## **Core Concept**
The question involves understanding the relationship between incidence and prevalence in the context of epidemiology. **Incidence** refers to the number of new cases that develop in a specified time period among a population at risk, while **prevalence** refers to the total number of cases of a disease in a population at a given time.

## **Why the Correct Answer is Right**
Given that the disease has 3 times more incidence in females compared to males but the same prevalence in both males and females, we can deduce the following: Let the incidence in males be (I_m) and in females be (3I_m). Let the duration of the disease be (D_m) for males and (D_f) for females. Prevalence is the product of incidence and duration of the disease. Since prevalence is the same in both males and females, we have: (I_m times D_m = 3I_m times D_f). This implies (D_m = 3D_f), or (D_f = frac{1}{3}D_m). This means the disease lasts 3 times longer in males than in females, which directly relates to option .

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option suggests the disease lasts equally long in males and females, which contradicts our deduction that (D_f = frac{1}{3}D_m).
- **Option B:** This option implies the disease lasts 3 times longer in females, which is the opposite of what we found ((D_f = frac{1}{3}D_m)).
- **Option D:** This option suggests the disease lasts 9 times longer in males, which does not align with (D_f = frac{1}{3}D_m).

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that **prevalence = incidence × duration**. This relationship can help in understanding how changes in incidence or disease duration can affect prevalence, and it's crucial for interpreting epidemiological data.

## **Correct Answer:** . The disease lasts 3 times longer in males than in females.