Read the information given below to answer the questions.

Diana is three times older than Jackson; Edward is half the age of Stephen. Jackson is older than Edward.

Which one of the following can be inferred?

The correct option is Diana is older than Stephen.

Let us analyze the given information step-by-step using mathematical inequalities and relationships based on their ages:

1. "Diana is three times older than Jackson"
This gives us the relationship between Diana's age ($D$) and Jackson's age ($J$):

$D=3J$

Since age is a positive quantity, this implies that Diana is older than Jackson ($D>J$).

2. "Edward is half the age of Stephen"
This gives us the relationship between Edward's age ($E$) and Stephen's age ($S$):

$E=\frac{1}{2}S$

Or equivalently:

$S=2E$

This means Stephen is twice as old as Edward ($S>E$).

3. "Jackson is older than Edward"
This provides the key inequality connecting Jackson and Edward:

$J>E$

4. Comparing Diana and Stephen:
We know that Diana's age is:

$D=3J$

Since $J>E$, substituting this inequality into Diana's equation shows:

$D>3E$

We also know that Stephen's age is:

$S=2E$

Comparing $D>3E$ and $S=2E$, since $3E>2E$ for any positive age $E$, we get:

$D>3E>2E=S$

Therefore:

$D>S$

Hence, it can be definitively inferred that Diana is older than Stephen.