To find the youngest person, we need to establish the age order based on the given statements.

Establishing Age Relationships

• Statement 1: A is older than M. ($A > M$)
• Statement 2: G is older than M but younger than A. ($A > G > M$)
• Statement 3: K is younger than R and M. ($R > K$ and $M > K$)
• Statement 4: M is older than R. ($M > R$)

Determining the Order

Let's combine these relationships:

1. From $A > G > M$, we know A is the oldest among A, G, and M.
2. From $M > R$ and $R > K$, we establish the order $M > R > K$.
3. Combining these results with the fact that $M > K$ (from statement 3), we get a comprehensive order: $A > G > M > R > K$.

Identifying the Youngest Person

The established age order is $A > G > M > R > K$. The person at the end of this sequence is the youngest.

Therefore, K is the youngest among all.