A three digit number is such that its hundredth digit is equal to the

Let a three digit number= PQR or more precisely 100P + 10Q + R

=> Hundred's digit (P) = Q * R [Q and R are prime numbers]

The only possible values of Q and R are (2, 3) or(3, 2) as P is a single-digit number. So, Q = 2 and R = 3 or Q = 3 and R = 2 and P = 6 in both case.

=> Difference between the number and its reverse is 297: 100P + 10Q + R - (100R + 10Q + P) = 297

=> 99P - 99R = 297

=> 11P - 11R = 33

=> 66 - 33 = 11R

=> R = 3 and hence Q = 2.

Therefore, ten's digit = Q = 2.

Answer A

­I Ian thank you very much for sharing your reasoning! It helped my a lot.
What I do not understand is when you say "reverse its digits to get CBA, then these numbers differ by roughly 300, then the digits A and C will differ buy three".
If CBA = 297, then ABC would = 792 which does not make any sense. None of the foud alternatives reverse to 297.


When I first read the question I understood the "reverse" number as the reciprocal.... Is this a huge misunderstanding? Or is it that the wording is confusing? I am not a native English speaker.
­

297 isn't either of the two numbers.

297 is the DIFFERENCE between the two numbers.

One of the two numbers could be called ABC, where A is hundreds place, B tens place and C the ones place.

The reverse of this number ABC means to create a new number CBA.

So the difference between these two numbers is:

ABC - CBA = 297

To facilitate this subtraction these numbers can be rewritten as:

(100A+10B+C) - (100C+10B+A)

which can be simplified to:

99(A-C) = 297.

Dividing through by 99:

A-C = 3 or A=C+3

So, because C is prime and A must be less than 10, these are the only choices for the pair:

A C
5 2
6 3
8 5

Now, it's further stipulated that A = B*C

So looking at the above options:

Can A=5 ?

5=B×2 NO B works

Can A=6 ?

6=B*3 YES. B=2

Can A=8 ?

8=B*5 NO B works

So, the only number that works is A=6 B=2 C=3

623

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