In a five digit number, the digit at the hundreds place is three-fourth of the digit at ten thousands place and the digit at tens place is two-third of the digit at hundreds place. The digit at tens place is square of the smallest prime number and the digit at thousands place is the largest single digit prime number. If the digit at unit place is the largest single digit odd number, then the number is

Question

Accepted Answer

To determine why Option 1 (87649) is the correct answer, let's analyze the conditions given in the question and see how they apply to each digit of the number:

1. **Digit at the Hundreds Place**: 
   - It is three-fourths of the digit at the Ten Thousands place.
   - In Option 1 (87649), the digit at the Ten Thousands place is 8. Three-fourths of 8 is 6, which matches the digit at the Hundreds place.

2. **Digit at the Tens Place**:
   - It is two-thirds of the digit at the Hundreds place.
   - In Option 1, the digit at the Hundreds place is 6. Two-thirds of 6 is 4, which matches the digit at the Tens place.

3. **Digit at the Tens Place as a Square**:
   - It is also given that the digit at the Tens place is the square of the smallest prime number.
   - The smallest prime number is 2, and its square is 4. This matches the digit at the Tens place in Option 1.

4. **Digit at the Thousands Place**:
   - It is the largest single-digit prime number.
   - The largest single-digit prime number is 7, which matches the digit at the Thousands place in Option 1.

5. **Digit at the Unit Place**:
   - It is the largest single-digit odd number.
   - The largest single-digit odd number is 9, which matches the digit at the Unit place in Option 1.

Now, let's explain why the other options are incorrect:

- **Option 2 (49327)**:
  - The digit at the Hundreds place is 3, which is not three-fourths of the digit at the Ten Thousands place (4).
  - The digit at the Tens place is 2, which is not two-thirds of the digit at the Hundreds place (3).
  - The digit at the Thousands place is 9, which is not the largest single-digit prime number (7).

- **Option 3 (83419)**:
  - The digit at the Hundreds place is 4, which is not three-fourths of the digit at the Ten Thousands place (8).
  - The digit at the Tens place is 1, which is not two-thirds of the digit at the Hundreds place (4).
  - The digit at the Thousands place is 3, which is not the largest single-digit prime number (7).

- **Option 4 (42937)**:
  - The digit at the Hundreds place is 9, which is not three-fourths of the digit at the Ten Thousands place (4).
  - The digit at the Tens place is 3, which is not two-thirds of the digit at the Hundreds place (9).
  - The digit at the Thousands place is 2, which is not the largest single-digit prime number (7).

In conclusion, Option 1 (87649) satisfies all the conditions given in the question, making it the correct answer.