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# 2001, the closing price of stock A and stock B are the same.

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2001, the closing price of stock A and stock B are the same. [#permalink]  20 Aug 2010, 11:51
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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
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Re: help [#permalink]  20 Aug 2010, 12:40
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.

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Re: help [#permalink]  20 Aug 2010, 12:45
Hi,

Stmt 1:

Let the closing stock price of both A and B (in 2001) be Rs 100.

Case 1:

Let the closing stock price of B at the end of 2002 be Rs 200. Then, A is Rs 216.

Price increase of stock A = Rs 116
Price increase of stock B = Rs 100

% by which price increase in stock A is greater than that in stock B =
((116 - 100) / 100) * 100 = 16%

Case 2:

Let the closing stock price of B at the end of 2002 be Rs 300. Then, A is Rs 324.

Price increase of stock A = Rs 224
Price increase of stock B = Rs 200

% by which price increase in stock A is greater than that in stock B =
((224 - 200) / 200) * 100 = 12%

Hence, statement 1 is not sufficient. Hope this clarifies.

I guess the reason why stmt 2 is not sufficient is fairly straightforward.

Thanks.
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Naveenan Ramachandran
4GMAT - Mumbai

Re: help   [#permalink] 20 Aug 2010, 12:45
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