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This is the fourth set under the CAT 2016 Sprint Preparation Series – LRDI 4. During these last 5 days, we will be covering around 300 questions that we expect to come across in CAT 2016. The answers to LRDI Sprint CAT 2016 – Day 4 will be posted at the end of the day and will include the solution, possible traps and things to keep in mind come similar question types in CAT 2016. You may go through the entire series here: CAT 2016 Sprint Preparation Series by Learningroots

# CAT 2016 Sprint Preparation Series – LRDI 4

## Set 1

There are blue vessels with known volumes v1, v2…, vm, arranged in ascending order of volume, v1 > 0.5 litre, and vm < 1 litre. Each of these is full of water initially. The water from each of these is emptied into a minimum number of empty white vessels, each having volume 1 litre. The water from a blue vessel is not emptied into a white vessel unless the white vessel has enough empty volume to hold all the water of the blue vessel. The number of white vessels required to empty all the blue vessels according to the above rules was n.

1. Among the four values given below, which is the least upper bound on e, where e is the total empty volume in the white vessels at the end of the above process?

a. m*(vm)

b. m*(1 – vm)

c. m*v1

d. m(1 – v1)

2. Let the number of white vessels needed be n1 for the emptying process described above, if the volume of each white vessel is 2 litres. Among the following values, which is the least upper bound on n1?

a. m/4

b. Smallest integer greater than or equal to (n/2)

c. n

d. Greatest integer less than or equal to (n/2)

## Set 2

There are 50 integers a1, a2 … a50, not all of them necessarily different. Let the greatest integer of these 50 integers be referred to as G, and the smallest integer be referred to as L. The integers a1 through a24 form sequence S1, and the rest form sequence S2. Each member of S1 is less than or equal to each member of S2.

3. All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?

a. Every member of S1 is greater than or equal to every member of S2.

b. G is in S1.

c. If all numbers originally in S1 and S2 had the same sign, then after the change of sign, the largest number of S1 and S2 is in S1.

d. None of the above

4. Elements of S1 are in ascending order, and those of S2 are in descending order. a24 and a25 are interchanged. Then which of the following statements is true?

a. S1 continues to be in ascending order.

b. S2 continues to be in descending order.

c. S1 continues to be in ascending order and S2 in descending order.

d. None of the above

5. Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then x cannot be less than

a. 2^10

b. the smallest value of S2

c. the largest value of S2

d. (G – L)

## Set 3

Rajiv reaches city B from city A in 4 hours, driving at speed of 35 kmph for the first two hour and at 45 kmph for the next two hours. Aditi follows the same route, but drives at three different speeds: 30, 40 and 50 kmph, covering an equal distance in each speed segment. The two cars are similar with petrol consumption characteristics (km per litre) shown in the figure below.

6. The quantity of petrol consumed by Aditi for the journey is

a. 8.3 l

b. 8.6 l

c. 8.9 l

d. 9.2 l

7. Zoheb would like to drive Aditi’s car over the same route from A to B and minimize the petrol consumption for the trip. What is the quantity of petrol required by him?

a. 6.67 l

b. 7 l

c. 6.33 l

d. 6.0 l

## Set 4

Recently, Ghosh Babu spent his winter vacation on Kyakya Island. During the vacation, he visited the local casino where he came across a new card game. Two players, using a normal deck of 52 playing cards, play this game. One player is called the ‘dealer’ and the other is called the ‘player’. First, the player picks a card at random from the deck. This is called the base card. The amount in rupees equal to the face value of the base card is called the base amount. The face values of ace, king, queen and jack are ten. For other cards the face value is the number on the card. Once the ‘player’ picks a card from the deck, the ‘dealer’ pays him the base amount. Then the ‘dealer’ picks a card from the deck and this card is called the top card. If the top card is of the same suit as the base card, the ‘player’ pays twice the base amount to the ‘dealer’. If the top card is of the same colour as the base card (but not the same suit), then the ‘player’ pays the base amount to the ‘dealer’. If the top card happens to be of a different colour than the base card, the ‘dealer’ pays the base amount to the ‘player’.

Ghosh Babu played the game four times. First time he picked eight of clubs and the ‘dealer’ picked queen of clubs. Second time, he picked ten of hearts and the ‘dealer’ picked two of spades. Next time, Ghosh Babu picked six of diamonds and the ‘dealer’ picked ace of hearts. Lastly, he picked eight of spades and the ‘dealer’ picked jack of spades. Answer the following questions based on these four games.

8. If Ghosh Babu stopped playing the game when his gain would be maximized, the gain in Rs. would have been

a. 12

b. 20

c. 16

d. 4

9. The initial money Ghosh Babu had (before the beginning of the game sessions) was Rs. X. At no point did he have to borrow any money. What is the minimum possible value of X?

a. 16

b. 8

c. 100

d. 24

10. If the final amount of money that Ghosh Babu had with him was Rs. 100, what was the initial amount he had with him?

a. 120

b. 8

c. 4

d. 96

## Set 5

A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

11. Which of the following is one of the married couples?

a. A & B

b. B & E

c. D & E

d. A & D

12. What is E’s profession?

a. Engineer

b. Lawyer

c. Professor

d. Accountant

13. How many members of the group are males?

a. 2

b. 3

c. 4

d. Cannot be determined

## Set 6

Five women decided to go shopping to M.G. Road, Bangalore. They arrived at the designated meeting place in the following order: 1. Archana, 2. Chellamma, 3. Dhenuka, 4. Helen, and 5. Shahnaz. Each woman spent at least Rs. 1000. Below are some additional facts about how much they spent during their shopping spree.

i. The woman who spent Rs. 2234 arrived before the lady who spent Rs. 1193.

ii. One woman spent Rs. 1340 and she was not Dhenuka.

iii. One woman spent Rs. 1378 more than Chellamma.

iv. One woman spent Rs. 2517 and she was not Archana.

v. Helen spent more than Dhenuka.

vi. Shahnaz spent the largest amount and Chellamma the smallest.

14. What was the amount spent by Helen?

a. Rs. 1193

b. Rs. 1340

c. Rs. 2234

d. Rs. 2517

15. Which of the following amounts was spent by one of them?

a. Rs. 1139

b. Rs. 1378

c. Rs. 2571

d. Rs. 2718

16. The woman who spent Rs. 1193 is

a. Archana

b. Chellamma

c. Dhenuka

d. Helen

Solutions

Set 1

1. This looks to be extremely confusing at first glance and am pretty sure a lot of people will skip this. However, it is as easy as it can get if you are a bit persistent.

Okay so let there be some 10 blue vessels with volume 0.6 liter each. Total volume is 6 liters. Now, we cannot empty more than one blue vessel into a white vessel as the residual capacity is less than the capacity of a blue vessel (this will be true for any volume). So, we will need the same number of white vessels i.e. 10. The amount of empty space in each vessel will be 0.4 and so, total of 4 liters will be empty. This is nothing but the deviation of each blue vessel from 1. The least upper bound is nothing but the maximum value that you can get for e. This will be possible when the empty space for the lesser ranked blue vessels is more. So, the maximum will be when it will be equal to that of v1. So, the correct option is d.

2. Let there be just 1 blue vessel. Ergo, there will be just 1 white vessel. Volume of this vessel will be 2 liters. Let the volume of the blue vessel be 0.6 liters. The value of n1 will be 1. As, m/4 = 0.25 and greatest integer less than or equal to n/2 is 0, options a and d are out. Now, let’s say that there are 3 blue vessels with 0.7, 0.8 and 0.9 liters of solution respectively. It will take us 2 white vessels to empty these solutions. So, m = 3, n1 = 2 and n = 3. So, option b fits the best.

Set 2

3. This is again extremely easy. We can either take values or use a bit of visualization to crack this.

You can take a set where all the elements are equal, say to 1 and check the options. All the 3 options are incorrect and so, correct option is d.

4. Here, we get that a25 is the largest number. So, S1 will continue to be in the ascending order. Now, as all the elements in S2 are greater than those in S1, we get that S2 will not be in descending order. So, option a.

5. Let the elements be 1, 2, 3, … 50. So, we need to add 26, 27, 28 … 49 to make them equal to 50 at least. So, we need to add 49 to each element at least. This is nothing but M – L i.e. 50 – 1 = 49 and so, our answer is option d.

Set 3

6. Total distance covered will be 35*2 + 45*2 = 160 km. So, she covered 160/3 at each of the three speeds. So, consumption will be 160/3 * 1/16 + 160/3 * 1/24 + 160/3 * 1/16 = 8.9 liters.

7. He should go at a speed of 40 km/hr. So, 160*1/24 = 6.67 liters.

Set 4

8. The game would look like this:

If he would have quit after round 2, he would have gained Rs. 12. Option a

9. The maximum negative that he had was Rs. 8 and so, he needed Rs. 8 at the start to make sure that he did not have to borrow any money. Option b.

10. As he effectively had Rs. 4 at the end, he would have had Rs. 96 at the start for the total to be equal to Rs. 100. Option c.

Set 5

11. We get that A-D is a couple with A being the husband and the lawyer and D being a housewife. C-F is another couple with C being the accountant and the husband and F being the professor. B is the other housewife and E is an engineer. So, option d is correct.

12. E is the engineer. Option a.

13. There will be 3 males as there are 3 females – 2 housewives and F who is a professor. Option b.

Set 6

14. There are only 2 possible cases – one where the largest spend is worth Rs. 2517 or where the largest spend is worth 1193 + 1378 or Rs. 2571. The completed table would look like this:

Case 1 is out as Dhenuka did not spend 1340.

So, case 2 is valid and Helen spent 1340. Option b.

15. 1139 was spent by Chellamma. Option a.

16. 1193 was spent by Dhenuka. Option c.

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