Question

lorenzo has the following data: 8, d, 8, 16, 29, 44, 26, 8, 16. if the range is 36, which number could d be? options: 29, 89. submit

Explanation:

Step1: Recall range definition

Range = Max value - Min value

Step2: Test d as minimum value

If $d$ is the minimum, then $\text{Max} - d = 36$. The current maximum in the data is 44, so $44 - d = 36$. Solving for $d$:
$d = 44 - 36 = 8$
But 8 is already in the data, and if $d=8$, the range would be $44-8=36$, which works, but 8 is not one of the options.

Step3: Test d as maximum value

If $d$ is the maximum, then $d - \text{Min} = 36$. The current minimum in the data is 8, so $d - 8 = 36$. Solving for $d$:
$d = 36 + 8 = 44$
44 is already in the data, and if $d=44$, the range is $44-8=36$, which works, but 44 is not an option.

Step4: Check given options

Check option 29: If $d=29$, the data set's max is 44, min is 8. Range = $44-8=36$, which matches the required range.
Check option 89: If $d=89$, the data set's max is 89, min is 8. Range = $89-8=81
eq 36$, which does not match.

Answer:

29