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.
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100% (04:20) correct
