# Numeric Logic

Dear students,
The topic for the day is “Numeric Logic” and currently lots of questions have been asked from this topic in CAT.Today we have picked up a set from CAT 2008 for practice.

Directions for Questions 1 to 5: Answer the following questions based on the information given below:
Abdul, Bikram and Chetan are three professional traders who trade in shares of a company XYZ Ltd. Abdul follows the strategy of buying at the opening of the day at 10 am and selling the whole lot at the close of the day at 3 pm. Bikram follows the strategy of buying at hourly intervals: 10 am, 11am, 12 noon, I pm. And 2 pm, and selling the whole lot at the close of the day, Further, he buys an equal number of shares in each purchase. Chetan follows a similar pattern as Bikram but his strategy is somewhat different. Chetan’s total investment amount is divided equally among his purchases. The profit or loss made by each investor is the difference between the sale value at the close of the day less the investment in purchase. The “return” for each investor is defined as the ratio of the profit or loss to the investment amount expressed as a percentage.

1. On a day of fluctuating market prices, the share price of XYZ Ltd. ends with a gain, i.e, it is higher at the close of the day compared to the opening value. Which trader got the maximum return on that day?
(a) Bikram (b) Chetan (c) Abdul (d) Bikram or Chetan (e) cannot be determined

2. Which one of the following statements is always true?
(a) Abdul will not be one with the minimum return
(b) Return for Chetan will be higher than that of Bikram
(c) Return for Bikram will be higher than that of Chetan
(d) Return for Chetan cannot be higher than that of Abdul
(e) none of the above

3. On a “boom” day the share price of XYZ Ltd. keeps rising throughout the day and dpeaks at the close of the day. Which trader got the minimum return on that day?
(a) Bikram (b) Chetan (c) Abdul (d) Abdul or Chetan (e) cannot be determined

One day, two other traders. Dane and Emily joined Abdul, Bikram and Chetan for trading in the shares of XYZ Ltd. Dane followed a strategy of buying equal numbers of shares at 10 am. 11 am and 12 noon, and selling the same numbers at 1 pm, 2 pm and 3 pm Emily, on the other hand, followed the strategy of buying shares using all her money at 10 am and selling all of them at 12 noon and again buying the shares for all the money at 1 pm and again selling all of them at the close of the day at 3 pm. At the close of the day the following was observed.
i. Abdul lost money in the transactions.
ii. Both Dane and Emily made profits.
iii. There was an increase in share price during the closing hour compared to the price at 2 pm.
iv. Share price at 12 noon was lower than the opening price

4. Share price was at its highest at
(a) 10 am        (b) 11 am            (c) 12 noon           (d) 1 pm            (e) cannot be determined

5. Which of the following is necessarily false?
(a) Share price was at its lowest at 2 pm
(b) Share price was at its lowest at 11 am
(c) Share price at 1 pm was higher than the share price at 2 pm
(d) Share price at 1 pm was higher than the share price at 12 noon
(e) None of the above

Solution –

1. We know that only the closing price is greater than the starting price but we don`t know how it changes in between, so this question can not be answered.

2. Since nothing is mentioned about the starting price and closing price and the prices in between, we cannot assure any of the first four options.

3. Bought the shares at 10 a.m. hence, he will get maximum return. Chetan invested equal amount, he will buy more shares of low price, whereas Bikram purchased equal numbers of shares so Bikram will get minimum return.

4. Same as before the price at 10 a.m. must be the highest.

5. Let the share prices at 10, 11, 12, 1, 2, 3 be a, b, c, d, e, f
Since Abdul lost all money, a>f
From Dan it can be observed, d+e+f>a+b+c
a>c and f>e
from Emily it can be observed, c+f>a+d
Thus we get sequence a>f>e>b and c>d
From these we can say a is the highest
Since e>b option (a) is false
Also c>d therefore option (d) is false.

Set analysis:-
Level of difficulty:- Moderate to difficult
Expected time to solve:- 10 to 12 minutes.

Hope you learnt!
See you with the next one tomorrow!
Happy learning!
Gajendra sir
CAT Coach