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
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