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Logical Reasoning Booster - Set 1 - Edwin Jose, CAT 100 percentiler (DILR)

Edwin Jose aced CAT 2015 with 99.99 percentile and scored a perfect 100 percentile in DILR section. Edwin works with IQuanta as a DILR mentor and runs his own offline classes in Trivandrum.

Below are 2 sets of Logical Reasoning questions with their detailed solutions.

DIRECTIONS : Answer the questions on the basis of the information given below.

Five friends, Amol, Mandar, Piyu, Shashi and Reena attended Sagar’s birthday party, where they partook of the sumptuous snacks and dinner. Each of the five friends gifted Sagar a different article – a fountain pen, a cell phone, a shirt, a jacket and an I-Pod – and Sagar, in return, gifted each of them a different article – a video game, a sweater, a perfume, a calculator and a pair of sunglasses. The following is additional information about the gifts given by the friends and the gifts received from Sagar.

  • Amol gifted the shirt and received the video game in return.
  • Shashi did not gift the I-Pod but received the perfume in return.
  • Mandar did not gift an electronic item and received the calculator in return.
  • The person who gifted the jacket received the sweater in return and Reena received the pair of sunglasses.

1. Who among the following gifted the jacket?

a) Mandar
b) Shashi

c) Reena
d) None of these

2. Which of the following statements is true?

a) Two of the friends who did not gift electronic items, received electronic items in return      
b) Piyu gifted the jacket and Shashi gifted the I-Pod                    
c) Shashi neither gifted nor did he receive an electronic item      
d) The person who gifted the cell phone received the calculator in return

3. Which of the following is the correct combination of friend, article gifted and article received in return?

a) Piyu – Fountain Pen – Sunglasses             
b) Shashi – I-Pod – Perfume                         
c) Reena – I-Pod – Sunglasses
d) None of these

4. Which of the following is false?

a) Only one friend whose name does not start with a vowel, received an electronic item in return
b) The friend whose name appears last in alphabetical order, gifted an electronic item and received a non electronic item in return        
c) In alphabetical order, the friend who gifted the I-Pod appears before at least two other friends
d) The friend whose name in alphabetical order appears in the middle neither gifted nor received an electronic item

Detailed Solution:

From the given information, we know that Amol, Shashi, Mandar and Reena received the video game, perfume, calculator and sunglasses respectively. This means that Piyu received the sweater and we can then conclude that she gifted the jacket.

Since Mandar did not gift an electronic item, he could have gifted the fountain pen, the shirt or the jacket.

But we know that the shirt and the jacket were gifted by Amol and Piyu respectively.

So Mandar must have gifted the fountain pen.

We still need to figure out who gifted the cell phone and the I-Pod. Since we know that Shashi did not gift the I-Pod, Reena must have gifted the I-Pod and Shashi must have gifted the cell phone.

We can now match the friend’s name with the gift given and the gift received as follows:

Amol – Shirt – Video Game; Mandar – Fountain Pen – Calculator; Piyu – Jacket – Sweater; Shashi – Cell Phone – Perfume; Reena – I-Pod – Sunglasses.

1. – (Ans.d) Piyu gifted the jacket.

2. – (Ans.a) Amol and Mandar gifted the shirt and the fountain pen respectively (non-electronic items) and received the video game and the calculator respectively (electronic items).

3. – (Ans.c) Reena gifted the I-Pod and received the pair of sunglasses in return.

4. – (Ans.c) Only Amol and Mandar received electronic items. So option 1 is true. Shashi gifted the cell phone and received the perfume. So option 2 is true.

Reena gifted the I-Pod and in alphabetical order, she would appear second last. So option 3 is not true.

In alphabetical order, Piyu appears in the middle and she gifted the jacket and received the sweater in return. So option 4 is true.

DIRECTIONS : Answer the questions on the basis of 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, 11 am, 12 noon, 1 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 percent- age.

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 peaks 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) 10am
(b) 11am
(c) 12noon
(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

Detailed solution :

1. Since we do not know what are the share prices during different times of the day we cannot come to any conclusion.

2. Abdul buys all his shares at 10 am while the other two purchases once every hour. Since the share prices throughout the day is not specified, we cannot compare the returns of Abdul with the other two. Let us observe the strategies adopted by Bikram and Chetan.

Bikram buys equal number of shares every one hour, irrespective of their prices.
Chetan invests equal amount every one hour, irrespective of the share prices. This means that higher the share price, lesser the number of shares purchased by him. This in turn reduces his return. So whenever the prices are changing, Chetan’s returns will be higher than Bikram’s. In case, the share prices remain the same, the returns of Bikram and Chetan will be equal.

Hence, the correct option is (5) – none of the above.

3. As the share prices are increasing throughout the day, the earlier a person invests, the more profitable it would be. Therefore, Abdul who invested in the beginning only, had reaped in the maximum return. Between Bikram and Chetan, Bikram bought a fixed number of shares every one hour, i.e. towards the end , he must have bought the same number of shares at an even higher rate. Meanwhile, Chetan invested same amount every one hour, i.e. he bought higher number of shares when the prices were low and vice versa. Hence, Chetan’s return will be definitely higher than Bikram’s.

Additional data for questions 4 to 5:

Let the share prices (in Rs.) at 10 am, 11 am, 12 noon, 1 pm, 2 pm and 3 pm be a, b, c, d, e and f respectively. Abdul purchased all his shares at 10 am and sold off the same at 3 pm. It is given that he incurred a loss. If he bought n shares, then his investment = na must be more than his sale price = nf, i.e. na>nf⇒ a > f L (i)

Similarly, Emily bought/sold same number of shares at 10 am/12 noon and 1 am/3 pm and finally made profit. i.e. c+f>a+d L (ii) Similar observation for Dane can be made

i.e. d+e+f>a+b+c   ……… (iii)

It is given that share price at 12 noon is less than the opening price, i.e. a > c

L (iv)
Also, share price at 2 pm is lower than the closing price
i.e.f > e L(v) From (i) and (ii), we get c>d L (vi) From (i), (iii) and (vi), we get e > b Hence,we have a>f>e>b and a>c>d.

4. The share price was the highest at 10 am.

5. Share price was lowest either at 11 am or 1 pm. Therefore, option (a) is false.
Share price at 1 pm was higher than that at 12 noon (equation (vi)).