Logical Reasoning Discussion

**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. |
If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true? I. Venkat earned not more than 36.25% return on average. II. Venkat earned not less than 33.75% return on average. III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results. IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry. |

✖ A. |
I and II only |

✔ B. |
II and IV only |

✖ C. |
II and III only |

✖ D. |
III and IV only |

**Solution:**

Option(**B**) is correct

Company C gave a return of Rs. 60.

$\therefore$ Total returns will be the minimum possible when B gives 1.5 times the initially expected returns.

$\therefore$ Total returns would be $20 + 15 + 60 + 40$ $= \text{Rs. }135$ $= 33.75\%$ of the initial investment.

Statement II is true.

Also, when returns are $33.75\%$, company B belongs to Auto or Steel Industry.

Statement IV is true and Statement III is false.

Total returns will be the maximum possible when D gives 1.5 times the initially expected returns.

$\therefore$ Total returns would be $20 + 10 + 60 + 60$ $= \text{Rs. }150 = 37.5\%$ of the initial investment.

Statement I is false.

Hence,** option B** is the correct choice.