The product o two numbers ab7 and cd5 could be where ab7 and cd5 are individually three digit numbers:

Options

A. a. 8135
B. b. 79236
C. c. 8735255
D. d. None of these

Answer

To solve the problem of finding the possible product of two three-digit numbers \( ab7 \) and \( cd5 \), we need to analyze the situation step by step.

### Step 1: Define the Numbers
Let:
- \( ab7 \) represent a three-digit number where \( a \) and \( b \) are digits (0-9) and the last digit is 7.
- \( cd5 \) represent a three-digit number where \( c \) and \( d \) are digits (0-9) and the last digit is 5.

### Step 2: Determine the Range of Products
The smallest three-digit number is 100, and the largest three-digit number is 999.

- The minimum product occurs when both numbers are at their minimum:
\[ 100 \times 100 = 10,000 \quad (\text{5 digits}) \]

- The maximum product occurs when both numbers are at their maximum:
\[ 999 \times 999 = 998001 \quad (\text{6 digits}) \]

### Step 3: Analyze the Number of Digits in the Product
From the calculations:
- The product of two three-digit numbers will yield either a 5-digit or a 6-digit number.
- A 4-digit number is not possible because the minimum product exceeds 9999.

### Step 4: Check the Last Digits
Next, we need to consider the last digits of the numbers:
- The last digit of \( ab7 \) is 7.
- The last digit of \( cd5 \) is 5.

When multiplying these two numbers, the last digit of the product can be determined by multiplying the last digits:
\[ 7 \times 5 = 35 \]
This means the last digit of the product will be 5.

### Step 5: Conclusion
Since the product of \( ab7 \) and \( cd5 \) must end in 5, and we have established that the product will be either a 5-digit or a 6-digit number, we can conclude that:
- The product cannot be a 4-digit number.
- The possible products of \( ab7 \) and \( cd5 \) will either be 5 or 6 digits long.

Given that the problem asks for the possible product of \( ab7 \) and \( cd5 \), we can conclude that the product cannot be a 4-digit number, and thus the answer is:
**None of these.**