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Source: 2024 AMC 8 P15

January 25, 2024
AMC2024 AMC 8AMC 8

Problem Statement

Let the letters FF, LL, YY, BB, UU, GG represent different digits. Suppose F‾L‾Y‾F‾L‾Y‾\underline{F}\underline{L}\underline{Y}\underline{F}\underline{L}\underline{Y} is the largest number that satisfies the equation 8⋅F‾L‾Y‾F‾L‾Y‾=B‾U‾G‾B‾U‾G‾.8 \cdot \underline{F}\underline{L}\underline{Y}\underline{F}\underline{L}\underline{Y} = \underline{B}\underline{U}\underline{G}\underline{B}\underline{U}\underline{G}. What is the value of F‾L‾Y‾+B‾U‾G‾\underline{F}\underline{L}\underline{Y} + \underline{B}\underline{U}\underline{G}?
<spanclass=′latex−bold′>(A)</span>1089<spanclass=′latex−bold′>(B)</span>1098<spanclass=′latex−bold′>(C)</span>1107<spanclass=′latex−bold′>(D)</span>1116<spanclass=′latex−bold′>(E)</span>1125<span class='latex-bold'>(A) </span> 1089\qquad<span class='latex-bold'>(B) </span> 1098\qquad<span class='latex-bold'>(C) </span> 1107\qquad<span class='latex-bold'>(D) </span> 1116\qquad<span class='latex-bold'>(E) </span> 1125
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