A two-digit number ab is multiplied by its reverse ba. The ones (units) and tens digits of the four-digit resultant number are both 0. What is the value of the smallest such two-digit number ab?
Answer:
25
- Since the units digit of the resultant number is zero, either a or b must be 5.
Without loss of generality, assume a=5.
Therefore, b is even. - Since the answer ends in 00
⟹ The answer is a multiple of 100 and hence is a multiple of 25.
Since b≠0 and ba ends in 5,ba is a multiple of 25.
The only 2-digit multiples of 25 ending in 5 are 25 and 75.
From step 1, b is even and 7 is not an even number.
Therefore ba=25
Therefore, the two possible values for ab are 25 and 52. - Hence, the smallest value of the two-digit number ab is 25.