mehdiov wrote:
2001, the closing price of stock A and stock B are the same. 2002, the closing price of two stocks both increased and price of A increased more than price of B. By what percent was the price increase of stock A greater than the price increase of stock B?
(1) 2002, the closing price of stock A is 8% greater than the closing price of stock B.
(2) The closing price of stock A is increased by 15% from 2001 to 2002.
For me the ste 1 is OK unless I did not get the question
Many thanks
Let the initial price of stocks A and B be \(x\);
Le the increase of stock A be \(a\), so after increase price of A is \(x+a\);
Le the increase of stock B be \(b\), so after increase price of B is \(x+b\);
Question: "By what percent was the price increase of stock A greater than the price increase of stock B" --> \(\frac{a-b}{b}=?\)
(1) 2002, the closing price of stock A is 8% greater than the closing price of stock B --> \(x+a=1.08(x+b)\) --> \(x=\frac{100a-108b}{8}\). Don't have the relationship between \(a\) and \(b\), hence can not calculate the value of \(\frac{a-b}{b}\). Not sufficient.
To illustrate this:
If initial price was 100$ and after increase price of B became 200$ (increase of B 100$), then price of A, after increase would be 216$, which is 8% more (increase of A 116$). In this case price increase of stock A would be \(\frac{116-100}{100}=0.16\) times more (16% more);
If initial price was 100$ and after increase price of B became 300$ (increase of B 200$), then price of A, after increase would be 3246$, which is 8% more (increase of A 224$). In this case price increase of stock A would be \(\frac{224-200}{100}=0.24\) times more (24% more).
(2) The closing price of stock A is increased by 15% from 2001 to 2002 --> \(x+a=1.15x\) --> \(x=\frac{20a}{3}\). Clearly not sufficient, as no info about the increase of stock B.
(1)+(2) \(x=\frac{100a-108b}{8}\) and \(x=\frac{20a}{3}\) --> \(\frac{100a-108b}{8}=\frac{20a}{3}\) --> \(35a=81b\), we have relationship between \(a\) and \(b\), hence we can find the ratio of \(\frac{a-b}{b}\). Sufficient.
Answer: C.