To determine the value of $x$ such that 35 is the median of the data set $\{21,7,45,33,62,x\}$, follow these steps:

1. Arrange the Data Set in Ascending Order:

The data set has 6 numbers, so the median will be the average of the 3rd and 4th numbers when arranged in order.

We need to place $x$ such that the median of the dataset is 35.

2. Determine the Position of $x$ to Make the Median 35:

- If $x$ is such that the 3rd and 4th numbers are $35$, then $x$ needs to be placed so that 35 is the median.

- Let’s test each option to see where $x$ fits.

3. Testing Different Values of $x$:

- Testing $x=33$:

Arranging the data set $\{7,21,33,33,45,62\}$:
- The 3rd and 4th numbers are 33 and 33.
- Median = $\frac{33+33}{2}=33$, which is not 35.

- Testing $x=37$:

Arranging the data set $\{7,21,33,37,45,62\}$:
- The 3rd and 4th numbers are 33 and 37.
- Median = $\frac{33+37}{2}=\frac{70}{2}=35$, which matches the given median.

Thus, the correct value for $x$ is $37$, which ensures that the median of the data set is 35.


The value of $x$ is 37.

The correct answer is C. 37.