Manogna father was 38 years old when she was born, while her mother was 36 years old when her brother, who is 4 years younger than Manogna, was born. What is the difference between the ages of her parents in years?

Introduction / Context:
This problems on ages question focuses on relative ages within a family. Instead of asking for an absolute age, it asks for the difference between the ages of the parents, using information from the times when their children were born. Such questions test your understanding of how age differences remain constant over time and how to interpret statements about being younger or older by a certain number of years.

Given Data / Assumptions:

• When Manogna was born, her father was 38 years old.
• Her brother is 4 years younger than Manogna.
• When the brother was born, the mother was 36 years old.
• We need the difference between the ages of the father and the mother.
• Age differences between adults remain constant over time.

Concept / Approach:
Key points in this type of problem are that age differences between the same two people do not change as years pass, and that birth events fix specific moments in time with known ages. We can express parent ages in terms of the current age of Manogna and then subtract to find the constant difference between the father and the mother. An algebraic approach is convenient but a timeline or reasoning with differences also works very well for such family based age puzzles.

Step-by-Step Solution:
Step 1: Let the present age of Manogna be M years. Step 2: At the time of her birth, the father was 38 years older than the newborn, so the present age of the father is M + 38. Step 3: The brother is 4 years younger than Manogna, so his present age is M − 4 years. Step 4: At the time of the brother birth, the mother was 36 years older than the newborn, so the present age of the mother is (M − 4) + 36 = M + 32 years. Step 5: The age difference between the parents is therefore (M + 38) − (M + 32) = 6 years.

Verification / Alternative check:
Notice that we did not actually need the exact present age of either parent or of the children. Since both ages were written in terms of M, that variable cancels out in the subtraction, leaving a constant difference of 6 years. This is consistent at all times in the past, present, and future, and it shows that the father is always 6 years older than the mother. You can choose any sample value for M to test and you will always get the same difference.

Why Other Options Are Wrong:
Option 2 years: This would mean the father is only slightly older than the mother, which does not agree with the calculations derived from the birth information.
Option 4 years: This difference also does not match the derived expressions for the parent ages when carefully written.
Option 8 years and Option 10 years: These values are larger than the true difference. Substituting them back into hypothetical ages for the parents does not match the conditions given at the two birth times.

Common Pitfalls:
Many learners try to track exact present ages and get lost in the details, or they incorrectly think that the stated numbers change over time. The most robust method is to express all relevant ages in terms of a simple variable, like the present age of one child, and remember that the age gap between the parents is fixed. Also, be careful with younger than and older than wording, which can be reversed by mistake if read too fast.

Final Answer:
The difference between the ages of Manogna parents is 6 years.