Instructions

Read the following scenario and answer the THREE questions that follow.
An investment company, WinLose, recruits employees to trade in the share market. For newcomers, they have a one-year probation period. During this period, the employees are given Rs. 1 lakh per month to invest the way they see fit. They are evaluated at the end of every month, using the following criteria:
1. If the total loss in any span of three consecutive months exceeds Rs. 20,000, their services are terminated at the end of that 3-month period,
2. If the total loss in any span of six consecutive months exceeds Rs. 10,000, their services are terminated at the end of that 6-month period.
Further, at the end of the 12-month probation period, if there are losses on their overall investment, their services are terminated.
Ratan, Shri, Tamal and Upanshu started working for WinLose in January. Ratan was terminated after 4 months, Shri was terminated after 7 months, Tamal was terminated after 10 months, while Upanshu was not terminated even after 12 months. The table below, partially, lists their monthly profits (In Rs. ‘000) over the 12-month period, where x, y and z are masked information.
Note:
1. A negative profit value indicates a loss.
2. The value in any cell is an integer.
Illustration: As Upanshu is continuing after March, that means his total profit during January-March (2z+2z+0) ≥ ─ Rs.20,000. Similarly, as he is continuing after June, his total profit during January-June ≥ ─ Rs.10,000, as well as his total profit during April-June ≥ ─ Rs.20,000.

Question 28

What BEST can be said about the profit generated by Upanshu at the end of his probation period?

Solution

As Ratan was terminated after 4 months, he did not register a loss of more than 20000 at the end of 3 months but registered a loss of more than 20000 in 2nd, 3rd and 4th month. This implies: x - 30 >= -20 and x - 35 < -20 ==> 15 > x >= 10. As x is an integer and x/2 must also be an integer x could be 10, 12 or 14.

For Shri, as he was terminated after 7 months, his loss for the first 6 months did not exceed 10000. It implies that x + 1.5y - 65 >= -10 ==> x+1.5y >= 55.
Also, for the first 6 months, his loss did not exceed 20000 for any group of 3 consecutive months. It implies that: x+y-25 >= -20 ==> x+y >= 5
y - 45 >= -20 ==> y >= 25 and 0.5y - 45 >= -20 ==> y >= 50.
Now, he could be terminated for 2 reasons i.e. 1. his loss for May, June, July exceeded 20000 OR 2. his loss for last 6 months exceeded 10000.
Case 1: 0.5y - 50 < -20 ==> y < 60.
Case 2: 1.5y - 95 < -10 ==> y < 56.667.
As y is also even, possible values for y are 50, 52, 54, 56 and 58.

As Tamal was terminated after 10 months, in ay consecutive period of 3 months for the first 9 months, his loss did not exceed 20000 and for any consecutive period of 6 months, his loss did not exceed 10000.
This implies: 0.5x + y + x >= -20 ==> 1.5x + y >= -20.
There are 2 cases for Tamal also.
Case 1: 5 + 10 - z < -20 ==> z > 35
Case 2: x - 20 + 20 -z < -10 ==> z -10 > x.

Similarly, for Upanshu, the equations will be that the total profits should exceed 0 : 5z - x + y - 81 >= 0
z -48 >= -20 ==> z >= 28 and y - x - 58 >= -10 ==> y -x >= 48. This is only possible when x = 10 and y = 58.

Profits generated by Upanshu at the end of his probation period are 5z + y-x - 81. Now, z >= 28 and y-x = 48 which gives 5z +y-x >= 188 and 5z +y-x -81 >= 107.
Thus, the correct answer is Option A i.e. atleast 107000.