If p is the sum of q and r, then which one of the following must equal q -r ?

Options

A. `p - r`
B. `p + r`
C. `p - 2r`
D. `p + 2r`

Answer

To solve the problem, we need to express \( q - r \) in terms of \( p \), given that \( p \) is the sum of \( q \) and \( r \).

### Step-by-Step Solution:

1. **Understand the Given Information:**
We know from the problem statement that:
\[ p = q + r \]

2. **Rearranging the Equation:**
We want to find an expression for \( q - r \). To do this, we can rearrange the equation for \( p \):
\[ q = p - r \]

3. **Substituting \( q \) in \( q - r \):**
Now, we can substitute the expression for \( q \) into \( q - r \):
\[ q - r = (p - r) - r \]

4. **Simplifying the Expression:**
Simplifying the right-hand side gives:
\[ q - r = p - r - r = p - 2r \]

5. **Final Expression:**
Thus, we find that:
\[ q - r = p - 2r \]

### Conclusion:
The expression that must equal \( q - r \) is:
\[ q - r = p - 2r \]