A symmetric distribution has a median of 10 and an IQR of 10. What is the value of the first quartile (Q1)?

The distribution is symmetric.
The Interquartile Range (IQR) is 10.
The Median is 10.

For a symmetric distribution, the median is exactly halfway between the first quartile ($Q1$) and the third quartile ($Q3$). This means the distance from $Q1$ to the median is equal to the distance from the median to $Q3$.
Mathematically, this can be expressed as:

The Interquartile Range (IQR) is defined as $Q3 - Q1$.
For a symmetric distribution, the distance from $Q1$ to the median is half of the IQR:

We are given $\text{IQR} = 10$ and $\text{Median} = 10$.

The First Quartile ($Q1$) is 5. This corresponds to the first option provided.