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

Step by Step Explanation:
  1. 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.
  2. Since the answer ends in 00
    The answer is a multiple of 100 and hence is a multiple of 25.
    Since b0 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.
  3. Hence, the smallest value of the two-digit number ab is 25.

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