# Question Bank - Logical Reasoning - Shashank Prabhu, CAT 100 Percentiler

• Similar to sticks and coins. As the last person to choose wins, we have to make sure that 12 sticks will be removed at the end of each round. So, whoever picks when there are 12x numbers left will lose. So, B will bring it to 76. Similarly, A will bring it to 52 to win the game.
Check this out for a similar concept - http://learningroots.in/cat-and-omet/lrdi/a-game-of-sticks/

• Q19) In order to promote sales, a shopkeeper is preparing a display of chocolates in blue and pink gift packs. Each gift pack will contain exactly three different chocolates from amongst 5 Star, Bournville, Crackle, Dairy Milk, Fruit n Nut, Gems and Silk. No chocolate can be packed in both gift packs. From past experience, the shopkeeper knows that the Bournville and the Dairy Milk must be on display in the blue and pink gift packs respectively. Also, the Gems can neither be displayed in the gift pack with the Dairy Milk nor in the gift pack with the 5 Star. Finally, the Fruit n Nut and the Silk must be on display in the same gift pack.

(1) Which of the following combinations of chocolates can be displayed in the blue gift pack?
a. Bournville, Crackle, Gems
b. Bournville, Crackle, Fruit n Nut
c. Bournville, 5 Star, Silk
d. Bournville, Dairy Milk, Gems

(2) Which of the following combinations of chocolates can be displayed in the pink gift pack?
a. Dairy Milk, 5 Star, Gems
b. Dairy Milk, Fruit n Nut, 5 Star
c. Dairy Milk, 5 Star, Crackle
d. Dairy milk, Gems, Silk

(3) If Silk is displayed in the blue gift pack, which of the following pairs of chocolates must be displayed in the pink gift pack?
a. Fruit n Nut, 5 Star
b. 5 Star, Crackle
c. Crackle, Gems
d. Fruit n Nut, Gems

(4) If Silk is displayed in the pink gift pack, which of the following pairs of chocolates could be displayed in the blue gift pack?
a. Fruit n Nut, 5 Star
b. 5 Star, Gems
c. Fruit n Nut, Crackle
d. Crackle, Gems

• Q20) A round table conference was conducted between India and England cricket players. 8 players were present in the conference, of which 4 were British and the rest were Indians.
We also know that –

1. Sachin Tendulkar and Anil Kumble were short tempered and hence had at least one British player nearby
2. Stuart Broad was feeling like Stuart Binny after being hit for six sixes by Yuvraj Singh, so he was not sitting near Yuvraj Singh
3. Saurav Ganguly never sits between two British players
4. Sachin Tendulkar was facing north
5. All the eight players secretly carried different weapons with them in their pockets. Each of the members carried exactly one of the 2 revolvers, 2 pistols, 1 needle, a pair of scissors and 2 knives
6. Anil Kumble always carried a knife
7. Stuart Broad never used a pistol
8. Yuvraj Singh and Kevin Pietersen never carried a revolver
9. The person carrying the needle sat to the left of James Anderson who carried scissors
10. The 2 members who carried revolvers sat together
11. Sachin Tendulkar never carried a pistol or a revolver and never sat with anyone who carried a pistol or a revolver
12. Two of the members who faced each other carried a revolver and a pistol respectively. The persons who carried knives faced each other
13. Paul Collingwood carried a knife

(1) Name the members who carried revolvers?
a) Saurav Ganguly and James Anderson
b) James Anderson and Kevin Pietersen
c) Saurav Ganguly and Kevin Pietersen
d) Stuart Broad and Saurav Ganguly

(2) Who sat between the members carrying a knife and a pair of scissors?
a) Sachin Tendulkar
b) Yuvraj Singh
c) Kevin Pietersen
d) Cannot be determined

(3) What did Kevin Pietersen carry?
a) Knife
b) Needle
c) Revolver
d) Pistol

(4) According to the given conditions, how many seating arrangements are possible?
a) 2
b) 3
c) 4
d) 1

(5) Who can sit to the right of James Anderson?
a) Yuvraj Singh
b) Kevin Pietersen
d) Paul Collingwood

• There are a few points that you would need to know in this set. And as is the case with CAT, there is bound to be some ambiguity wrt questions. At least you can get it clarified here on the group but in the actual test, it would be a completely different situation. And the moment you are surprised or annoyed, you have basically lost your edge. So, make suitable assumptions in such cases and move ahead.

The few things that I want to emphasize on are: In bullet 1, AK and ST have at least one british player 'nearby'. Which essentially means that they have to have at least one british person as their neighbour. In bullet 3, SG does not sit next to two british players. Which means that he can sit next to either two indians or an indian and a british player. I think if you take care of these statements, it should be easy. The overall level was moderate to tough for this set and this will probably be the 4th or 5th set that you will be solving during the test.

The answers are DDDAB and you will get 2 cases: clockwise starting with ST, PC, SB, SG, YS, AK, KP, JA or ST, AK, SN, SG, YS, PC, KP, JA. The weapons are: PC and AK - knife, JA - scissors, SB and SG - revolver, KP and YS - pistol, ST - needle.

• Q21) Six scientists A, B, C, D, E, and F are to present a paper each at a one-day conference. Three of them will present their papers in the morning session before the lunch break whereas the other three will be presented in the afternoon session. The lectures have to be scheduled in such a way that they comply with the following restrictions: B's should present his paper immediately before C's presentation; their presentations cannot be separated by the lunch break. D must be either be the first or the last scientist to present his paper.

1. In case C is to be the fifth scientist to present his paper, then B must be
(a) first
(b) second
(c) third
(d) fourth
(e) sixth

2. B could be placed for any of the following places in the order of presenters EXCEPT
(a) first
(b) second
(c) third
(d) fourth
(e) fifth

3. In case F is to present his paper immediately after D presents his paper, C could be scheduled for which of the following places in the order of presenters?
(a) first
(b) second
(c) third
(d) fourth
(e) fifth

4. In case F and E are the fifth and sixth presenters respectively then which of the following must be true?
(a) A is first in the order of presenters.
(b) A is third in the order of presenters.
(c) A is fourth in the order of presenters.
(d) B is first in the order of presenters.
(e) C is fourth in the order of presenters.

• Q22) 250 candidates appeared in an examination having two papers - Mathematics and English. 200 candidates secured pass marks in mathematics paper and 175 candidates in English.

(1) The number of candidates who secured passing marks in both the papers
a. Lies between 125 and 175
b. Lies between 50 and 125
c. Lies between 50 and 200
d. Is 125

(2) The number of candidates who secured passing marks in at least one paper lies between
a. 200 and 250
b. 175 and 250
c. 175 and 200
d. 125 and 200

(3) The number of candidates who failed to clear both the papers lies between
a. 0 and 50
b. 50 and 75
c. 0 and 75
d. 50 and 125

• Q23) Ruchika and her sisters Shillu, Kavita and Anupama were tossing a basketball in the living room when the ball slipped from the hands of one of them and broke their Mom’s favourite vase. Uttam, their elder brother, saw the culprit breaking the vase. Their Mom came rushing into the room after hearing the noise. “My favorite vase,” she sobbed as she began picking up the shards. “Who did this?” she asked.

Ruchika said, “Shillu did it.”
Shillu said, “Anupama did it.”
Kavita said, “I did not do it.”
Anupama said, “Shillu lied.”

Their Mom turned to Uttam for the truth. Uttam did not give a straight answer and said, “Only one of the girls is telling the truth the other three are lying.”

Who broke the vase? Assume that Uttam always tells the truth.

[OA: Kavita]

• Q24)

[OA: 1 - 40, 2 - 20, 3 - 20, 4 - no one]

• @shashank_prabhu 1)a 2) d )b

• @shashank_prabhu d) salunkhe

• @shashank_prabhu sir can we have detail solution of this problem?

• @shashank_prabhu not just for this question for all the questions....

• Q25) Following the success of the Triwizard Tournament (which was virtually a Quadrawizard Tournament), HSWAW announced a new tournament called the Hexawizard Tournament. In the Hexawizard Tournament, 6 wizards compete in a “round robin” format: that is, each wizard duels with every other wizard exactly once. A wizard gets 3 points for a win, 1 point for a tie (a draw), and 0 points for a loss. What is the difference between the maximum total points and the minimum total points that can be gained by all wizards (added together) in the Hexawizard Tournament?

[OA: 15]

• Total of 6c2 = 15 matches. If each has a decisive winner, there will be 45 points distributed. If all of them are draws, there will be 2 points per match that will be distributed and so, a total of 30 points at minimum. So, the difference will be 15.

• Q26) On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races but you can see the horses as they cross the finish line. What is the minimum number of races we need to conduct to get the top 3 fastest horses?
a. 6
b. 7
c. 8
d. 10

[OA: Option b]

• 5 winners from the first five races. Another race to determine who is the fastest. Now, positions 2 and 3 need to be figured out. The important thing to not here is that the horses who came 2nd and 3rd need not be the 2nd and 3rd fastest as they have competed with only the winner from the particular group and not the other horses. So, to be sure that a 'deserving' horse has got through to the final, we select those horses who have a chance of being the 2nd and 3rd fastest.

Let the horses be represented by
p1, p2.... p5
p6, p7.... p10
.
.
p21, p22.. p25

Let p1, p6, p11, p16 and p21 win the races. As p16 and p21 have come 4th and 5th in this race, they cannot be among the three fastest horses. So, the entire branch of p16 and p21 is out. Now, p1 is the fastest horse in the first race and so, there is a chance that p2 and p3 are the second and the third fastest overall. Similarly, p6 is the fastest horse in the second race and there is a chance that p7 could be the third fastest (understand that p1 is the fastest and so, the best case scenario for p6 would be if he comes in the 2nd place and the best case scenario for p7 is when he comes in the 3rd place. As the 3 positions would have been taken, p8 cannot feature in the contenders' list). Finally, p11 would be a part of the final race having won his round and being in the 3rd position in the previous race. So, the final race will have p2, p3, p6, p7, p11 in it the top two of whom would win.

Total of 5 + 1 + 1 = 7 races.

• Q27) A closed bag contains 3 green hats and 2 red hats. Amar, Akbar, Anthony all close their eyes, take a hat, put it on, and close the bag. When they open their eyes, Amar looks at Akbar and Anthony, but can't deduce the color of his own hat. Akbar now tries to deduce his own hat's color but can't be certain. What color is Anthony's hat?

[OA: Green]

• Amar does not say anything and so, Akbar knows that either him and Anthony have both green or one green and one red between them. If Anthony had a red, Akbar would have known that he would be wearing green. But because he doesnt say anything, Anthony has to be wearing a green hat.

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