• I am a 2 digit number.
• The digit in tens place and the digit in units place are consecutive prime numbers.
• The sum of digits is multiple of 3 and 4. The number is :

Question

• I am a 2 digit number. 
• The digit in tens place and the digit in units place are consecutive prime numbers. 
• The sum of digits is multiple of 3 and 4. The number is :

Accepted Answer

To determine why Option 1 (57) is the correct answer, let's analyze the given conditions and apply them to each option:

1. **Condition Analysis:**
   - The number is a 2-digit number.
   - The digits in the tens and units places are consecutive prime numbers.
   - The sum of the digits is a multiple of both 3 and 4.

2. **Option 1: 57**
   - Tens digit: 5
   - Units digit: 7
   - Consecutive prime numbers: 5 and 7 are consecutive prime numbers.
   - Sum of digits: 5 + 7 = 12, which is a multiple of both 3 and 4 (since 12 is divisible by 3 and 4).
   - Therefore, Option 1 satisfies all the conditions.

3. **Option 2: 23**
   - Tens digit: 2
   - Units digit: 3
   - Consecutive prime numbers: 2 and 3 are consecutive prime numbers.
   - Sum of digits: 2 + 3 = 5, which is not a multiple of 3 and 4.
   - Therefore, Option 2 does not satisfy the condition regarding the sum of the digits.

4. **Option 3: 35**
   - Tens digit: 3
   - Units digit: 5
   - Consecutive prime numbers: 3 and 5 are consecutive prime numbers.
   - Sum of digits: 3 + 5 = 8, which is not a multiple of 3 and 4.
   - Therefore, Option 3 does not satisfy the condition regarding the sum of the digits.

5. **Option 4: 13**
   - Tens digit: 1
   - Units digit: 3
   - Consecutive prime numbers: 1 is not a prime number, so 1 and 3 cannot be consecutive prime numbers.
   - Therefore, Option 4 does not satisfy the condition regarding consecutive prime numbers.

In conclusion, Option 1 (57) is the only option that meets all the specified conditions: it is a 2-digit number with consecutive prime numbers in the tens and units places, and the sum of its digits is a multiple of both 3 and 4.