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## Analytical Reasoning Set 1

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

## Questions Set 1

Q1) What is the minimum average return Venkat should have earned during the year?
1) 30%
2) 31.25%
3) 33%
4) Cannot be determined

Q2) If Venkat earned 35% return on average during the year, then which of these statements would necessarily be true?

I) Company A belonged either to Auto or to Steel industry.
II) Company B did not announce extraordinarily good results.
III) Company A announced extraordinarily good results.
IV) Company D did not announce extraordinarily good results.
1) I and II only
2) II and III only
3) III and IV only
4) II and IV only

Q3) If Venkat earned 38.75% return on average during the year, then which of these statements 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.
1) I and II only
2) II and III only
3) I and IV only
4) II and IV only

SOLUTIONS:

1) Minimum return will be gained if the extraordinarily performing stocks(double and 1.5 growth) are the ones whose expected returns are lowest (10% and 20%). Taking the minimum value of the expected returns as 10. We have to see which of the two values of 10 and 20 multiplied with 2 and 1.5 and vice-versa yield the minimum value.
Now, compare the minimum value between 20×2+10×1.5 and 10×2+20×1.
Minimum average return is

2) If the average return is 35%, then the total return is 35*4 = 140
Possible arrangements of 140 are
(i) 40×1.5+30+20×2+10
A = 20×2(Cement or IT)
B = 10, C = 30
D = 40×1.5 (Steel or Auto)
or
(ii) 40 + 30×2 + 20×1.5 + 10
A = 20×1.5(Steel or Auto)
B = 10, C = 30×2(Cement or IT)
D = 40
Hence, Statements ii and iii are correct.

3) If the average return is 35%, then the total return is 38.75*4 = 155
Possible arrangements of 155 is
20 + 10 + 30×1.5 + 40×2
A = 20, B = 10
C = 30(Steel or Auto)
D = 40(Cement or IT)
Hence, Statements i and iv are correct.

Logical Reasoning