Test: Caselets- 1


10 Questions MCQ Test General Aptitude for GATE 2020 | Test: Caselets- 1


Description
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QUESTION: 1

Inst.

In a recently held survey there were 7500 persons in a local area. Out of those, 2500 opted only for Company A’s liquor, 1850 opted only for Company B’s liquor and 950 opted only for company C’s liquor. The number of persons opting for all the companies is 1000. The number of persons opting only for Company A and C is 250. The number of people opting only for Company B and C is 200 and the number of those opting only for Company A and B is 150.

Q.

How many persons opted for at least two companies liquor?

Solution:

Number of persons opted for at least two companies liquor = 1000 + 250 + 200 + 150 = 1600

QUESTION: 2

In a recently held survey there were 7500 persons in a local area. Out of those, 2500 opted only for Company A’s liquor, 1850 opted only for Company B’s liquor and 950 opted only for company C’s liquor. The number of persons opting for all the companies is 1000. The number of persons opting only for Company A and C is 250. The number of people opting only for Company B and C is 200 and the number of those opting only for Company A and B is 150.

Find the number of persons who opted for Company A’s liquor.

Solution:

Number of persons who opted for Company A’s liquor = 2500 + 150 + 1000 + 250 = 3900

QUESTION: 3

In a recently held survey there were 7500 persons in a local area. Out of those, 2500 opted only for Company A’s liquor, 1850 opted only for Company B’s liquor and 950 opted only for company C’s liquor. The number of persons opting for all the companies is 1000. The number of persons opting only for Company A and C is 250. The number of people opting only for Company B and C is 200 and the number of those opting only for Company A and B is 150.

How many persons opted for only one company’s liquor?

Solution:

Number of persons opted for only one company’s liquor = 2500 + 1850 + 950 

= 5300

 

QUESTION: 4

In a recently held survey there were 7500 persons in a local area. Out of those, 2500 opted only for Company A’s liquor, 1850 opted only for Company B’s liquor and 950 opted only for company C’s liquor. The number of persons opting for all the companies is 1000. The number of persons opting only for Company A and C is 250. The number of people opting only for Company B and C is 200 and the number of those opting only for Company A and B is 150.

How many persons did not participate in the survey?

Solution:

Number of person who did not participate in the survey = 7500 - ( 2500 + 150 + 1000 + 1850 + 200 + 250 + 950)

= 600

QUESTION: 5

In a recently held survey there were 7500 persons in a local area. Out of those, 2500 opted only for Company A’s liquor, 1850 opted only for Company B’s liquor and 950 opted only for company C’s liquor. The number of persons opting for all the companies is 1000. The number of persons opting only for Company A and C is 250. The number of people opting only for Company B and C is 200 and the number of those opting only for Company A and B is 150.

Q. The number of persons opting only for Company A’s liquor is what percent of the total number of persons opting for only Company B’s and only Company C’s liquor?

Solution:

QUESTION: 6

Inst.

16 teams participated in Eurofootball tournament. These are divided into two groups A and B with each group having 8 teams. At the first stage, each team played against all other teams of its group once and top four teams from each group qualified for the quarterfinals. At the second stage, the team having first rank in group A will play with the team having first rank in the group B. Similarly, the team having second rank in group A will play with the team having second rank in group B and so on. After the first stage, every match is a knock-out match (means the team losing any match after the first stage will be out of the tournament.)

In the third stage the winner of the quarterfinals will play the semifinal and in the fourth stage the winner of the semifinal will play the finals. If two or more teams end up with the same score the team with higher number of goals is placed higher in the point table. Two points are given for a win, no point is given for a loss and no match ends in a tie.

Q.

The minimum number of points scored by a team that qualifies for the quarterfinals can be

Solution:

Minimum number of matches won by a team in the first stage to qualify for quarterfinals = 2. 
Since after qualifying for the Quarterfinals a team has to win quarterfinal and semifinal to qualify for the finals. 
∴ Minimum number of matches won by a team to qualify for finals = 2 + 1(quarterfinal) + 1 semifinal = 4

QUESTION: 7

Inst.

16 teams participated in Eurofootball tournament. These are divided into two groups A and B with each group having 8 teams. At the first stage, each team played against all other teams of its group once and top four teams from each group qualified for the quarterfinals. At the second stage, the team having first rank in group A will play with the team having first rank in the group B. Similarly, the team having second rank in group A will play with the team having second rank in group B and so on. After the first stage, every match is a knock-out match (means the team losing any match after the first stage will be out of the tournament.)

In the third stage the winner of the quarterfinals will play the semifinal and in the fourth stage the winner of the semifinal will play the finals. If two or more teams end up with the same score the team with higher number of goals is placed higher in the point table. Two points are given for a win, no point is given for a loss and no match ends in a tie.

Q.

The maximum number of matches a team can play that does not qualify for the quarterfinals can be

Solution:
QUESTION: 8

Inst.

16 teams participated in Eurofootball tournament. These are divided into two groups A and B with each group having 8 teams. At the first stage, each team played against all other teams of its group once and top four teams from each group qualified for the quarterfinals. At the second stage, the team having first rank in group A will play with the team having first rank in the group B. Similarly, the team having second rank in group A will play with the team having second rank in group B and so on. After the first stage, every match is a knock-out match (means the team losing any match after the first stage will be out of the tournament.)

In the third stage the winner of the quarterfinals will play the semifinal and in the fourth stage the winner of the semifinal will play the finals. If two or more teams end up with the same score the team with higher number of goals is placed higher in the point table. Two points are given for a win, no point is given for a loss and no match ends in a tie.

Q. What is the minimum number of matches required to be won by a team to qualify for the finals?

Solution:

Solution : 

The correct option is Option D.

To qualify for the playoffs in the IPL, there are different conditions (Considering 8 teams in total are playing the league matches) :-

  1. If a team scores 15 points or more in total (Win gives 2 points and No Result gives 1 point), then that team qualifies for the playoffs.

  2.  If a team scores less than 15 points in total, then qualifying depends on the points of other teams and their Net Run Rates.

  3. And Hence the Top 4 teams based on the total number of Points and Net Run Rates qualifies for the playoffs.

QUESTION: 9

Inst.

16 teams participated in Eurofootball tournament. These are divided into two groups A and B with each group having 8 teams. At the first stage, each team played against all other teams of its group once and top four teams from each group qualified for the quarterfinals. At the second stage, the team having first rank in group A will play with the team having first rank in the group B. Similarly, the team having second rank in group A will play with the team having second rank in group B and so on. After the first stage, every match is a knock-out match (means the team losing any match after the first stage will be out of the tournament.)

In the third stage the winner of the quarterfinals will play the semifinal and in the fourth stage the winner of the semifinal will play the finals. If two or more teams end up with the same score the team with higher number of goals is placed higher in the point table. Two points are given for a win, no point is given for a loss and no match ends in a tie.

Q.

What is the total number of matches played before the finals?

Solution:

Group A & B has 8C2matches in the 1st round. Hence total 56 in 1st round. (1st stage)
4 teams from each group qualify to 2nd round, and play against each other once, eliminating 4 losers out of this. This round has 4 matches. (2nd stage)
Next round has 4 teams, and hence 2 matches and 2 losers. (2nd stage)
Next round has 2 teams, hence 1 match. (2nd stage)
Hence, there are totally, 56 + 4 + 2  = 62 matches.
 

QUESTION: 10

Inst.

16 teams participated in Eurofootball tournament. These are divided into two groups A and B with each group having 8 teams. At the first stage, each team played against all other teams of its group once and top four teams from each group qualified for the quarterfinals. At the second stage, the team having first rank in group A will play with the team having first rank in the group B. Similarly, the team having second rank in group A will play with the team having second rank in group B and so on. After the first stage, every match is a knock-out match (means the team losing any match after the first stage will be out of the tournament.)

In the third stage the winner of the quarterfinals will play the semifinal and in the fourth stage the winner of the semifinal will play the finals. If two or more teams end up with the same score the team with higher number of goals is placed higher in the point table. Two points are given for a win, no point is given for a loss and no match ends in a tie.

Q.

What is the total number of points scored by all the teams in the tournament?

Solution:

In first stage, teams are divided into two groups of 8 teams each.
They play a match against everyone exactly one i.e. 8C2 matches in every group.
So,
2 x >8C2 = 56 matches for the first stage.
8C2 = 8! / (2!)(6!) = 4 x 7 = 28
In second stage, there are 8 teams in a “knockout stage”.
There will be one winner, so 8 – 1 = 7
So, total number of matches is 56 + 7 = 63
1 win = 2 points
⇒ 63 * 2
⇒ 126

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