A three-digit prime number is such that the digit in the unit place is equal to the sum of the other two, and if the other digits are interchanged, we still have a prime number of three digits. Then the total number of such primes is:

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answer is B.

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Detailed Solution

Concept: Suppose a three-digit number is a prime number. This means that the last digit of the 3-digit number is odd. Now look at all the possibilities 1, 3, 5, 7, 9. Here, the last digit 1 is not possible because it does not meet the prescribed condition of summing the other two numbers. For 3, the other 2 digits are 1 and 2. The resulting three-digit number can be either 123 or 213, neither of which is a prime number. For 5, numbers ending in 5 are not prime numbers. Similarly, the sum of the 9 digits is 1.8 and 2.7, 3.6 and 4.5, both of which are not prime and are rejected. Well, for 7, the sum of the digits would be 1.6, 2.5 and 3.4. Therefore, the possible numbers are 167, 617, 347, 437, 257, 527.
Where 527 is divisible by 17 and 437 is divisible by 19. Therefore, the sum of the prime numbers is 167, 617, 347, 257.
Therefore, there are four prime numbers.
Hence, the correct answer is option (2).

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