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

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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Video solution from Quant Reasoning starts at 15:40 here:

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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.

I think the try and error will consume a lot of time. I prefer the solution of Brunel

A simply way to solve this question is by assuming values

Statement 1 is not sufficient because we have no information about B and we can get more than 1 answer

Statement 2 is not sufficient because again, we we have no information about B.

When we combine both the statements we get

Assume the starting value of both the stocks is 100.
Let the increase in stock B be x

Now,
1.15(100)=1.08(100+x)
115=108+1.08x
7=1.08x
x=7/1.08
x=6.48

Hope this was helpful

You can follow similar approach in such questions

Aryan Chandel
+91 8169397962

stmt 1
A B
2001 X X
2002 108 100

Price increase for A = (108-X)/X
Price increase for B = (100-X)/X

Question asks : By what percent was the price increase of A greater than the price increase of B
(Price increase for A - Price increase for B)/Price increase for B

Not Sufficient (X is not known)

stmt 2:
Price increase for A = 15%, We dont know anything abt B --> Not Sufficient

Combining 1 and 2

15=(108-X)/X
108=16X

Stmt 1 + stmt 2 together sufficient

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