Question

Called ultimate addition, u(x) is defined to be the sum of all digit of an integer until the result is single digit integer. If m is a two-digit integer, how many possibility of m such that u(m) = u(50654)?A. 2 B. 5 C. 8 D. 10 E. 12

Answer 1

Answer: A) 2

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Work Shown:

u(50654) = 5+0+6+5+4 = 20

u(20) = 2+0 = 2

u(50654) = 2

We want to find all possible values of m such that u(m) = 2 and also m is some two-digit integer.

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Possible values of m are: m = 11, m = 20

u(m) = u(11) = 1+1 = 2

u(m) = u(20) = 2+0 = 2

and that's it. There are no other ways to have two positive integers add up to 2.