If a number is as much greater than 31 as it is less than 75, then the number is

Options

A. a) 106
B. b) 44
C. c) 74
D. d) 53

Answer

To solve the problem, we need to find a number \( X \) that is as much greater than 31 as it is less than 75. We can set this up mathematically.

### Step-by-step Solution:

1. **Understanding the Problem**:
We need to find a number \( X \) such that the difference between \( X \) and 31 is equal to the difference between 75 and \( X \).

2. **Setting Up the Equation**:
We can express this relationship with the equation:
\[ X - 31 = 75 - X \]

3. **Solving the Equation**:
To solve for \( X \), we will first add \( X \) to both sides:
\[ X + X - 31 = 75 \]
This simplifies to:
\[ 2X - 31 = 75 \]

4. **Isolating \( X \)**:
Next, we add 31 to both sides:
\[ 2X = 75 + 31 \]
This gives us:
\[ 2X = 106 \]

5. **Dividing by 2**:
Finally, we divide both sides by 2 to solve for \( X \):
\[ X = \frac{106}{2} = 53 \]

Thus, the number is \( \boxed{53} \).