求助 Prep 一道数学题。

vincentchang83

The cost of a square slab is proportional to its thickness and also proportional to the square of its length.  What is the cost of a square slab that is 3 meters long and 0.1 meter thick?

(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.


上面是prep的一道题。 答案是 D。 可是我觉得 条件一只能推导出 0.1 meter thick 是 160. 不sufficient. 条件2 推出 1 meter long 是 200. 也不sufficient. 但1+2 ： 推出 160+200*3 = 760 USD.

不知道大家是怎么看的？

rayleefd

Based on the given information, we can have the formula as follow:
Cost = A* T*L*L, in which T stands for thickness, L stands for Length, and A is the constant
If we put the data in premise (1) and (2), we can solve the equation and get the A in both cases. Actually, A = 400
Then each premise alone is sufficient to help solve the problem

2bethere

2楼正解。
Given it's proportional to both Thickness and Length, it must be multiplied together, thus Price = a * Thickness * Length^2

You are thinking that Price = a*Thickness + b*Length^2 or Price = a*(Thickness+Length^2), which is not always proportional.

vincentchang83

rayleefd 发表于 2015-8-18 14:03
Based on the given information, we can have the formula as follow:
Cost = A* T*L*L, in which T stand ...

Ha, Thanks for the detailed reply. I got it now!

vincentchang83

2bethere 发表于 2015-8-18 14:34
2楼正解。
Given it's proportional to both Thickness and Length, it must be multiplied together, thus ...

多谢， 这下明白了~~ 估计考试遇到这种题， 直接放弃了。。。。