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Sum of Two Bases

Source: 1966 AHSME #39

August 31, 2011
geometric sequencealgebrasystem of equationsAMC

Problem Statement

In base R1R_1 the expanded fraction F1F_1 becomes 0.373737...0.373737..., and the expanded fraction F2F_2 becomes 0.737373...0.737373.... In base R2R_2 fraction F1F_1, when expanded, becomes 0.252525...0.252525..., while fraction F2F_2 becomes 0.525252...0.525252.... The sum of R1R_1 and R2R_2, each written in base ten is:
(A) 24(B) 22(C) 21(D) 20(E) 19\text{(A)}\ 24 \qquad \text{(B)}\ 22\qquad \text{(C)}\ 21\qquad \text{(D)}\ 20\qquad \text{(E)}\ 19
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