Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scorers from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order.

**Q1) How many players among those listed definitely scored less than Yuvraj in the tournament?a. 0b. 1c. 2d. More than 2**

**Q2) Which of the players had the best M-index from the tournament?a. Rahulb. Sauravc. Virenderd. Yuvraj**

**Q3) For how many Indian players is it possible to calculate the exact M-index?a. 0b. 1c. 2d. More than 2**

**Q4) Among the players mentioned, who can have the lowest R-index from the tournament?a. Only Kaif, Rahul or Yuvrajb. Only Kaif or Rahulc. Only Kaif or Yuvrajd. Only Kaif**

Read the question fully and thoroughly, and form a table. From game 1,

Y = 40, V = 130, K = 28. They form 90% of the score. i.e. 198 is 90% of total score.

Rest 10% score is 22 runs, which can be shared by S&R and “other players not in the list” in any way. (Also 22 is less than 28, which is the 3rd highest score in this match)

From game 2,

K = 51. S = 75. R = 49. They form 70% of the score. i.e. 175 is 70% of total score.

Rest 30% is 75 runs, which is to be shared between Y&V and “other players not in the list”. However, the 3rd highest score in the game is 49. So the individual scores of Y&V will be less than 49.

From game 3,

Y = 87, S = 50, R = 55. They form 50% of the total score, which is 192.

So the rest 192 can be shared between V&K and “other players not in the list”, but in such a way that the individual scores of V&K is less than 50.

The table will look like:

Q# 1,

To find the no: of players having scored definitely less than Y, we need to minimize Y’s score, and maximize others’ score and then check.

Y would have scored a minimum of 40 + 0 + 87 = 127 runs in the tournament.

The maximum scores of

V = 130 + 48 + 49 > 127

K = 28 + 51 + 49 >127

S = 22 + 75 + 50 >127

R = 22 + 49 + 55 < 127

Q# 2,

M index will be the middle score. Let us calculate the max. possible M index for all.

Y = 48, V = 49, K = 49, S = 50, R = 49.

Q#3,

Y -> Depends on game 2 score. If game 2 score < 40, M index will be 40, else game 2 score.

V -> Depends on game 2 & 3 score. If game 2 < game 3, then game 2, else, game 3 score.

K -> Depends on game 3 score. If game 3score game 1 score is less than 23. So M score is 50 exactly.

R ->game 1 score is less than 23. So M score is 49 exactly.

Q# 4,

Lowest possible R index means lowest difference between highest and lowest score.

Y = Lowest possible is 87 – 48 = 39

V = Lowest possible is 130 – 49

K = 51 – 49 = 2

S = 75 – 22

R = 55 – 22

**(CAT 2004)Twenty one participants from four continents (Africa, Americas, Australasia, and Europe) attended a United Nations conference. Each participant was an expert in one of four fields, labour, health, population studies, and refugee relocation.**

**The following five facts about the participants are given.**

**The number of labour experts in the camp was exactly half the number of experts in each of the three other categoriesAfrica did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category.None of the continents sent more than three experts in any category.If there had been one less Australasian expert, then the Americas would have had twice as many experts as each of the other continents.Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australasia.**

**Q1) Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex?A. At least oneB. At most twoa. Only A and not Bb. Only B and not Ac. Both A and Bd. Neither A nor B**

**Q2) Which of the following numbers cannot be determined from the information given?a. Number of labour experts from the Americasb. Number of health experts from Europe.c. Number of health experts from Australasiad. Number of experts in refugee relocation from Africa**

**Q3) Which of the following combinations is NOT possible?a. 2 experts in population studies from the Americas and 2 health experts from Africa attended the conference.b. 2 experts in population studies from the Americas and 1 health expert from Africa attended the conference.c. 3 experts in refugee relocation from the Americas and I health expert from Africa attended the conference.d. Africa and America each had 1 expert in population studies attending the conference.**

**Q4) If Ramos is the lone American expert in population studies, which of the following is NOT true about the numbers of experts in the conference from the four continents?a. There is one expert in health from Africa.b. There is one expert in refugee relocation from Africa.c. There are two experts in health from the Americas.d. There are three experts in refugee relocation from the Americas.**

Read the question thoroughly and fully, form a table with the “fixed” and less confusing details first, and then proceed.

Total participants = 21. 3 categories have the same participant and Labour has half of the other 3 (Clue # 1) . So if Labour is x, other 3 have 2x. Sum of all is 21. 7x – 21, So x = 3.

From Clue #4, Australia has 1 more participant than Europe and Africa, and America had twice of Europe and Africa. Let EU and AF have y. Aust has y+1, and America 2y. Again, total is 21. So y = 4.

Labor from Africa is 0.

Australasia population is 2 or 2+ (as given in clue 5). Also, totally there are 5 australasians, and all the other categories have minimum 1 (from clue 2). So population can have only 2 australasians, and other 3 categories 1 each.

Europe, has 1 in each section. (Total from Europe is 4, and all sections have atleast 1; clue 2).

Labor has totally 3. We have 1 from AU and EU. So AM has 1.

We are not sure of the other sections, and hence, we can fill it like the diagram below.

1 health in Africa and 3 in America. (So that total health is 6)

2 health in Africa and 2 in America. (So that total health is 6)

1 population in Africa and 2 in America. (So that total population is 6)

2 population in Africa and 1 in America. (So that total population is 6)

1 refugee in Africa and 3 in America. (So that total refugee is 6)

2 refugee in Africa and 2 in America. (So that total refugee is 6)

Q#1, Alex is in refugee relocation and America. Excluding Alex, we can have atleast 1 and atmost 2 americans in Refugee.

Q# 2, Answer from table.

Q# 3, Answer from table/solution section 2g above.

Q# 4, 1 American expert in population studies, as given in question. So 2 population from Africa, which means 1 health and 1 refugee in Africa. (As Africa total is 4). That means 3 health and 3 refugee from America. (As America total is 8 )

**(CAT 2004)The year was 2006. All six teams in Pool A of World Cup hockey play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goals For – Goals Against) qualifies. In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.**

**In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches(a) Spain won both the fourth and fifth round matches.(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.**

**Q1) Which one of the following statements is true about matches played in the first two rounds?a. Germany beat New Zealand by 1 goal to 0.b. Spain beat New Zealand by 4 goals to 0.c. Spain beat South Africa by 2 goals to 0.d. Germany beat South Africa by 2 goals to 1.**

**Q2) Which one of the following statements is true about matches played in the first two rounds?a. Pakistan beat South Africa by 2 goals to 1b. Argentina beat Pakistan by I goal to 0.c. Germany beat Pakistan by 2 goals to 1d. Germany beat Spain by 2 goals to 1.**

**Q3) Which team finished at the top of the pool after five rounds of matches?a. Argentinab. Germanyc. Spaind. Cannot be determined from the data.**

**Q4) If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?a. Argentinab. Germanyc. Spaind. Cannot be determined from the data.**

Read the question carefully, thoroughly. This is one of the best questions, I have come across among the past few years’ CAT, and it might be a bit confusing and eat up your time.

Let us focus on the 1st 2 matches initially :

Germany:Germany has 2 wins, 3 goals for and 1 against. So Germany wins are 2-1 and 1-0.

Argentina:Argentina has 2 wins, 2 goals for and 0 against. So Argentina wins are 1-0 and 1-0.

Pakistan:Pakistan has 1 win, 1 loss, 2 goals for and 1 against. So, its loss is 0-1 and win is 2-0.

South Africa:SA has 2 losses, 1 goal for and 4 against. So, it could either be

0-1 and 1-3, or 0-2 and 1-2.

We know that Germany played against Spain, and won. Victory could be 2-1 or 1-0. If German victory (vs. Spain) was 2-1, then Spain should have hit 4 goals in the next match, and conceded 0. If German victory (vs. Spain) was 1-0, then Spain should have hit 5 goals in the next match, and conceded 1. In either way, Spain has to hit a minimum of 4 goals in the next match.

Also, from the table, we see that only Germany and Spain has hit a minimum of 3 goals. Germany can’t hit 3 goals in a single match, as I have mentioned already the scores of German matches (see point a) above ), and Spain needs to hit minimum 4 goals in its 2nd match (above point). So the option d (i) (0-1 and 1-3) for SA will not happen. Hence d (ii) is correct.

So, for SA, the match scores were 0-2 and 1-2.

Spain, NZ:

As said before, Spain wins 1 match 4-0 or 5-1 and loses the other one 1-2 or 1-0 against Germany.

Suppose Spain loses against Germany with the score 1-2. So, the next match Spain will win 4-0. That will be against NZ. So, NZ’s other match score will be 1-2.

If NZ’s score should be 1-2, then there should be some team which defeated NZ with that score, i.e. 2-1. However, if you see, the score 2-1 is there only for Germany and SA, (which means Germany played against SA). There is no 3rd game with the score 2-1 and hence, that is not possible, and hence Spain cannot lose 2-1 against Germany.

So, the score of Germany Vs Spain is 1-0.

Means Spain vs NZ will be 5-1, and NZ’s next match score will be 0-1.

So, now we have the following table :

This means, the following was the matches played in the 1st 2 rounds :

Germany v Spain 1-0 (We know Germany played Spain from the question)

Germany v SA 2-1

Argentina v NZ 1-0 (Only 2 teams with 0-1, NZ and Pakistan)

Argentina v Pakistan1-0 (Only 2 teams with 0-1, NZ and Pakistan)

Spain v NZ 5-1

Pakistan v SA 2-0

Q#1and Q#2 can be answered from above.

Now for the next section: 3, 4, 5 rounds.

3rd round –

Germany Vs Argentina – Draw

Spain vs Pakistan – Draw

NZ vs SA – Draw.

If the result is a draw, goal difference remains the same.

So, after 3rd round,

Germany – 7 points, Goal difference = 2

Argentina – 7 points, Goal difference = 2

Spain – 4 points, Goal difference = 3

Pakistan –4 points, Goal difference = 1

NZ – 1 point, Goal difference = -5

SA - 1 point, Goal difference = -3

4th and 5th round : The remaining matches were :

Spain Vs SA

Spain vs Argentina

Pakistan vs Germany

Pakistan vs NZ

Germany vs NZ

Argentina vs SA

We know that Spain and Pakistan won both the matches (4th and 5th). So Spain won against SA and Argentina, and Pakistan won against Germany and NZ (Pakistan’s: 1-0 victory).

Also Germany and Argentina won their 5th round matches. Hence they won against NZ and SA respectively. (Both 3-0 victories)

So, we know:

Germany – 10 points, GD < 5. (GD was 2 after 3rd round, then 5th round they won by 3 goals, 4th round they lost.)

Argentina – 10 points. GD < 5. (GD was 2 after 3rd round, then 5th round they won by 3 goals, 4th round they lost.)

Spain – 10 points. GD > 5. (GD was 3 after 3rd round, they won 2 matches. Winning should be atleast by 1 goal)

Pakistan – 10 points. GD = 1. (GD was 1 after 3rd round, and they won the remaining 2 matches by 1 goal)

NZ and SA – 1 point and negative GD.

Spain was the group topper, and it qualified for the next round.

**(CAT 2005)The table below reports the gender, designation and age-group of the employees in an organization. It also provides information on their commitment to projects coming up in the months of January (Jan), February (Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportunities (B), Communication Skills (C), & E-Governance (E).**

**For each workshop, exactly four employees are to be sent, of which at least two should be Females and at least one should be Young. No employee can be sent to a workshop in which he or she is not interested in. An employee cannot attend the workshop on(a) Communication Skills, if he or she is committed to internal projects in the month of January;(b) Business Opportunities, if he or she is committed to internal projects in the month of February;(c) E-governance, if he or she is committed to internal projects in the month of March.**

**Q1) Assuming that Parul and Hari are attending the workshop on Communication Skills (C), then which of the following employees can possibly attend the C workshop?(1) Rahul and Yamini(2) Dinesh and Lavanya(3) Anshul and Yamini(4) Fatima and Zeena**

**Q2) How many Executives (Exe) cannot attend more than one workshop?(1) 2(2) 3(3) 15(4) 16**

**Q3) Which set of employees cannot attend any of the workshops?(1) Anshul, Charu, Eashwaran and Lavanya(2) Anshul, Bushkant, Gayatri and Urvashi(3) Charu, Urvashi, Bushkant and Mandeep(4) Anshul, Gayatri, Eashwaran and Mandeep**

Q# 1,

At least 1 young, 2 females are necessary in a group.

Parul is young and female. So we need 1 more female.

Also CS – January, he/she should be free.

Consider the options :

Rahul and Yamini are free in Jan, and Yamini is female. So they are possible.

All other options have atleast 1 person not free in January.

Q#2,

There are totally 6 executives – with the starting letter D, G, K, P, U, Z

D interested in B,C,E and is committed in Jan, Apr. So he can attend B, E

G is interested only in E.

K interested in B, C, E and is committed in Jan, Apr. So she can attend B, E.

Similarly, work out for others.

Q#3,

Work out similar to Q#2.

Start with employees with only 1 interest. Then move on to 2 and then 3. In this way, we can eliminate options and find out the answer quickly.

We could see that employees starting with E, G, U, A, B cannot attend any workshops.

**(CAT 2005)In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of-first round plays the winner of match No. 16 of first round and is designated match No. I of second round. Similarly, the winner of match No, 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.**

**Q1) If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?(1) Justine Henin(2) Nadia Petrova(3) Patty Schnyder(4) Venus Williams**

**Q2) If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semifinals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?(1) Dinara Safina(2) Justine Henin(3) Nadia Petrova(4) Patty Schnyder**

**Q3) If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?(1) Anastasia Myskina(2) Flavia Pennetta(3) Nadia Petrova(4) Svetlana Kuznetsova**

**Q4) If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?(1) Amelie Mauresmo(2) Elena Dementieva(3) Kim Clijsters(4) Lindsay Davenport**

Q# 1,

No upsets in 1st round – So, seed 1 – 16 goes to 2nd round.

6, 7, 8 upset in 2nd round. So instead of 6, 7, 8, the qualifiers will be 11, 10, 9 to the 3rd round.

So now we have 1,2,3,4,5,11,10,9 in the quarter finals.

Davenport is 2. So she will face 10 in the quarters.

Q# 2,

1st 16 qualify from 1st round.

2nd round 6 and 8 loses. So 11 and 9 qualifies.

3rd round will have 1, 2, 3, 4, 5, 11, 7, and 9.

Sharapova is 1. She will play 9 in quarter finals.

Q# 3,

After 1st round, we have only odd numbered seeds now. i.e. 2 is defeated by 31, 4 by 29, 6 by 27 and so on.

So, we have 1,29,3,27,5,25………..15,17 to the second round.

No upsets in second round. So after second round, we have :

1,15,3,13,5,11,7,9 will move to the 3rd round.

We need to find the lowest seeded player facing Sharapova in Semis. Sharapova will play the winner of 13 vs 5 in semis. So 13 should be the winner so that Sharapova faces the lowest seeded player possible.

Q#4,

Top 8 seeds make it to quarters. So we have 1,2,3,4,5,6,7,8 in quarters.

Sharapova is 1.

We will have 1 vs 8 in quarters, 1 vs (4/5) in semis, and 1 vs (2/3/6/7) in finals.

Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scorers from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order.

**Q1) How many players among those listed definitely scored less than Yuvraj in the tournament?a. 0b. 1c. 2d. More than 2**

**Q2) Which of the players had the best M-index from the tournament?a. Rahulb. Sauravc. Virenderd. Yuvraj**

**Q3) For how many Indian players is it possible to calculate the exact M-index?a. 0b. 1c. 2d. More than 2**

**Q4) Among the players mentioned, who can have the lowest R-index from the tournament?a. Only Kaif, Rahul or Yuvrajb. Only Kaif or Rahulc. Only Kaif or Yuvrajd. Only Kaif**

Read the question fully and thoroughly, and form a table. From game 1,

Y = 40, V = 130, K = 28. They form 90% of the score. i.e. 198 is 90% of total score.

Rest 10% score is 22 runs, which can be shared by S&R and “other players not in the list” in any way. (Also 22 is less than 28, which is the 3rd highest score in this match)

From game 2,

K = 51. S = 75. R = 49. They form 70% of the score. i.e. 175 is 70% of total score.

Rest 30% is 75 runs, which is to be shared between Y&V and “other players not in the list”. However, the 3rd highest score in the game is 49. So the individual scores of Y&V will be less than 49.

From game 3,

Y = 87, S = 50, R = 55. They form 50% of the total score, which is 192.

So the rest 192 can be shared between V&K and “other players not in the list”, but in such a way that the individual scores of V&K is less than 50.

The table will look like:

Q# 1,

To find the no: of players having scored definitely less than Y, we need to minimize Y’s score, and maximize others’ score and then check.

Y would have scored a minimum of 40 + 0 + 87 = 127 runs in the tournament.

The maximum scores of

V = 130 + 48 + 49 > 127

K = 28 + 51 + 49 >127

S = 22 + 75 + 50 >127

R = 22 + 49 + 55 < 127

Q# 2,

M index will be the middle score. Let us calculate the max. possible M index for all.

Y = 48, V = 49, K = 49, S = 50, R = 49.

Q#3,

Y -> Depends on game 2 score. If game 2 score < 40, M index will be 40, else game 2 score.

V -> Depends on game 2 & 3 score. If game 2 < game 3, then game 2, else, game 3 score.

K -> Depends on game 3 score. If game 3score game 1 score is less than 23. So M score is 50 exactly.

R ->game 1 score is less than 23. So M score is 49 exactly.

Q# 4,

Lowest possible R index means lowest difference between highest and lowest score.

Y = Lowest possible is 87 – 48 = 39

V = Lowest possible is 130 – 49

K = 51 – 49 = 2

S = 75 – 22

R = 55 – 22

**(CAT 2004)Twenty one participants from four continents (Africa, Americas, Australasia, and Europe) attended a United Nations conference. Each participant was an expert in one of four fields, labour, health, population studies, and refugee relocation.**

**The following five facts about the participants are given.**

**The number of labour experts in the camp was exactly half the number of experts in each of the three other categoriesAfrica did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category.None of the continents sent more than three experts in any category.If there had been one less Australasian expert, then the Americas would have had twice as many experts as each of the other continents.Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australasia.**

**Q1) Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex?A. At least oneB. At most twoa. Only A and not Bb. Only B and not Ac. Both A and Bd. Neither A nor B**

**Q2) Which of the following numbers cannot be determined from the information given?a. Number of labour experts from the Americasb. Number of health experts from Europe.c. Number of health experts from Australasiad. Number of experts in refugee relocation from Africa**

**Q3) Which of the following combinations is NOT possible?a. 2 experts in population studies from the Americas and 2 health experts from Africa attended the conference.b. 2 experts in population studies from the Americas and 1 health expert from Africa attended the conference.c. 3 experts in refugee relocation from the Americas and I health expert from Africa attended the conference.d. Africa and America each had 1 expert in population studies attending the conference.**

**Q4) If Ramos is the lone American expert in population studies, which of the following is NOT true about the numbers of experts in the conference from the four continents?a. There is one expert in health from Africa.b. There is one expert in refugee relocation from Africa.c. There are two experts in health from the Americas.d. There are three experts in refugee relocation from the Americas.**

Read the question thoroughly and fully, form a table with the “fixed” and less confusing details first, and then proceed.

Total participants = 21. 3 categories have the same participant and Labour has half of the other 3 (Clue # 1) . So if Labour is x, other 3 have 2x. Sum of all is 21. 7x – 21, So x = 3.

From Clue #4, Australia has 1 more participant than Europe and Africa, and America had twice of Europe and Africa. Let EU and AF have y. Aust has y+1, and America 2y. Again, total is 21. So y = 4.

Labor from Africa is 0.

Australasia population is 2 or 2+ (as given in clue 5). Also, totally there are 5 australasians, and all the other categories have minimum 1 (from clue 2). So population can have only 2 australasians, and other 3 categories 1 each.

Europe, has 1 in each section. (Total from Europe is 4, and all sections have atleast 1; clue 2).

Labor has totally 3. We have 1 from AU and EU. So AM has 1.

We are not sure of the other sections, and hence, we can fill it like the diagram below.

1 health in Africa and 3 in America. (So that total health is 6)

2 health in Africa and 2 in America. (So that total health is 6)

1 population in Africa and 2 in America. (So that total population is 6)

2 population in Africa and 1 in America. (So that total population is 6)

1 refugee in Africa and 3 in America. (So that total refugee is 6)

2 refugee in Africa and 2 in America. (So that total refugee is 6)

Q#1, Alex is in refugee relocation and America. Excluding Alex, we can have atleast 1 and atmost 2 americans in Refugee.

Q# 2, Answer from table.

Q# 3, Answer from table/solution section 2g above.

Q# 4, 1 American expert in population studies, as given in question. So 2 population from Africa, which means 1 health and 1 refugee in Africa. (As Africa total is 4). That means 3 health and 3 refugee from America. (As America total is 8 )

**(CAT 2004)The year was 2006. All six teams in Pool A of World Cup hockey play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goals For – Goals Against) qualifies. In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.**

**In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches(a) Spain won both the fourth and fifth round matches.(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.**

**Q1) Which one of the following statements is true about matches played in the first two rounds?a. Germany beat New Zealand by 1 goal to 0.b. Spain beat New Zealand by 4 goals to 0.c. Spain beat South Africa by 2 goals to 0.d. Germany beat South Africa by 2 goals to 1.**

**Q2) Which one of the following statements is true about matches played in the first two rounds?a. Pakistan beat South Africa by 2 goals to 1b. Argentina beat Pakistan by I goal to 0.c. Germany beat Pakistan by 2 goals to 1d. Germany beat Spain by 2 goals to 1.**

**Q3) Which team finished at the top of the pool after five rounds of matches?a. Argentinab. Germanyc. Spaind. Cannot be determined from the data.**

**Q4) If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?a. Argentinab. Germanyc. Spaind. Cannot be determined from the data.**

Read the question carefully, thoroughly. This is one of the best questions, I have come across among the past few years’ CAT, and it might be a bit confusing and eat up your time.

Let us focus on the 1st 2 matches initially :

Germany:Germany has 2 wins, 3 goals for and 1 against. So Germany wins are 2-1 and 1-0.

Argentina:Argentina has 2 wins, 2 goals for and 0 against. So Argentina wins are 1-0 and 1-0.

Pakistan:Pakistan has 1 win, 1 loss, 2 goals for and 1 against. So, its loss is 0-1 and win is 2-0.

South Africa:SA has 2 losses, 1 goal for and 4 against. So, it could either be

0-1 and 1-3, or 0-2 and 1-2.

We know that Germany played against Spain, and won. Victory could be 2-1 or 1-0. If German victory (vs. Spain) was 2-1, then Spain should have hit 4 goals in the next match, and conceded 0. If German victory (vs. Spain) was 1-0, then Spain should have hit 5 goals in the next match, and conceded 1. In either way, Spain has to hit a minimum of 4 goals in the next match.

Also, from the table, we see that only Germany and Spain has hit a minimum of 3 goals. Germany can’t hit 3 goals in a single match, as I have mentioned already the scores of German matches (see point a) above ), and Spain needs to hit minimum 4 goals in its 2nd match (above point). So the option d (i) (0-1 and 1-3) for SA will not happen. Hence d (ii) is correct.

So, for SA, the match scores were 0-2 and 1-2.

Spain, NZ:

As said before, Spain wins 1 match 4-0 or 5-1 and loses the other one 1-2 or 1-0 against Germany.

Suppose Spain loses against Germany with the score 1-2. So, the next match Spain will win 4-0. That will be against NZ. So, NZ’s other match score will be 1-2.

If NZ’s score should be 1-2, then there should be some team which defeated NZ with that score, i.e. 2-1. However, if you see, the score 2-1 is there only for Germany and SA, (which means Germany played against SA). There is no 3rd game with the score 2-1 and hence, that is not possible, and hence Spain cannot lose 2-1 against Germany.

So, the score of Germany Vs Spain is 1-0.

Means Spain vs NZ will be 5-1, and NZ’s next match score will be 0-1.

So, now we have the following table :

This means, the following was the matches played in the 1st 2 rounds :

Germany v Spain 1-0 (We know Germany played Spain from the question)

Germany v SA 2-1

Argentina v NZ 1-0 (Only 2 teams with 0-1, NZ and Pakistan)

Argentina v Pakistan1-0 (Only 2 teams with 0-1, NZ and Pakistan)

Spain v NZ 5-1

Pakistan v SA 2-0

Q#1and Q#2 can be answered from above.

Now for the next section: 3, 4, 5 rounds.

3rd round –

Germany Vs Argentina – Draw

Spain vs Pakistan – Draw

NZ vs SA – Draw.

If the result is a draw, goal difference remains the same.

So, after 3rd round,

Germany – 7 points, Goal difference = 2

Argentina – 7 points, Goal difference = 2

Spain – 4 points, Goal difference = 3

Pakistan –4 points, Goal difference = 1

NZ – 1 point, Goal difference = -5

SA - 1 point, Goal difference = -3

4th and 5th round : The remaining matches were :

Spain Vs SA

Spain vs Argentina

Pakistan vs Germany

Pakistan vs NZ

Germany vs NZ

Argentina vs SA

We know that Spain and Pakistan won both the matches (4th and 5th). So Spain won against SA and Argentina, and Pakistan won against Germany and NZ (Pakistan’s: 1-0 victory).

Also Germany and Argentina won their 5th round matches. Hence they won against NZ and SA respectively. (Both 3-0 victories)

So, we know:

Germany – 10 points, GD < 5. (GD was 2 after 3rd round, then 5th round they won by 3 goals, 4th round they lost.)

Argentina – 10 points. GD < 5. (GD was 2 after 3rd round, then 5th round they won by 3 goals, 4th round they lost.)

Spain – 10 points. GD > 5. (GD was 3 after 3rd round, they won 2 matches. Winning should be atleast by 1 goal)

Pakistan – 10 points. GD = 1. (GD was 1 after 3rd round, and they won the remaining 2 matches by 1 goal)

NZ and SA – 1 point and negative GD.

Spain was the group topper, and it qualified for the next round.

**(CAT 2005)The table below reports the gender, designation and age-group of the employees in an organization. It also provides information on their commitment to projects coming up in the months of January (Jan), February (Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportunities (B), Communication Skills (C), & E-Governance (E).**

**For each workshop, exactly four employees are to be sent, of which at least two should be Females and at least one should be Young. No employee can be sent to a workshop in which he or she is not interested in. An employee cannot attend the workshop on(a) Communication Skills, if he or she is committed to internal projects in the month of January;(b) Business Opportunities, if he or she is committed to internal projects in the month of February;(c) E-governance, if he or she is committed to internal projects in the month of March.**

**Q1) Assuming that Parul and Hari are attending the workshop on Communication Skills (C), then which of the following employees can possibly attend the C workshop?(1) Rahul and Yamini(2) Dinesh and Lavanya(3) Anshul and Yamini(4) Fatima and Zeena**

**Q2) How many Executives (Exe) cannot attend more than one workshop?(1) 2(2) 3(3) 15(4) 16**

**Q3) Which set of employees cannot attend any of the workshops?(1) Anshul, Charu, Eashwaran and Lavanya(2) Anshul, Bushkant, Gayatri and Urvashi(3) Charu, Urvashi, Bushkant and Mandeep(4) Anshul, Gayatri, Eashwaran and Mandeep**

Q# 1,

At least 1 young, 2 females are necessary in a group.

Parul is young and female. So we need 1 more female.

Also CS – January, he/she should be free.

Consider the options :

Rahul and Yamini are free in Jan, and Yamini is female. So they are possible.

All other options have atleast 1 person not free in January.

Q#2,

There are totally 6 executives – with the starting letter D, G, K, P, U, Z

D interested in B,C,E and is committed in Jan, Apr. So he can attend B, E

G is interested only in E.

K interested in B, C, E and is committed in Jan, Apr. So she can attend B, E.

Similarly, work out for others.

Q#3,

Work out similar to Q#2.

Start with employees with only 1 interest. Then move on to 2 and then 3. In this way, we can eliminate options and find out the answer quickly.

We could see that employees starting with E, G, U, A, B cannot attend any workshops.

**(CAT 2005)In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of-first round plays the winner of match No. 16 of first round and is designated match No. I of second round. Similarly, the winner of match No, 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.**

**Q1) If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?(1) Justine Henin(2) Nadia Petrova(3) Patty Schnyder(4) Venus Williams**

**Q2) If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semifinals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?(1) Dinara Safina(2) Justine Henin(3) Nadia Petrova(4) Patty Schnyder**

**Q3) If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?(1) Anastasia Myskina(2) Flavia Pennetta(3) Nadia Petrova(4) Svetlana Kuznetsova**

**Q4) If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?(1) Amelie Mauresmo(2) Elena Dementieva(3) Kim Clijsters(4) Lindsay Davenport**

Q# 1,

No upsets in 1st round – So, seed 1 – 16 goes to 2nd round.

6, 7, 8 upset in 2nd round. So instead of 6, 7, 8, the qualifiers will be 11, 10, 9 to the 3rd round.

So now we have 1,2,3,4,5,11,10,9 in the quarter finals.

Davenport is 2. So she will face 10 in the quarters.

Q# 2,

1st 16 qualify from 1st round.

2nd round 6 and 8 loses. So 11 and 9 qualifies.

3rd round will have 1, 2, 3, 4, 5, 11, 7, and 9.

Sharapova is 1. She will play 9 in quarter finals.

Q# 3,

After 1st round, we have only odd numbered seeds now. i.e. 2 is defeated by 31, 4 by 29, 6 by 27 and so on.

So, we have 1,29,3,27,5,25………..15,17 to the second round.

No upsets in second round. So after second round, we have :

1,15,3,13,5,11,7,9 will move to the 3rd round.

We need to find the lowest seeded player facing Sharapova in Semis. Sharapova will play the winner of 13 vs 5 in semis. So 13 should be the winner so that Sharapova faces the lowest seeded player possible.

Q#4,

Top 8 seeds make it to quarters. So we have 1,2,3,4,5,6,7,8 in quarters.

Sharapova is 1.

We will have 1 vs 8 in quarters, 1 vs (4/5) in semis, and 1 vs (2/3/6/7) in finals.