Question 1199769
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Possibly the fastest way to solve the problem is by trying different bases and finding the one that works.  But you can get better practice in problem-solving skills by solving the problem using logical reasoning.<br>
(1) The sum of the units digits in base 10 is 14; since the last digit in the sum in the unknown base is 2, the unknown base must be an integer that is a divisor of 14-2 = 12.
(2) The addition in base 10 gives the result 124; since the addition in the unknown base gives a sum 102 using smaller digits, the base is greater than 10.<br>
The only integer that satisfies both conditions is 12.<br>
ANSWER: 12<br>