AMC 8 2024 Problem 15

AMC8 2024 年第 15 题

整除与因数★★★☆☆
Let the letters F, L, Y, B, U, and G represent distinct digits.
Suppose F‾ L‾ Y‾ F‾ L‾ Y‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} is the greatest six-digit number that satisfies the following equation:
8⋅F‾ L‾ Y‾ F‾ L‾ Y‾=B‾ U‾ G‾ B‾ U‾ G‾8 \cdot \underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} = \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}\,\underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}
What is the value of F‾ L‾ Y‾+B‾ U‾ G‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} + \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}?
用 F、L、Y、B、U、G 表示不同数字。
若 F‾ L‾ Y‾ F‾ L‾ Y‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} 为满足下列等式的最大六位数：
8⋅F‾ L‾ Y‾ F‾ L‾ Y‾=B‾ U‾ G‾ B‾ U‾ G‾8 \cdot \underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} = \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}\,\underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}
求 F‾ L‾ Y‾+B‾ U‾ G‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} + \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}} 的值。
  1. A.1089
  2. B.1098
  3. C.1107
  4. D.1116
  5. E.1125

正确答案 · Correct Answer

C

解析 · Solution

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