \( b \) is the maximum, then it will be greater than or equal to 8. The maximum could potentially be 8, but that would require a minimum of 5 (the next lowest number), giving us a range of \( 8 - 5 = 3 \). However, since "b" cannot be greater than 8 in this scenario, it cannot be greater than 8.
- **Case 2**: If \( b \) is a minimum. For \( b \) to be a minimum, we will consider possible minimum values \( b \):
- If \( b = 5 \): then maximum \( 8 \), minimum \( 5 \), range = \( 8 - 5 = 3 \) (valid).
- If \( b < 5\) (like 4, 3, 2, or 1): then maximum will still be 8, and minimum will not yield a valid range of 3.
- If \( b = 6\) or higher: then it invalidates the range since maximum becomes \( 8 (7, 5, 6) \) will then make it less than the value above and would not produce a 3-min range because the minimum will be below 8.
The only possible value for \( b \) maintaining a range of 3 in the data "b758" is:
- **Possible value of \( b \)**: **5.**
Thus, the number could be 5.
The range of a set of numbers is calculated as the difference between the maximum and minimum values of the set.
Given the number "b758," the digits are composed of \( b, 7, 5, \) and \( 8 \). To find the range, we need to identify the maximum and minimum values in this set.
1. Identify the minimum and maximum possibility of \( b \):
- If \( b \) is the smallest digit (minimum), then it would be less than all other digits (5, 7, and 8).
- If \( b \) is the largest digit (maximum), then it should be greater than all other digits.
To satisfy the condition that the range is 3, we can set up the following scenarios:
- **Case 1**: If \( b \) is the maximum, then it will be greater than or equal to 8. The maximum could potentially be 8, but that would require a minimum of 5 (the next lowest number), giving us a range of \( 8 - 5 = 3 \). However, since "b" cannot be greater than 8 in this scenario, it cannot be greater than 8.
- **Case 2**: If \( b \) is a minimum. For \( b \) to be a minimum, we will consider possible minimum values \( b \):
- If \( b = 5 \): then maximum \( 8 \), minimum \( 5 \), range = \( 8 - 5 = 3 \) (valid).
- If \( b < 5\) (like 4, 3, 2, or 1): then maximum will still be 8, and minimum will not yield a valid range of 3.
- If \( b = 6\) or higher: then it invalidates the range since maximum becomes \( 8 (7, 5, 6) \) will then make it less than the value above and would not produce a 3-min range because the minimum will be below 8.
The only possible value for \( b \) maintaining a range of 3 in the data "b758" is:
- **Possible value of \( b \)**: **5.**
Thus, the number could be 5.