A two-digit number is multiplied by its reverse . The ones (units) and tens digits of the four-digit resultant number are both What is the value of the smallest such two-digit number
Answer:
- Since the units digit of the resultant number is zero, either or must be
Without loss of generality, assume
Therefore, is even. - Since the answer ends in
The answer is a multiple of and hence is a multiple of
Since and ends in is a multiple of
The only -digit multiples of ending in are and
From step 1, is even and is not an even number.
Therefore
Therefore, the two possible values for are and . - Hence, the smallest value of the two-digit number is