题目

If $A,B,C$ and $D$ are positive integers such that $4A=9B,17C=11D$, and $5C=12 A$, then the arrangement of the four numbers from greatest to least is

选项

A.

CDAB

B.

BACD

C.

DCAB

D.

DCBA

E.

BDAC

解析

利用给定的比例比较这些数。 1. 由 \(4A = 9B\) \[ A = \frac{9}{4}B \] 所以 \(A > B\) 2. 由 \(5C = 12A\) \[ C = \frac{12}{5}A \] 代入 \(A = \frac{9}{4}B\): \[ C = \frac{12}{5} \times \frac{9}{4}B = \frac{27}{5}B = 5.4B \] 到目前为止:\(C > A > B\) 3. 由 \(17C = 11D\) \[ D = \frac{17}{11}C \approx 1.545C \] 所以:\(D > C\) 4. 合并所有比较结果 \[ D > C > A > B \] 从大到小的排列为 \(DCAB\) 答案:C
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