Question

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:

• A. $2$
• B. $4$
• C. $6$
• D. $3$
• E. Answer Required

Answer 1

The correct option is B $4$

The last digit has to be odd,otherwise, it won't be prime at very first hand.

Now if we further check for $1,3,5,7,9$,-

Last digit $1$ isn't possible because it won't satisfy the other option of summing and reversing.

For $3$, other $2$ digits would be $1,2$-that's not prime.

Last digit $5$-not a prime.

Similarly for $9$, digit sum would be $18$ which is not a prime.

Therefore, only possibility is $7$.

So the pairs are: $1,6$ and $2,5$ and $3,4$

Thus numbers can be $167,617,347,437,257,527$

$527$ is divisible by $17$

$437$ is divisible by $19$

Therefore, the total number of primes are $167,617,347,257$.

Hence, there are $4$ primes.