CAT 2025 Lesson : Caselets - Case 3

Read the following and answer the questions that follow

Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs. 100, while at the end of the fifth day it was priced at Rs. 110. At the end of each day, the MCS share price either went up by Rs. 10, or else, it came down by Rs. 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day.

The beginning price of MCS share on a given day was the same as the ending price of the previous day.

Chetan and Michael started with the same number of shares and amount of cash, and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days.

• Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price.
• If on any day, the closing price was above Rs. 110, then Michael sold 10 shares of MCS, while if it was below Rs. 90, he bought 10 shares, all at the closing price.
[CAT 2006]

7) If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

(1) Rs. 90
(2) Rs. 100
(3) Rs. 110
(4) Rs. 120
(5) Rs. 130

8) If Michael ended up with Rs. 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?

(1) Michael had 10 less shares than Chetan.
(2) Michael had 10 more shares than Chetan.
(3) Chetan had 10 more shares than Michael.
(4) Chetan had 20 more shares than Michael.
(5) Both had the same number of shares.

9) If Chetan ended up with Rs. 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?

(1) Rs. 90
(2) Rs. 100
(3) Rs. 110
(4) Rs. 120
(5) Not uniquely determinable

10) What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?

(1) Rs. 3700
(2) Rs. 4000
(3) Rs. 4700
(4) Rs. 5000
(5) Rs. 6000

11) If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3?

(1) Rs. 90
(2) Rs. 100
(3) Rs. 110
(4) Rs. 120
(5) Rs. 130

Solution

The price of the shares begins with Rs. 100 on day 1 and ends with Rs. 110 at the end of day 5. This is possible if the stock price increased on 3 days and decreased on 2 days (UUUDD) in any order.

The number ways it is possible is $\dfrac{5!}{3! \times 2!}$= 10 ways.

During each day, there are 2 possibilities- either prices can go up or come down.



If the price is 80 on day 2, then it will go up on each of the other 3 days to reach 110 on day 5.
If the price is 130 on day 3, then it will go down on each of the other 2 days to reach 110 on day 5.

The below flow chart shows the amount of money received or spent by Chetan with each change of share price The total amount with Chetan at the end of day 5 under each case is Rs. 1300 more than the initial money with him.



The following flow chart shows the amount of money received or spent by Michael with each change of share price.


Chetan/Michael receive money when they sell shares and spend when they purchase shares.

7) As we already know the price will go up on 3 days and come down on 2 days, Chetan will definitely sell 30 shares and buy 20 shares,

We need to check about Michael. If Michael sold the shares on only 1 day, then the share price must be 120 on one day, after which it would fall to 110.



In all of the cases the share price on day 3 is Rs. 110

Answer: (3) Rs. 110

8) The total amount of money with Chetan at the end of day 5 will be 1300 more than the initial amount with him.

There are 3 possible scenario in which Michael receives 1200.

Scenario 1 –> 110, 120, 110, 100 and 110
Scenario 2 –> 110, 100, 110, 120 and 110
Scenario 3 –> 90, 100, 110, 120 and 110

In all these scenarios Michael ends up selling 10 shares. We know that Chetan always ends up selling 10 shares. This means that they will be having equal shares at the end of day 5.

Answer: (5) Both had the same number of shares.

9) We know that the total amount of money with Chetan at the end of day 5 will be 1300 more than the initial amount with him.

Then Michael should not buy or sell any shares. From the above representation in the case solution, the price at the end of day 4 will be Rs. 100.

Answer: (2) Rs. 100

10) We know that the total amount of money with Chetan at the end of day 5 will be 1300 more than the initial amount with him.

Michael can receive a maximum of Rs. 3700.

Therefore the maximum amount of money with both of them at the end of day 5 is 1300 + 3700 = 5000

Answer: (4) Rs. 5000

11) In any case Chetan will end up selling 10 shares. This means that Michael needs to buy 10 shares to have 20 shares more than Chetan. This is possible in only 1 scenario.

Price of Shares – 90, 80, 90, 100 and 110.

The price of the share at the end of day 3 is Rs. 90

Answer: (1) Rs.90

Answer:
7) (3) Rs. 110
8) (5) Both had the same number of shares.
9) (2) Rs. 100
10) (4) RS. 5000
11) (1) Rs. 90