In the process of numbering the pages of a book the printer uses 3189 digits, the number of pages in the book is?

Options

A. 1000
B. 1074
C. 1075
D. 1080

Explanation

To find the number of pages in the book using 3189 digits, we can break down the problem step by step.

### Step 1: Count digits used for pages 1 to 9
- Pages 1 to 9 are single-digit pages.
- There are 9 pages in total.
- Each page uses 1 digit.

**Calculation:**
\[ \text{Total digits for pages 1 to 9} = 9 \times 1 = 9 \text{ digits} \]

### Step 2: Count digits used for pages 10 to 99
- Pages 10 to 99 are two-digit pages.
- The total number of pages from 10 to 99 is \(99 - 10 + 1 = 90\).
- Each page uses 2 digits.

**Calculation:**
\[ \text{Total digits for pages 10 to 99} = 90 \times 2 = 180 \text{ digits} \]

### Step 3: Count digits used for pages 100 to 999
- Pages 100 to 999 are three-digit pages.
- The total number of pages from 100 to 999 is \(999 - 100 + 1 = 900\).
- Each page uses 3 digits.

**Calculation:**
\[ \text{Total digits for pages 100 to 999} = 900 \times 3 = 2700 \text{ digits} \]

### Step 4: Calculate total digits used up to page 999
- Now, we add the digits used from all the ranges:
\[ \text{Total digits used} = 9 + 180 + 2700 = 2889 \text{ digits} \]

### Step 5: Determine remaining digits for pages 1000 and above
- The total digits used so far is 2889, and the total digits available is 3189.
- The remaining digits are:
\[ \text{Remaining digits} = 3189 - 2889 = 300 \text{ digits} \]

### Step 6: Count pages from 1000 onwards
- Pages 1000 and above are four-digit pages.
- Each page uses 4 digits.
- Let \(x\) be the number of pages from 1000 onwards.

**Calculation:**
\[ 4x = 300 \implies x = \frac{300}{4} = 75 \text{ pages} \]

### Step 7: Calculate total number of pages in the book
- The total number of pages in the book is the sum of pages from all ranges:
\[ \text{Total pages} = 999 + 75 = 1074 \]

### Final Answer
The number of pages in the book is **1074**.

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