求解释一个prep07的逻辑题目

aaanity

A firm‘s two departments performed with remarkable consistency over the past two
years: in each of those years, the pharmaceuticals department has accounted for roughly
20 percent of dollar sales and 40 percent of profits, and the chemicals department for the
balance.
Which of the following can properly be inferred regarding the past two years from the
statement above?
A. Total dollar sales for each of the firm's department departments have
remained roughly constant.
B. The pharmaceuticals department has faced stiffer competition in its
markets than has the chemicals department.
C. The chemicals department has realized lower profits per dollar of sales
than has the pharmaceuticals department.
D. The product mix offered by each of the firm's department departments
has remained unchanged.
E. Highly profitable products accounted for a higher percentage of the
chemicals department's sales than of those of the pharmaceuticals
department.
正确答案C
对题目和其他选项没有疑惑
但是对于C选项这个profits per dollar of sales 究竟怎么算有些疑问
某网课的老师说可以直接用百分比相除 pharmaceuticals department用40%÷20%  chemicals department用60%÷80% 即可
但是我认为百分比不能直接相除 应该假设slaes和profits的值 然后用具体的数字相除 因为sales和profits的数值是不一样的呀

aaanity

dd我自己 求大神回复

ST5

你老师讲的是一种简化算法，但是正确的。加入公司total sales: x, total profit y:
那么 pharma profit per sales dollar: 40% * y / (20% * x)
那么 chemic profit per sales dollar: 60% * y / (80% * x)
比较这两个结果的时候y/x是个固定值可以不看。就和你老师的算法一样。
这个题目我觉得反倒是题目要留意 the chemicals division for the balance. 其实补充完整是 the chemicals division accounts for the balance of sales and profits. balance在这里有余额，剩余的意思。
不过如你所说，其实这道题根据排除法也可以算出来。