# Quantitative Reasoning – Passage Based – FIFA 2014!

2014_QNR 23. Directions : (Questions i to iv). Read the following passage and answer the questions that follow :
Football is one of the most popular games played. The 20 th Federation of International Football Association (FIFA) World Cup football tournament was organized in Brazil from 12 June to 13 July 2014. The participating teams were divided in 8 groups of 4-teams each. There were five stages of the tournament:
1. First Stage : Group Stage
2. Second Stage : Round of 16
3. Third Stage : Quarter-finals
4. Fourth Stage : Semi-finals
5. Fifth Stage : Final
Each team in the first stage played one match against each of the other teams of the group. Top two teams from each group qualified for Round of 16. Second stage onwards the matches were knockout games i.e. only winning team of a match will advance to the next stage. In the second stage, each team played only one match against one of the other teams and half the teams qualified for the next stage. Same process was followed for advancement up to fifth stage. One extra match was played between losers of semi-finals to decide the third and fourth place teams.

Final match was played between Germany and Argentina. Germany became the world champion by defeating Argentina with a score of 1 – 0 in the final match. During the final match, a total 1501 passes were made of which only 1152 were completed. In all, 171 goals were scored in the tournament. The last titleholders, Spain, were eliminated at the group stage while the host nation finished fourth in the tournament. The Colombian team won “FIFA Fair Play Award” with the tournament’s best disciplinary and sportsmanship record.

(i) How many total matches were played in the first stage of the tournament ?

(a) 36

(b) 48

(c) 52

(d) 64

(ii) What were the average goals scored per match in the tournament ?
(a) 2.67

(b) 2.71

(c) 3.56

(4) 3.00

(iii) How many matches must a team have played if they finished fourth in the
tournament ?
(a) 4

(b) 5

(c) 6

(d) 7

(iv) Which one of the following diagrams correctly shows the percentage of completed and
uncompleted passes during the final match ?

Ans: (i)  How many total matches were played in the first stage of the tournament ?

In the first stage, every group has 4 teams and each of them play against each other only once. Total matches =6. Since there are 8 groups. Total matches = 48. Option b.

{If there are 4 teams P,Q,R,S,  matches will be between (P,Q) , (P,R) , (P,S) , (Q,R) , (Q,S) , (R,S) . For practice find out how many matches would be there if there were 30 teams in a group?}

(ii) What were the average goals scored per match in the tournament ?

We know that total goals scored in the tournament is 171. We need to find out total matches played in the tournament.

Matches played in the first stage= 48.

Matches played in the second stage= 8. [16 teams participate and each team played only one match against one of the other in a knock-out fashion.]

Similarly, matches played in the third stage= 4.

Similarly, matches played in the fourth and fifth stage= 2 & 1.

Total matches = 48 + 8 + 4 + 2 + 1=63.

Average goals per match= 171/63 =19/7 = 2.71. Option b.

(iii) How many matches must a team have played if they finished fourth in the tournament ?

Since the teams in the final are the first two, the fourth ranker must have played the Semis; the fourth ranker must have played 3 matches in group stage, one match in second round knock out, one match in quarters and at least one match in semis.

At this stage, the team would have played 3 + 1 + 1 + 1=6 matches. Additionally the team would have played the “third position match”( match between the losers of semi-final matches to determine the third and fourth ranked team). So total matches for the fourth ranked team= 6+1=7. Option d.

(iv) During the final match, a total 1501 passes were made of which only 1152 were completed.

Completed percentage: 1152/ 1502 ≈ 1150/1500 =23/30≈80%. Option B.