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 information will be sufficient to estimate Diana’s age?

To determine which information is sufficient to find Diana’s age, let us first express the relationships given in the statement using mathematical equations.

Let the ages of Diana, Jackson, Edward, and Stephen be represented by $D$, $J$, $E$, and $S$ respectively.

From the problem statement, we have two key relationships:
1. Diana is three times older than Jackson (i.e. three times Jackson's age):
$D=3J$
2. Edward is half the age of Stephen:
$E=\frac{1}{2}S$ or $S=2E$

Our goal is to find a unique numerical value for Diana's age, $D$. To do this, we need to find the numerical value of Jackson's age, $J$.

Now, let us evaluate the additional information provided in statements A and B:

Statement A: Edward is 10 years old.
This gives us $E=10$.
Using this in the second equation, Stephen's age is $S=2\times 10=20$ years.
However, knowing $E=10$ alone does not give us the exact age of Jackson ($J$), so Statement A alone is not sufficient.

Statement B: Both Jackson and Stephen are older than Edward by the same number of years.
This means the difference between Jackson's age and Edward's age is equal to the difference between Stephen's age and Edward's age:
$J-E=S-E$
Adding $E$ to both sides gives:
$J=S$
This statement tells us that Jackson and Stephen are the exact same age, but without any numerical values, Statement B alone is not sufficient.

Combining Statements A and B:
From Statement A, we know $E=10$, which gives Stephen's age $S=20$.
From Statement B, we know $J=\mathrm{S<br>}$, which means Jackson's age is $J=20$.
Now we can substitute $J=20$ into the formula for Diana's age:

Thus, both statements A and B together are necessary and sufficient to estimate Diana's age.

The correct option is Both A and B above.