Numerical Logic
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Common Information

Venkat, a stockbroker, invested a part of his money in the stock of four companies - A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order.

At the time of investment, the price of each stock was Rs.100. Venkat purchased only one stock of each of these companies. He was expecting returns of $20\%$, $10\%$, $30\%$, and $40\%$ from the stock of companies A, B, C and D, respectively.

Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry.

As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns.

For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies, which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.

Q.

Common Information Question: 3/4

If Venkat earned a $38.75\%$ return on average during the year, then which of these statement(s) would necessarily be true?

I. Company C belonged either to Auto or to Steel Industry.

II. Company D belonged either to Auto or to Steel Industry.

III. Company A announced extraordinarily good results.

IV. Company B did not announce extraordinarily good results.

 A.

I and II only

 B.

II and III only

 C.

I and IV only

 D.

II and IV only

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Solution:
Option(C) is correct

Venkat earned a return of 38.75% = Rs. 155

$\therefore$ He earned Rs. 55 more than expected.

$\Rightarrow 55 = x + 0.5y$

where $x$ and $y$ correspond to expected returns on stocks that gave extraordinarily good results.

But $x$ and $y$ can be 20, 10, 30 or 40.

If $x = 20$, $y = 70$, which is not possible.

If $x = 10$, $y = 90$, which is not possible.

If $x = 30$, $y = 50$, which is not possible.

If $x = 40$, $y = 30$, which is possible.

Thus company C and company D announced returns that were respectively one and a half and two times the initially expected returns.

$\therefore$ Company C belonged to either Auto or Steel Industry and Company A and B did not announce extraordinarily good results.

Statements I and IV are true.

Hence, option C is the correct choice.


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