.
First digit of the number is 2.
If the last digit is x, then adding the number with the reversed one and looking into the last digit of the sum, we have this equation
2 + x = 7.
So, we conclude that the last digit of the number is x = 7-2 = 5.
Thus the unknown number is of the form 2t5, where t is the tens digit.
Next, adding 2t5 (original number)
5t2 (reversed number)
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767
we conclude that t+t = 2t = 6, which implies t = 3.
ANSWER. The number is 235.
Solved.
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Notice that the sum of digits in my number is 2+3+5 = 10, as stated.
But in my solution, I did not use this fact.
So, this condition is excessive and is not necessary for the solution.
If such excessive condition is valid, then it is CONSISTENT with the answer, as we see it in this case.
Had it be not valid by the observation, it would contradict the solution (which is not the case).
So, you should be careful with such additional excessive statements and check them after completing your analysis
to be sure that everything is Ok (!)