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Group Question
Answer the following question based on the information given below.
A company is looking for people who can dance in its annual function. The company building has three floors and a total workforce of 600. The table below gives the proportion of males in the company and of employees who can dance. Floors 2 and 3 have the same number of workers, the sum of which is equal to the number of workers on floor 1.
Q. How many male employees does floor 1 have?
Solution: Let the number of floors 2 as well as 3 be x each.
Hence, number of employees on floor 1 is 2x. 2x + x + x = 600 ••• x = 150
Number of employees on floors 1, 2 and 3 is 300, 150 and 150 respectively.
Total number of males = 0.45 x 600 = 270 and total number of females = 600  270 = 330
Total number of males on floor 2 = 0.6 x 150 = 90 Total number of males on floor 3 = 0.5 x 150 = 75 Total number of males on floor 1 = 270  (90 + 75) = 105
Subtracting number of males from total workforce on each floor, number of females on floors 1, 2 and 3 is 195, 60 and 75 respectively.
Since total number of dancers is 30% of the workforce, number of dancers = 180 and number of nondancers = 420.
Number of dancers on floor 1 = 0.3 x 300 = 90 Number of dancers on floor 2 = 0.2 x 150 = 30 Number of dancers on floor 3 = 180  (90 + 30) = 60 Subtracting number of dancers from total workforce on each floor, number of nondancers on floors 1, 2 and 3 is 210, 120 and 90 respectively.
Thus, the entire filled table is as shown below.
Thus, floor 1 has 105 males.
Ans: 105
A company is looking for people who can dance in its annual function. The company building has three floors and a total workforce of 600. The table below gives the proportion of males in the company and of employees who can dance. Floors 2 and 3 have the same number of workers, the sum of which is equal to the number of workers on floor 1.
Q. If 20% of the males on floor 3 are dancers, what is the difference between female dancers and male nondancers on that floor?
Consider the solution to the first question, Since 20% of the 75 males on floor 3 are dancers, there are 15 male dancers and 60 male nondancers.
Since there are 60 dancers in all on floor 3, 60  15 of them i.e. 45 are female dancers. Required difference = 60  45 = 15 Ans: 15
A company is looking for people who can dance in its annual function. The company building has three floors and a total workforce of 600. The table below gives the proportion of males in the company and of employees who can dance. Floors 2 and 3 have the same number of workers, the sum of which is equal to the number of workers on floor 1.
Q. If floors 2 and 3 are combined to form a single group, what is the 3 maximum number of females in that group who cannot dance? It is known that atleast 3/5th of the males in that group are non dancers?
Solution: Consider the solution to the first question.
Total number of males and females in the new group is 165 and 135 respectively.
Total number of dancers and nondancers in this group is 90 and 210 respectively.
Since, atleast 3/5th of males in this group are nondancers, minimum number of male non dancers = 3/5 x 165 = 99. There are at most 210  99 i.e. 111 nondancers left.
Since the number of females is more than this, and the number of female nondancers is to be maximized, all 111 nondancers can be females. ••• Maximum number of females in the group who cannot dance =111
Ans: 111
A company is looking for people who can dance in its annual function. The company building has three floors and a total workforce of 600. The table below gives the proportion of males in the company and of employees who can dance. Floors 2 and 3 have the same number of workers, the sum of which is equal to the number of workers on floor 1.
Q. If each floor has equal number of males who are non dancers, what is the maximum number of females who are non dancers?
Solution: Let the number of male non dancers on each floor be x. ••• The number of female non dancers = 420  3x To maximize the value of (420  3x), the value of x has to be maximized.
Since the second floor has the least number of dancers, the maximum number of female nondancers on this floor will decide the minimum number of male nondancers.
Assume that all 30 dancers on floor 2 are males.
Hence, minimum number of male nondancers = 90  30 = 60
Thus, the maximum number of female nondancers = 420  180 = 240 Ans : 240
Read the following information carefully and answer the questions which follow.
6 people Anil, Biswas, Deepak, Eshan, Gaurav and Harsh participated in the finals of the Tata Crucible quiz competition. At the end of the final round, no two of them had the same points. After the end of the competition, Sumit asked the six people about their standings. Each one of them gave a different statement as given below.
Anil: Biswas was ranked 6th in the quiz
Biswas: Deepak stood 4th in the quiz
Deepak: Harsh secured the fifth position in the quiz
Eshan: Gaurav was the winner of the quiz
Gaurav: Anil secured the third position in the quiz
Harsh: Eshan secured the second position
Sumit is aware of the fact that people who secured first, second and third positions are truth tellers while the people who secured fourth, fifth and sixth positions are liars.
Which of the following statements can be made by Biswas?
We know that the people who secured top 3 ranks are truth tellers while the bottom three ranked people are liars. Let’s start by assuming that Anil is a truthteller. It would mean that Biswas was ranked sixth. Hence Biswas must be a liar. Moreover, Deepak will not have secured 4th rank. But we cannot proceed any further.
Now let us assume that Biswas is a truth teller. It would mean Deepak would have secured the 4th position in the quiz. Hence Deepak must be a liar. Now Deepak says that Harsh secured the fifth position in the quiz. Since Deepak is a liar, hence this must not be true. Moreover, Since Anil said that Biswas was ranked 6th is also false. Hence Anil must also be a liar. Gaurav said that Anil secured 3rd position which means that Anil should be a truth teller. But since Anil is a liar so Gaurav will also be a liar. This would mean that Eshan is also a liar. Thus, we have 4 liars which is a contradiction to what has been given. Hence, our assumption must be wrong. Hence Biswas is a liar.
Now let us assume that Deepak is a truth teller. This would imply that Harsh is a liar which in turn would imply that Eshan did not get second rank. We cannot infer anything else.
Now let us assume that Eshan is a truth teller. This would mean that Gaurav is also a truth teller which in turn would mean that Anil is also a truth teller. Hence all others must be liars. Eshan said that Gaurav is a winner and Gaurav said that Anil stood third. Hence Eshan must be second. But this would make Harsh also a truth teller. Hence it contradicts the given information. So Eshan must be a liar.
Let us assume that Gaurav is a truth teller. It would mean that Anil is a truth teller and Biswas got a sixth rank. But we cannot proceed any further.
Now let us assume that Harsh is a truth teller. This would mean that Eshan is a truth teller. But we just concluded that Eshan is a liar. Hence, Harsh must also be a liar. Thus, Biswas, Eshan and Harsh must be liars and Anil, Deepak and Gaurav will be truth tellers.
Thus, the final standings of the quiz would be
For a particular industry, Supply Efficiency is measured in terms of the actual supply of a product as a percentage of its demand. Similarly, the Market Potential measures the demand for a product compared in percentage terms to the production capacity for that product. The graph below shows the Supply Efficiency and Market Potential for a product in this industry.
Q. If the Production Capacity of the industry remains constant at 1 lakh tons every year, what is the average supply (in tons) for the given period?
Supply for 2012 = 65% of 80% of 100000 = 52000 tons. Supply for 2013 = 70% of 90% of 100000 = 63000 tons. Supply for 2014 = 60% of 80% of 100000 = 48000 tons. Supply for 2015 = 80% of 65% of 100000 = 52000. tons Average = (52000 + 63000 + 48000 + 52000)/4 = 53750 tons Hence, option 1.
For a particular industry, Supply Efficiency is measured in terms of the actual supply of a product as a percentage of its demand. Similarly, the Market Potential measures the demand for a product compared in percentage terms to the production capacity for that product. The graph below shows the Supply Efficiency and Market Potential for a product in this industry.
Q. If the product supply remains unchanged for the given period, what trend does the Production Capacity show?
Solution: Consider the solution to the first question.
Supply/Production Capacity = (Supply Efficiency/100) x (Market Potential/100) Let the supply for each year be 1 unit. Production Capacity = 10000/(Supply Efficiency x Market Potential) Hence, Production Capacity for each year is: 2012: 10000/(65 x 80) = 1.923 2013: 10000/(70 x 90) = 1.587
2014: 10000/(60 x 80) = 2.083 2015: 10000/(65 x 80) = 1.923 Thus, the Production Capacity fluctuates each year.
Hence, option 3.
For a particular industry, Supply Efficiency is measured in terms of the actual supply of a product as a percentage of its demand. Similarly, the Market Potential measures the demand for a product compared in percentage terms to the production capacity for that product. The graph below shows the Supply Efficiency and Market Potential for a product in this industry.
Q. Which of these years shows the highest increase in the difference between the Production Capacity and Supply over the previous year, if the Demand for the product is 80000 tons for each year?
Solution: 2012: Supply = 65% of Demand = 0.65 x 80000 = 52000. Demand = 80% of Production i.e. Production = 80000/0.8 = 100000. Difference between Production and Supply = 100000  52000 = 48000 tons
2013: Supply = 70% of Demand = 0.7 x 80000 = 56000. Demand = 90% of Production i.e. Production = 80000/0.9 = 88888.88. Difference between Production and Supply = 88888.88  56000 = 32888.88 tons 2014: Supply = 60% of Demand = 0.6 x 80000 = 48000. Demand = 80% of Production i.e. Production = 80000/0.8 = 100000. Difference between Production and Supply = 100000  48000 = 52000 2015: Supply = 80% of Demand = 0.8 x 80000 = 64000
Demand = 65% of Production i.e. Production = 80000/0.65 = 123076.92 Difference between Production and Supply = 123076.92  64000 = 59076.92 tons
2013 can be ignored as the difference decreases rather than increases. Increase in 2014 = 52000  32888.88 = 19111.12 tons Increase in 2015 = 59076.92  52000 = 7076.92 tons Thus, the highest increase is in 2014.
Hence, option 3.
Group Question
Answer the following question based on the information given below.
A district has eight villages. A population census was conducted in these villages
The sex ratio is defined as the number of females per 1000 males e.g. 1250 males and 1180 females in a village, sex ratio = (1180/1250) x 1000 = 944.
Q. What is the overall sex ratio for all the eight villages taken altogether (Rounded off to the nearest multiple of 10)?
Consider village A.
A sex ratio of 880 implies that for every 1000 males, there are 880 females. In such a case, total population of the village = 1000 + 880 = 1880
Thus, a village with population 1880 will have 880 females.
Hence, for the same sex ratio, village A with population 1645 will have 1645 x (880/1880) = 770 females Hence, number of males in village A = 1645  770 = 875 Similarly, the number of males and females in each village is as tabulated below:
Overall sex ratio = (6010/6615) x 1000 = 908.54 After rounding to the closest multiple of 10, the closest value is 910. Hence, option 3.
A district has eight villages. A population census was conducted in these villages
The sex ratio is defined as the number of females per 1000 males e.g. 1250 males and 1180 females in a village, sex ratio = (1180/1250) x 1000 = 944.
Q. Which village has the highest number of females?
Solution: Marks Consider the solution to the first question.Village G has the highest number of females i.e. 844 Hence, option 4.
A district has eight villages. A population census was conducted in these villages
The sex ratio is defined as the number of females per 1000 males e.g. 1250 males and 1180 females in a village, sex ratio = (1180/1250) x 1000 = 944.
Q. Which of these is the correct sequence of states in ascending order of male population?
Solution: Consider the solution to the first question.
Among the given sequences, only E (800) < B (840) < A (875) < H (900) is in the correct ascending order.
Option 2 is incorrect as H > D Option 3 is incorrect a sC > B > E > F Option 4 is incorrect as C > A Hence, option 1.
A district has eight villages. A population census was conducted in these villages
The sex ratio is defined as the number of females per 1000 males e.g. 1250 males and 1180 females in a village, sex ratio = (1180/1250) x 1000 = 944.
Q. In how many villages is the female population between 700 and 800?
Solution: Marks Consider the solution to the first question.Only villages A and H have female population between 700 and 800.Hence, option 2.
Group Question
Answer the following question based on the information given below.
There are three trade unions  Viram, Vishram and Vikram  and three thousand six hundred workers in a company. Becoming a member of a trade union is optional. Also, a worker can be a member of more than one of the given unions. There are 500 workers who are members of atleast two trade unions while Vishram has 1400 members. There are 100 workers who are members of only Viram and Vikram, whereas 200 Vishram members are also Vikram members only. 500 workers are members of only Vikram where as 20% of Viram members are members of exactly one more union. Oneeighth of all the workers in the company are members of exactly two unions.
Q. How many workers are members of all the three unions?
Solution: Represent the three trade unions as shown below.
Let h = number of workers who do not opt for any trade union. a + b + c + d + e + f + g + h = 3600 ... (1) Oneighth of all the workers are members of exactly two unions. : . d + e + f = 3600/8 = 450 ... (2) Also, 500 workers are members of atleast two trade unions. so d + e + f + g = 500 ... (3), g = 50
100 workers are members of only Viram and Vikram i.e. e = 100
500 workers are members o f only Vikram i.e. b = 500.
200 Vishram members are also Vikram members only. The part common to Vishram and Vikram only is f . i . e f. d = 450 (100 + 200) i.e. d. There are 1400 members in Vishram. c + d + f + g = 140. So c = 1400  (150 + 200 + 50) i.e. c = 1000
20% of Viram members are members of exactly one more union. Total members in Viram = a + d + e + g = (d + e) x 5 = (150 + 100) x 5 = 1250
a = 1250  (250 + 50) = 950 h = 3600  (1250 + 500 + 200 + 1000) = 650 Thus, number of workers who are members of all three unions = 50
Ans: 50
There are three trade unions  Viram, Vishram and Vikram  and three thousand six hundred workers in a company. Becoming a member of a trade union is optional. Also, a worker can be a member of more than one of the given unions. There are 500 workers who are members of atleast two trade unions while Vishram has 1400 members. There are 100 workers who are members of only Viram and Vikram, whereas 200 Vishram members are also Vikram members only. 500 workers are members of only Vikram where as 20% of Viram members are members of exactly one more union. Oneeighth of all the workers in the company are members of exactly two unions.
Q. How many workers are members of only Viram or only Vikram?
Consider the solution to the first question.
Number of workers who are members of only Viram or only Vikram = 950 + 500 = 1450
Ans: 1450
There are three trade unions  Viram, Vishram and Vikram  and three thousand six hundred workers in a company. Becoming a member of a trade union is optional. Also, a worker can be a member of more than one of the given unions. There are 500 workers who are members of atleast two trade unions while Vishram has 1400 members. There are 100 workers who are members of only Viram and Vikram, whereas 200 Vishram members are also Vikram members only. 500 workers are members of only Vikram where as 20% of Viram members are members of exactly one more union. Oneeighth of all the workers in the company are members of exactly two unions.
Q. How many workers do not opt for any trade union?
Solution: 15. Consider the solution to the first question, 3
Marks Number of workers who do not opt for any trade union = 650
Ans: 650
There are three trade unions  Viram, Vishram and Vikram  and three thousand six hundred workers in a company. Becoming a member of a trade union is optional. Also, a worker can be a member of more than one of the given unions. There are 500 workers who are members of atleast two trade unions while Vishram has 1400 members. There are 100 workers who are members of only Viram and Vikram, whereas 200 Vishram members are also Vikram members only. 500 workers are members of only Vikram where as 20% of Viram members are members of exactly one more union. Oneeighth of all the workers in the company are members of exactly two unions.
Q. If 10 workers give up their Vikram membership and take up Vishram memebership, how many workers will now have membership of all the three unions?
Solution: Consider the solution to the first question. The 10 members are taking up Vishram membership. Hence, they could not originally have had membership of all three unions.
Similarly, they are now giving up Vikram membership. Hence, they still do not have membership of all three unions.
Hence, number of members of all three unions remains constant at 50.
Ans: 50
Group Question
Answer the following question based on the information given below.
Every student in a particular class has to select five subjects from Philosophy, Sociology, History, Economics, Anthropology, French, German, Russian and Ecology, subject to the following conditions.
1. Exactly one language out of French, German and Russian can be chosen.
2. Exactly one out of Philosophy and Sociology must be chosen.
3. If Economics is chosen, then Ecology must be chosen.
4. Sociology and Anthropology cannot be chosen together.
Q. If a student selects Sociology and French as two of his subjects, which of these combinations must he definitely choose?
Solution: The student has selected Sociology and French. Three more subjects are to be chosen. Now, the available subjects are Economics, Ecology, History and Anthropology.
Since Sociology and Anthropology cannot be selected together, Anthropology is rejected.
Hence, the three remaining subjects i.e. Economics, Ecology and History have to be mandatorily selected.
Hence, option 3.
Every student in a particular class has to select five subjects from Philosophy, Sociology, History, Economics, Anthropology, French, German, Russian and Ecology, subject to the following conditions.
1. Exactly one language out of French, German and Russian can be chosen.
2. Exactly one out of Philosophy and Sociology must be chosen.
3. If Economics is chosen, then Ecology must be chosen.
4. Sociology and Anthropology cannot be chosen together.
Q. If Prof. Dave teaches History and German, what percentage of possible course combinations are not taught by Prof. Dave?
Solution: First identify the total number of course combinations possible.
Exactly one out of the three given languages can be chosen.
This implies that if a language is selected, it has to be one of French,
German and Russian. However, it also implies that no language is chosen at all.
Case 1: No language is chosen.
Now, one of Philosophy and Sociology can be chosen in 2C_{1} ways.
If Sociology is selected, Anthropology cannot be selected.
Hence, only three subjects remain i.e. History, Economics and Ecology.
Since a combination of five subjects cannot be made in this case, sociology cannot be selected.
Hence, Philosophy is definitely selected.
Now, a valid combination can be made as Philosophy, Anthropology, History, Economics and Ecology.
Case 2: Exactly one language is chosen.
One language out of three can be chosen in 3C_{1} = ways Now, four subjects are left.
As seen above, when Sociology is selected, a combination of four subjects is possible i.e. Sociology, History, Economics and Ecology.
Hence, there are three valid combinations here (French/German/Russian), Sociology, History, Economics and Ecology.
When Philosophy is selected, there are three subjects left to be selected and four options available.
Note that if Economics is chosen, then Ecology must be chosen.
Hence, consider the case where Economics is chosen.
Hence, the number of valid combinations here is  (French/German/Russian), Philosophy, Economics, Ecology, (History/Anthropology) Exam Reports
i.e 3 x 2 = 6 combinations If Economics is not chosen, Ecology can still be chosen. Here, History and Anthropology both get selected.
Hence, the number of valid combinations is  (French/German/Russian), Philosophy, Ecology, History, Anthropology i.e. 3 combinations If neither Economics nor Ecology is chosen, there are only two subjects (History and Anthropology) left for three slots.
Hence, no valid combination is possible.
Hence, total possible combinations = 1 + 3 + 6 + 3 = 13 For a course combination to be not taught by Prof. Dave, it has to have neither History nor German.
There are only two such combinations: French, Philosophy, Economics, Ecology, Anthropology
and
Russian, Philosophy, Economics, Ecology, Anthropology ••• Required percentage = (2/13) x 100 = 15.38%
Hence, option 4.
Every student in a particular class has to select five subjects from Philosophy, Sociology, History, Economics, Anthropology, French, German, Russian and Ecology, subject to the following conditions.
1. Exactly one language out of French, German and Russian can be chosen.
2. Exactly one out of Philosophy and Sociology must be chosen.
3. If Economics is chosen, then Ecology must be chosen.
4. Sociology and Anthropology cannot be chosen together.
Q. Which of the following statements must be true?
Solution: Consider the solution to the previous question. It lists all the possible course combinations.
First start with the options where the chosen subjects are given.
Option 1: Let Russian and Philosophy be chosen, Here, the other three subjects can be Economics, Ecology, (History/Anthropology) or Ecology, History, Anthropology.
Hence, Anthropology may or may not be chosen.
Hence, the statement in option 1 is not definitely true.
Option 3: Let Russian and Sociology be chosen.
Here, the other three subjects have to be History, Economics and Ecology.
Hence, the statement in option 3 is definitely false.
Option 2: Philosophy, Russian and French are not chosen.
Here, the only possible combination is German, Sociology, History, Economics and Ecology.
Hence, Anthropology cannot be chosen but German must be chosen. Hence, the statement in option 2 is definitely true. Hence, option 2.
Every student in a particular class has to select five subjects from Philosophy, Sociology, History, Economics, Anthropology, French, German, Russian and Ecology, subject to the following conditions.
1. Exactly one language out of French, German and Russian can be chosen.
2. Exactly one out of Philosophy and Sociology must be chosen.
3. If Economics is chosen, then Ecology must be chosen.
4. Sociology and Anthropology cannot be chosen together.
Q. How many of the following statement(s) is/are false?
I. A course combination cannot be formed if no language is chosen.
II. If German and Philosophy are selected, History has to be selected.
III. Economics and Ecology (if selected), are always selected together.
Solution: Consider the solution to the earlier questions.
Statement I: It has been proved that a course combination can be formed without languages. i.e. Philosophy, Anthropology, History, Economics, Ecology Hence, statement I is false.
Statement II: It can be shown that a course combination having German and Philosophy may not have History. i.e. German, Philosophy, Economics, Ecology, Anthropology.
Hence, statement II is false.
Statement III: On of the original conditions is: “If Economics is chosen, Ecology is also chosen”. It also means that if Economics is not chosen, Ecology may or may not be chosen.
A valid combination without Economics but having Ecology is French, Philosophy, Ecology, History, Anthroplogy Hence, statement III is false.
Hence, all the three given statements are false.
Hence, option 2.
Group Question
Answer the following question based on the information given below.
There is a shooting game played by 5 people  Harsh, Amit, Nitin, Deepak and Yash. The rules of the game are:
• There is a target which can be kept at 10, 20, 40, 80 or 100 m.
• There are 10 shots taken by each of the players and they are free to keep their target wherever they wish to.
• If the target is shot, points equal to the distance at which it was kept are scored else no point is awarded, e.g. if the target is kept at 80 and the player shoots the target, 80 points are scored.
The table below shows the scores of the players after the entire game is over. However, some data is intentionally missing.
The following information is also known:
• All five players scored unique scores.
• 50% of the shots that hit the target were 40 pointers.
• Amit shot the target atleast thrice.
• Deepak never shifted his target.
• Nitin scored each possible score at least once and scored between 320 and 360 (both excluded).
• The 100 pointer was shot by any player only once.
• Yash did not miss any shot and won the game.
• 36 shots hit at the target at all.
Q. What is the sum of the minimum and maximum possible score of Yash?
Solution: Since each player takes 10 shots, total shots = 5 x 10 = 50 Of these, 36 hits the target. Hence, 14 did not hit the target and were zero pointers.
Also, number of 40 pointer shots is half of all the shots that hit the target i.e. 36/2= 18.
Consider Harsh’s score using only the given data of 8 shots. i.e. 10(1) + 20(2) + 40(4) + 80(1) = 10 + 40 + 160 + 80 = 290 Since this is the same as his final score, his remaining 2 shots were 0 pointers and he did not hit any 100 pointer shot.
Deepak never shifted his target and scored 280 in all. Hence, he scored the same in each shot that he hit i.e. his score per shot has to be a factor of 280
This is possible for a score per shot of 10 (28 shots), 20 (14 shots) and 40 (7 shots). Since total shots per player is 10, Deepak hit 7 40pointer shots and 3 0pointer shots. He did not hit any other shot at all.
Observe that there are only two 100pointer shots hit such that one player could have hit exactly one such shot. Three players  Amit, Nitin and Yash could have done this.
From the original table, Amit hit atleast three shots but he has not hit any 10 or 20 pointer. If he hit the 100 pointer, his total score would go above 200 (which is not possible).
Hence, Amit did not hit the 100 pointer while Nitin and Yash hit one 100 pointer each.
Finally, since Yash did not miss any shot, Yash hit no 0 pointers.
Thus, the table at this stage becomes:
Nitin scored every possible shot atleast once and scored between 320 and 360. Hence, his possible score is 330, 340 or 350 Let him score a, b and c 20, 80 and 0 pointers respectively. a + b + c = 6. Also, total score = 10(1) + 20(a) + 40(2) + 80(b) + 100(1) = 20a + 80b + 190
When total = 350, 20a + 80b + 190 = 350 20a + 80b =160. a + 4b = 8.
Similarly, when total = 340, a + 4b = 7.5 (which is not possible as a and b are natural numbers). Hence, total score of Nitin cannot be 340.
When total = 330, a + 4b = 7 Case 1: a + 4b = 8 This is solved for a = 4 and b= 1. Hence, c = 1 Using the value o f c, number o f 0 pointers for Amit = 14  ( 2 + 1 + 3 + 0) = 8
Thus, the table becomes:
Now, let the number of 40 and 80pointers hit by Amit be p and q respectively. p + q = 10  (8 + 0 + 0 + 0) = 2 Also, 40/7 + 80# = 200 i.e. p + 2q = 5
These two equations, when solved do not give a natural number value of p.
Hence, this entire case is invalid, i.e. the score of Nitin cannot be 350. Hence, his score is 330. i.e. a + 4b = 7. This is solved for a = 3 and b= 1. Hence, c = 2 Using the value o f c, number o f 0 pointers for Amit = 14  ( 2 + 2 + 3 + 0) = 7. Thus, the table becomes:
Here, p + q = 10  ( 7 + 0 + 0 + 0) = 3 Also, p + 2q = 5. On solving, q = 2 and p = 1 Hence, number of 40pointers scored by Yash = 18  ( 4 + 2 + 7 + l ) = 4 Thus, the table becomes:
Let the number of 20pointers and 80pointers hit by Yash be x andy respectively.
Total score of Yash = 10(3) + 20(x) + 40(4) + 80(y) + 100(1) = 20x + 80y + 290. Also, x + y = 10  (0 + 3 + 4+ 1) = 2. For maximum score for Yash, x = 0 andy = 2. Maximum score = 20(0) + 80(2) + 290 = 450 For minimum score for Yash, x = 1 andy = 1
Minimum score = 20(1) + 80(1) + 290 = 390 Sum of maximum and minimum score = 450 + 390 = 840
Ans: 840
Note: When x = 2 and y = 0, total score = 20(2) + 80(0) + 290 = 330. Since this is the same as the total score of Nitin, this case is not possible.
There is a shooting game played by 5 people  Harsh, Amit, Nitin, Deepak and Yash. The rules of the game are:
• There is a target which can be kept at 10, 20, 40, 80 or 100 m.
• There are 10 shots taken by each of the players and they are free to keep their target wherever they wish to.
• If the target is shot, points equal to the distance at which it was kept are scored else no point is awarded, e.g. if the target is kept at 80 and the player shoots the target, 80 points are scored.
The table below shows the scores of the players after the entire game is over. However, some data is intentionally missing.
The following information is also known:
• All five players scored unique scores.
• 50% of the shots that hit the target were 40 pointers.
• Amit shot the target atleast thrice.
• Deepak never shifted his target.
• Nitin scored each possible score at least once and scored between 320 and 360 (both excluded).
• The 100 pointer was shot by any player only once.
• Yash did not miss any shot and won the game.
• 36 shots hit at the target at all.
Q. How many shots of Amit scored 40 points?
Solution: Consider the solution to the first question.
Only one shot hit by Amit was a 40pointer.
Ans: 1
There is a shooting game played by 5 people  Harsh, Amit, Nitin, Deepak and Yash. The rules of the game are:
• There is a target which can be kept at 10, 20, 40, 80 or 100 m.
• There are 10 shots taken by each of the players and they are free to keep their target wherever they wish to.
• If the target is shot, points equal to the distance at which it was kept are scored else no point is awarded, e.g. if the target is kept at 80 and the player shoots the target, 80 points are scored.
The table below shows the scores of the players after the entire game is over. However, some data is intentionally missing.
The following information is also known:
• All five players scored unique scores.
• 50% of the shots that hit the target were 40 pointers.
• Amit shot the target atleast thrice.
• Deepak never shifted his target.
• Nitin scored each possible score at least once and scored between 320 and 360 (both excluded).
• The 100 pointer was shot by any player only once.
• Yash did not miss any shot and won the game.
• 36 shots hit at the target at all.
Q. If the total score of all five players taken together is 1550, what can be the maximum number of shots that were hit to score 20 points each?
Solution: Consider the solution to the first question.
Total number of 20pointer shots = 2 + 0 + 3 + 0 + x = x + 5 Total score = 290 + 200 + 330 + 280 + n = 1550, where n is the total score of Yash. Total score of Yash = 450 In this case, number of 20pointers hit by Yash = 0 ••• Number of 20pointer hsots, = 0 + 5 = 5 Ans: 5
There is a shooting game played by 5 people  Harsh, Amit, Nitin, Deepak and Yash. The rules of the game are:
• There is a target which can be kept at 10, 20, 40, 80 or 100 m.
• There are 10 shots taken by each of the players and they are free to keep their target wherever they wish to.
• If the target is shot, points equal to the distance at which it was kept are scored else no point is awarded, e.g. if the target is kept at 80 and the player shoots the target, 80 points are scored.
The table below shows the scores of the players after the entire game is over. However, some data is intentionally missing.
The following information is also known:
• All five players scored unique scores.
• 50% of the shots that hit the target were 40 pointers.
• Amit shot the target atleast thrice.
• Deepak never shifted his target.
• Nitin scored each possible score at least once and scored between 320 and 360 (both excluded).
• The 100 pointer was shot by any player only once.
• Yash did not miss any shot and won the game.
• 36 shots hit at the target at all.
Q. Taken together, how many 40 or 80 pointer shots did Nitin and Amit hit?
Solution: Consider the solution to the first question.
Number of 40 and 80 pointer shots hit by Nitin is 2 and 1 respectively.
Number of 40 and 80 pointer shots hit by Amit is 1 and 2 respectively. Required total = 2 + l + l + 2 = 6 Ans: 6
Group Question
Answer the following question based on the information given below.
i. Ten chairs numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are situated adjacent to one another in two different rows. Both rows contain five chairs each facing each other.
ii. Ten Indian cricketers are sitting on these chairs. They are Shikar, Rohit, Virat, Yuvraj, Suresh, Mahendra, Ravichandran, Hardik, Jasprit and Ashish, not necessarily in the same order.
iii. Odd numbered cannot be opposite or adjacent to odd numbered chairs. The same applies to even numbered chairs as well.
iv. Chair 8 is occupied by Rohit and his chair is to the extreme left of one row.
v. Hardik sits on chair 5.
vi. Chairs 4 and 6 are not in the same row as chair 8 and chair 2 is not in the middle of its row.
vii. Virat sits on an odd numbered chair in the same row as Rohit but they do not sit adjacent to each other.
viii. Suresh and Mahendra’s chairs are adjacent to chair 6 but Mahendra’s chair is not adjacent to chair 4.
ix. Shikar’s and Ashish’s chairs are in the same row.
x. Yuvraj's chair is even numbered and is diagonally opposite to chair 1, such that Yuvraj is at the farthest possible distance from chair 1.
xi. Chair 6 is second from the left.
xii. No two consecutive chairs are consecutively numbered and Ravichandran’s chair is neither opposite to nor adjacent to Suresh’s chair.
Q. On which chair is Virat sitting?
Solution: Since an odd numbered chair is not opposite or adjacent to an odd numbered chair (and the same for even numbered chairs), the arrangement of chairs is:
Both arrangements will be mirror images of each other. Hence, consider any one (also because none of the information pertains to drection faced by any of the people). Say, the arrangement considered is:
Rohit is on chair 8 and at the extreme left of a row. Also, chair 6 is second from the left in its row.
Hence, the arrangement is:
Since chairs 4 and 6 are not in the same row as chair 8 (Rohit’s chair), Rohit’s row has chairs 2 and 10, while chair 4 is in the other row. Also, chair 2 is not in the middle of the row.
Hence, the arrangement is:
Yuvraj sits on an even numbered chair and is diagonally opposite to chair 1, at the farthest possible distance from chair 1.
Hence, Yuvraj has to be at the other comer of Rohit’s row (i.e. on chair 2) and chair 1 is opposite Rohit.
Also, Virat is on an odd numbered chair in the same row as Rohit but not adjacent to Rohit.
Finally, Suresh and Mahendra are adjacent to chair 6 but Mahendra is not adjacent to chair 4. Hence, the arrangement becomes:
Since no two adjacent chairs are consecutively numbered, the numbering of the odd chairs becomes:
Since Hardik is on chair 5, Hardik is next to Rohit.
Since Ashish and Shikhar are in the same row, they are on chairs 6 and 4, in no specific order.
Since Ravichandran is not opposite Suresh, he is on chair 1.
Hence, the only person remaining i.e. Jasprit is on chair 10.
Thus, the final arrangement is:
Thus, Virat is on chair 7.
Hence, option 1.
i. Ten chairs numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are situated adjacent to one another in two different rows. Both rows contain five chairs each facing each other.
ii. Ten Indian cricketers are sitting on these chairs. They are Shikar, Rohit, Virat, Yuvraj, Suresh, Mahendra, Ravichandran, Hardik, Jasprit and Ashish, not necessarily in the same order.
iii. Odd numbered cannot be opposite or adjacent to odd numbered chairs. The same applies to even numbered chairs as well.
iv. Chair 8 is occupied by Rohit and his chair is to the extreme left of one row.
v. Hardik sits on chair 5.
vi. Chairs 4 and 6 are not in the same row as chair 8 and chair 2 is not in the middle of its row.
vii. Virat sits on an odd numbered chair in the same row as Rohit but they do not sit adjacent to each other.
viii. Suresh and Mahendra’s chairs are adjacent to chair 6 but Mahendra’s chair is not adjacent to chair 4.
ix. Shikar’s and Ashish’s chairs are in the same row.
x. Yuvraj's chair is even numbered and is diagonally opposite to chair 1, such that Yuvraj is at the farthest possible distance from chair 1.
xi. Chair 6 is second from the left.
xii. No two consecutive chairs are consecutively numbered and Ravichandran’s chair is neither opposite to nor adjacent to Suresh’s chair.
Q. What is the sum of the chair numbers of Hardik’s row?
Solution: Consider the solution to the first question.
The chairs in Hardik’s row are 2, 5, 7, 8 and 10. Required sum = 2 + 5 + 7 + 8 + 10 = 32
Hence, option 4.
i. Ten chairs numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are situated adjacent to one another in two different rows. Both rows contain five chairs each facing each other.
ii. Ten Indian cricketers are sitting on these chairs. They are Shikar, Rohit, Virat, Yuvraj, Suresh, Mahendra, Ravichandran, Hardik, Jasprit and Ashish, not necessarily in the same order.
iii. Odd numbered cannot be opposite or adjacent to odd numbered chairs. The same applies to even numbered chairs as well.
iv. Chair 8 is occupied by Rohit and his chair is to the extreme left of one row.
v. Hardik sits on chair 5.
vi. Chairs 4 and 6 are not in the same row as chair 8 and chair 2 is not in the middle of its row.
vii. Virat sits on an odd numbered chair in the same row as Rohit but they do not sit adjacent to each other.
viii. Suresh and Mahendra’s chairs are adjacent to chair 6 but Mahendra’s chair is not adjacent to chair 4.
ix. Shikar’s and Ashish’s chairs are in the same row.
x. Yuvraj's chair is even numbered and is diagonally opposite to chair 1, such that Yuvraj is at the farthest possible distance from chair 1.
xi. Chair 6 is second from the left.
xii. No two consecutive chairs are consecutively numbered and Ravichandran’s chair is neither opposite to nor adjacent to Suresh’s chair.
Q. Which of these represents the correct chair numbers in one of the rows?
Solution: Consider the solution to the first question.
The chair numbers in one row are 1, 3, 4, 6, 9 and in the other are 2, 5, 7, 8, 10.
Hence, option 3.
i. Ten chairs numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are situated adjacent to one another in two different rows. Both rows contain five chairs each facing each other.
ii. Ten Indian cricketers are sitting on these chairs. They are Shikar, Rohit, Virat, Yuvraj, Suresh, Mahendra, Ravichandran, Hardik, Jasprit and Ashish, not necessarily in the same order.
iii. Odd numbered cannot be opposite or adjacent to odd numbered chairs. The same applies to even numbered chairs as well.
iv. Chair 8 is occupied by Rohit and his chair is to the extreme left of one row.
v. Hardik sits on chair 5.
vi. Chairs 4 and 6 are not in the same row as chair 8 and chair 2 is not in the middle of its row.
vii. Virat sits on an odd numbered chair in the same row as Rohit but they do not sit adjacent to each other.
viii. Suresh and Mahendra’s chairs are adjacent to chair 6 but Mahendra’s chair is not adjacent to chair 4.
ix. Shikar’s and Ashish’s chairs are in the same row.
x. Yuvraj's chair is even numbered and is diagonally opposite to chair 1, such that Yuvraj is at the farthest possible distance from chair 1.
xi. Chair 6 is second from the left.
xii. No two consecutive chairs are consecutively numbered and Ravichandran’s chair is neither opposite to nor adjacent to Suresh’s chair.
Q. Which of the following statements is definitely true?
Solution: Consider the solution to the first question.
The statements in options 3 and 4 are definitely false while the statement in option 1 may or may not be true.
The statement in option 2 is definitely true.
Hence, option 2.
Group Question
Answer the following question based on the information given below.
Twelve people  Manish, Urvashi, Lakshya, Tripti, Ishant, Paridhi, Roger, Ojasvee, Nizam, Gurpreet, Emily and Dhanush  work in three different cities  Bangalore, Pune and Gurgaon  with exactly four of them working in each city. They work as either Business Analysts, Developers or Software Engineers, with an equal number of professionals of each type. Each city has atleast one professional of each type.
1. Manish is not a Business Analyst and does not work in Bangalore.
2. Urvashi is a Developer and Paridhi is a Software Engineer.
3. Lakshya works in the same city as Paridhi.
4. Emily is a Developer who works in the same city as Tripti.
5. Ojasvee is a Business Analyst who works in Bangalore.
6. Gurpreet is a Developer and Nizam is a Business Analyst; and both of them work in Gurgaon.
7. Dhanush is a Software Engineer who works in Pune.
8. Roger works in Bangalore and Paridhi works in Pune.
9. The number of Developers working in Bangalore is two.
Q. Who among the following is a Business Analyst working in Pune?
Solution: There are four people working in each city and there are four people each working as Developers, Business Analysts and Software Developers.
Also, each city has atleast one professional of each type i.e. each city has professionals in the ratio 2 : 1 : 1 .
From the direct data given, the table can be initially filled as shown below:
Since Bangalore has two Developers, Bangalore = 2 Developers + 1 Software Engineer + 1 Business Analyst From the table above, Pune has two Software Engineers.
Hence, Pune = 1 Developer + 2 Software Engineers + 1 Business Analyst
Hence, Gurgaon = 1 Developer + 1 Software Engineer + 2 Business Analysts
Emily and Tripti are from the same city. Since three of the four people from Pune are identified, EmilyTripti cannot be from Pune (as that would take the count of Pune to 5).
Also, since the only developer from Gurgaon is identified (Gurpreet), Emily cannot be from Gurgaon.
Hence, Emily and Tripti are from Bangalore. This identifies all the people from Banglaore.
By the same logic as above, Urvashi cannot be from Gurgaon. Hence, Urvashi is from Pune. This identifies all the people from Pune as well.
Hence, the only remaining people (Manish and Ishant) have to be from Gurgaon.
In Pune, Paridhi = Dhanush = Software Engineer, Urvashi = Developer. Hence, Lakshya = Business Analyst Since Manish is not a Business Analyst and Gurpreet is the only developer from Gurgaon, Manish is a Software Engineer.
Hence, Ishant is the other Business Analyst from Gurgaon.
Hence, Tripti and Roger are a Developer and Software Engineer from Bangalore, in no specific order.
Thus, the final arrangement is:
Thus, among the options, Lakshya is the Business Analyst workng in Pune.
Hence, option 1.
Twelve people  Manish, Urvashi, Lakshya, Tripti, Ishant, Paridhi, Roger, Ojasvee, Nizam, Gurpreet, Emily and Dhanush  work in three different cities  Bangalore, Pune and Gurgaon  with exactly four of them working in each city. They work as either Business Analysts, Developers or Software Engineers, with an equal number of professionals of each type. Each city has atleast one professional of each type.
1. Manish is not a Business Analyst and does not work in Bangalore.
2. Urvashi is a Developer and Paridhi is a Software Engineer.
3. Lakshya works in the same city as Paridhi.
4. Emily is a Developer who works in the same city as Tripti.
5. Ojasvee is a Business Analyst who works in Bangalore.
6. Gurpreet is a Developer and Nizam is a Business Analyst; and both of them work in Gurgaon.
7. Dhanush is a Software Engineer who works in Pune.
8. Roger works in Bangalore and Paridhi works in Pune.
9. The number of Developers working in Bangalore is two.
Q. Who are the two Developers working in Bangalore?
Solution: Marks Consider the solution to the first question.
Emily and Tripti/Roger are the two Developers working in Bangalore. Hence, option 4.
Twelve people  Manish, Urvashi, Lakshya, Tripti, Ishant, Paridhi, Roger, Ojasvee, Nizam, Gurpreet, Emily and Dhanush  work in three different cities  Bangalore, Pune and Gurgaon  with exactly four of them working in each city. They work as either Business Analysts, Developers or Software Engineers, with an equal number of professionals of each type. Each city has atleast one professional of each type.
1. Manish is not a Business Analyst and does not work in Bangalore.
2. Urvashi is a Developer and Paridhi is a Software Engineer.
3. Lakshya works in the same city as Paridhi.
4. Emily is a Developer who works in the same city as Tripti.
5. Ojasvee is a Business Analyst who works in Bangalore.
6. Gurpreet is a Developer and Nizam is a Business Analyst; and both of them work in Gurgaon.
7. Dhanush is a Software Engineer who works in Pune.
8. Roger works in Bangalore and Paridhi works in Pune.
9. The number of Developers working in Bangalore is two.
Q. What is the correct profession and city combination for Ishant?
Solution: Marks Consider the solution to the first question.
Ishant is the Business Analyst from Gurgaon.
Hence, option 2.
Twelve people  Manish, Urvashi, Lakshya, Tripti, Ishant, Paridhi, Roger, Ojasvee, Nizam, Gurpreet, Emily and Dhanush  work in three different cities  Bangalore, Pune and Gurgaon  with exactly four of them working in each city. They work as either Business Analysts, Developers or Software Engineers, with an equal number of professionals of each type. Each city has atleast one professional of each type.
1. Manish is not a Business Analyst and does not work in Bangalore.
2. Urvashi is a Developer and Paridhi is a Software Engineer.
3. Lakshya works in the same city as Paridhi.
4. Emily is a Developer who works in the same city as Tripti.
5. Ojasvee is a Business Analyst who works in Bangalore.
6. Gurpreet is a Developer and Nizam is a Business Analyst; and both of them work in Gurgaon.
7. Dhanush is a Software Engineer who works in Pune.
8. Roger works in Bangalore and Paridhi works in Pune.
9. The number of Developers working in Bangalore is two.
Q. Which of these combinations is definitely incorrect?
Solution: Consider the solution to the first question.The combination in option 4 is correct, while the combinations in options 1 and 2 may or may not be incorrect.The combination in option 3 is definitely incorrect as Nizam works in Gurgaon and not Pune.Hence, option 3.
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