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2019 · Q15

If a, b and c are positive integers such that 1/(a + 1/(b + 1/(c + 1/2))) = 16/23, then what is the mean of a, b and c?

Elementary MathematicsNumber System
  1. A1
  2. B2
  3. C1.33
  4. D2.33

Explanation

Invert: a + 1/(b + 1/(c+1/2)) = 23/16 = 1 + 7/16, so a = 1. Then b + 1/(c+1/2) = 16/7 = 2 + 2/7, so b = 2. Then c + 1/2 = 7/2, so c = 3. Mean of 1, 2, 3 is 2.