## Core Concept
The Secondary Attack Rate (SAR) is a measure used in epidemiology to determine the spread of a disease within a defined group, such as a family, school, or other closed community. It is calculated as the number of new cases among contacts within the incubation period of the disease, divided by the number of exposed contacts. The measles virus has a typical incubation period of about 10-14 days, but it can range from 7 to 21 days.

## Why the Correct Answer is Right
To calculate the SAR, we first need to identify the primary case and the secondary cases. The primary case occurred on January 1st. The 3 cases that occurred on January 3rd are considered secondary cases because they developed the disease within a short period after the primary case, indicating they were infected by the primary case. The remaining cases developed 2-3 weeks later, which is beyond the typical secondary case timeframe for measles given its incubation period.

Given:
- Primary case: 1
- Total secondary cases: 35 - 1 (primary case) = 34
However, for SAR calculation, we consider the exposed population. Assuming the 3 cases on January 3rd were infected by the primary case, we consider the rest of the cohort minus the primary case and those 3 as exposed. But accurately, we should focus on the number of exposed contacts.

The total number of children = 100,
Primary case = 1,
Secondary cases = 35.

The number of exposed contacts = 100 - 1 (primary case) = 99.

SAR = (Number of new cases among contacts) / (Number of exposed contacts)
Given 35 - 1 = 34 new cases (excluding the primary case),
SAR = 34 / 99.

## Why Each Wrong Option is Incorrect
**Option A:** This option might be incorrect based on miscalculation or incorrect assumption of exposed contacts or new cases.
**Option B:** Similarly, this could be due to incorrect numbers used for calculation or misunderstanding of who are considered exposed or as new cases.
**Option C:**
**Option D:** This seems to align with a plausible calculation given the scenario.

## Clinical Pearl / High-Yield Fact
A key point to remember is that the Secondary Attack Rate is particularly useful for diseases that are highly infectious and occur in relatively closed populations, like schools, households, or cruise ships. For measles, which has a high basic reproduction number (R0), the SAR can be quite high, especially in unimmunized populations.

## Correct Answer: B. 34/99 ≈ 0.343 or 34.3%.