If `1001 xx111 = 110000 + 11 xx ........,` then the number in the blank space is

Options

A. 121
B. 211
C. 101
D. 111

Answer

To solve the equation \(1001 \times 111 = 110000 + 11 \times \text{(blank space)}\), we will follow these steps:

### Step 1: Calculate \(1001 \times 111\)
First, we need to multiply \(1001\) by \(111\).

\[ 1001 \times 111 = 1001 \times (100 + 10 + 1) = 1001 \times 100 + 1001 \times 10 + 1001 \times 1 \]

Calculating each term:
- \(1001 \times 100 = 100100\)
- \(1001 \times 10 = 10010\)
- \(1001 \times 1 = 1001\)

Now, adding these results together:
\[ 100100 + 10010 + 1001 = 111111 \]

### Step 2: Set up the equation
Now we have:
\[ 111111 = 110000 + 11 \times \text{(blank space)} \]

### Step 3: Isolate the term with the blank space
To find the blank space, we can rearrange the equation:
\[ 111111 - 110000 = 11 \times \text{(blank space)} \]

Calculating the left side:
\[ 111111 - 110000 = 1111 \]

So we have:
\[ 1111 = 11 \times \text{(blank space)} \]

### Step 4: Solve for the blank space
Now, divide both sides by \(11\):
\[ \text{(blank space)} = \frac{1111}{11} \]

Calculating this gives:
\[ \text{(blank space)} = 101 \]

### Final Answer
Thus, the number in the blank space is \(101\).

---