## Core Concept
The respiratory rate is an essential vital sign in pediatric patients, and it varies by age. Fast breathing, or tachypnea, in infants and children is defined by specific respiratory rate thresholds.

## Why the Correct Answer is Right
For children under 5 years of age, the World Health Organization (WHO) defines tachypnea (fast breathing) as follows:
- **Infants 0-5 months:** ≥ 60 breaths per minute
- **Infants 6-11 months:** ≥ 50 breaths per minute
- **Children 1-5 years:** ≥ 40 breaths per minute
Therefore, for a 6-month-old child, fast breathing is defined as a respiratory rate of more than 50 breaths per minute.

## Why Each Wrong Option is Incorrect
- **Option A:** This option does not align with the definition for a 6-month-old child.
- **Option B:** This option suggests 40 breaths per minute, which is the threshold for children aged 1-5 years, not 6 months.
- **Option D:** This option suggests 60 breaths per minute, which is the threshold for infants 0-5 months, not specifically for 6 months.

## Clinical Pearl / High-Yield Fact
A key point to remember is that these thresholds are critical for the assessment of respiratory distress in pediatric patients. For instance, a respiratory rate of more than 50 breaths per minute in a 6-month-old child indicates tachypnea and potential respiratory distress.

## Correct Answer: C. 50.