**> Ranking and Ordering: Introduction**

**> Ranking and Ordering: Solved Examples**

**> Ranking and Ordering: Solved Examples – 2**

**> Ranking and Ordering: Solved Examples – 3**

**> Ranking and Ordering: Solved Examples – 4**

**> Ranking and Ordering: Solved Examples – 5**

**> Ranking and Ordering: Solved Examples – 6**

**> Ranking and Ordering: Solved Examples – 7**

**> Ranking and Ordering: Solved Examples – 8**

**> Ranking and Ordering: Solved Examples – 11**

**> Ranking and Ordering: Solved Examples – 12**

**> Ranking and Ordering: Solved Examples – 13**

**> Ranking and Ordering: Solved Examples – 14**

**> Ranking and Ordering: Solved Examples – 15**

**> Ranking and Ordering: Solved Examples – 16**

**> Ranking and Ordering: Solved Examples – 17**

**Practice Exercise 1: Study the following information carefully and answer the questions that follow.**

**Seven people – P, Q, R, S, T, U, and V have a seminar but not necessarily in the same order, on seven different months (of the same year) namely January, February, March, June, August, October, and December. Each of them also likes a different fruit namely Banana, Grapes, Papaya, Orange, Mango, Litchi, and Apple, but not necessarily in the same order.**

**R has a seminar in a month which has less than 31 days. Only two people have a seminar between R and S. The one who likes banana has a seminar immediately before T. Only one person has a seminar before the one who likes Papaya. Q has a seminar immediately after the one who likes Papaya. Only three people have a seminar between Q and the one who likes Mango. T likes neither Mango nor Papaya. P has a seminar immediately before T. V likes Apple. The one who likes Grapes has a seminar in the month, which has less than 31 days. The one who has a seminar in March does not like Orange.**

**1. **Which of the following represents the month in which S has a seminar?

A. January

B. Cannot be determined

C. October

D. December

E. June

**2. **Which of the following represents the people who have a seminar in January and June respectively?

A. V, S

B. U, S

C. Q, T

D. V, R

E. U, R

**3. **How many people have a seminar between the months in which V and R have a seminar?

A. None

B. Two

C. Three

D. One

E. More than three

**4. **As per the given arrangement, R is related to Banana and P is related to Orange following a certain pattern. Which of the following is V related to, following the same pattern?

A. Mango

B. Litchi

C. Apple

D. Papaya

E. Grapes

**5. **Which of the following fruits does U like?

A. Orange

B. Papaya

C. Mango

D. Banana

E. Grapes

**> R has a seminar in a month which has less than 31 days. Only two people have a seminar between R and S.**

There are two possibilities:

**> Only one person has a seminar before the one who likes Papaya. Q has a seminar immediately after the one who likes Papaya. Only three people have a seminar between Q and the one who likes Mango.**

**> T likes neither Mango nor Papaya. P has a seminar immediately before T.**

This is not possible in Case 1. So, we reject this case.

**> V likes Apple. The one who likes Grapes has a seminar in the month, which has less than 31 days. The one who likes banana has a seminar immediately before T.**

**> The one who has a seminar in March does not like Orange.**

Now let’s answer the questions:

**1. **S has a seminar in December. **So, D is the correct option.**

**2. **V has a seminar in January and R has a seminar in June. **So, D is the correct option.**

**3. **Two people have a seminar between the months in which V and R have a seminar. **So, B is the correct option.**

**4. **Following the pattern given, V is related to Papaya.** So,**** D is the correct option.**

**5. **U likes Papaya.** So, B is the correct option.**

**Practice Exercise 2: Study the following information to answer the questions.**

**Each of the six buildings P, Q, R, S, T, and U houses different number of offices. S has more offices than only T and R. Q has more number of offices than P but less than U. R does not house the least number of offices. The building which houses the least number of offices has 5 offices. The building which has the second-highest number of offices has 23 offices. S has 11 less number of offices than Q.**

**1. **Which of the following buildings has the second least number of offices?

A. Q

B. U

C. R

D. P

E. T

**2. **If the number of offices in P is an even number which is divisible by 2 as well as 3. How many does P have?

A. 20

B. 24

C. 16

D. 18

E. 12

**3. **Which of the following is the number of offices in R?

A. 25

B. 12

C. 13

D. 14

E. 11

**> S has more offices than only T and R.**

Number of houses: S > T, R

**> Q has more number of offices than P but less than U.**

Number of houses: U > Q > P > S > T, R

**> R does not house the least number of houses.**

Number of houses: U > Q > P > S > R > T

**> The building which houses the least number of offices has 5 offices.**

This implies T has 5 houses.

**> The building which has the second-highest number of offices has 23 offices.**

This implies Q has 23 houses.

**> S has 11 less number of offices than Q.**

This implies S has 12 offices.

Now let’s answer the questions:

**1. **R has the second least number of offices.** So, C is the correct option.**

**2. **P has more than 12 and less than 23 offices. Since the number of offices in P is divisible by 2 as well as 3, it has 18 offices. **So, D is the correct option.**

**3. **R has more than 5 and less than 12 offices. Therefore, it can possibly have 11 offices. **So, E is the correct option.**

**Practice Exercise 3: Study the information given below and answer the questions based on it.**

**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 semi-finals. 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 has 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 resulted in a draw. 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.**

**1. **Which one of the following statements is true about the matches played in the first two rounds?

A. Pakistan beat South Africa by 2 goals to 1.

B. Argentina beat Pakistan by 1 goal to 0.

C. Germany beat Pakistan by 2 goals to 1.

D. Germany beat Spain by 2 goals to 1.

**2. **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. Germany beat Pakistan by 2 goals to 1.

D. Germany beat South Africa by 2 goals to 1.

**3. **Which team finished at the top of the pool after five rounds of matches?

A. Argentina

B. Germany

C. Spain

D. Cannot be determined

**4. **If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?

A. Argentina

B. Germany

C. Spain

D. Cannot be determined

It is given that the opening match was played between Germany and Spain.

Let’s analyze the “Goals For” and “Goals Against” columns. It will help us figure out which teams played against each other in the first two rounds.

**> **Germany won its matches by 2 – 1 and 1 – 0.

**> **Argentina won its matches by 1 – 0 and 1 – 0.

**> **Pakistan won its one match by 2 – 0 and lost the other by 0 – 1.

**> **If Spain lost the match against Germany by 0 – 1, it would have won its second match by 5 – 1. It must have defeated New Zealand. That implies New Zealand lost its second match by 0 – 1.

**> **If Spain lost the match against Germany by 1 – 2, it would have won its second match by 4 – 0. Again, it must have defeated New Zealand. This implies New Zealand lost its second match by 1 – 2, which could only be against Germany.

**> **Seeing the goals of the winning teams, South Africa must have lost its one match by 1 – 2 and the other by 0 – 2.

There is only one team which won by 2 – 1, which is Germany. Therefore, New Zealand must have lost its second match by 0 – 1 and hence, Germany must have defeated Spain by 1 – 0.

South Africa lost its second match by 0 – 2 and only Pakistan won a match by 2 – 0. This implies South Africa lost one match to Pakistan.

Both New Zealand and Pakistan must have lost to Argentina by 0 – 1.

**> In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches resulted in a draw.**

**> Spain won both the fourth and fifth round matches.**

**> Pakistan won both the fourth and fifth round matches by 1 goal to 0.**

**> Both Argentina and Germany won their fifth round matches by 3 goals to 0.**

Now let’s answer the questions:

**1. **Argentina beat Pakistan by 1 goal to 0.** So, B is the correct option.**

**2. **Germany beat South Africa by 2 goals to 1.** So, D is the correct option.**

**3. **Germany, Argentina, Spain, and Pakistan secured 3 wins and played 1 draw each. Let’s see their goal difference (Goals For – Goals Against).

(Note that if a team loses, it would lose by a minimum of 1 goal, and if it wins, it would win by a minimum of 1 goal.)

The goal difference for Germany = 1 + 3 + 2 – 1 – 1 = 4

The goal difference for Argentina = 1 + 1 + 3 – minimum (1) = maximum 4

The goal difference for Spain = 5 + minimum (1) + minimum (1) – 1 – 1 = at least 5

The goal different for Pakistan = 1 + 1 + 2 – 1 = 3

Therefore, the goal difference is maximum for Spain. Hence, it finishes at the top of the pool. **So, C is the correct option.**

**4. **This cannot be possible as Spain and Germany will have a higher goal difference than Pakistan. **So, D is the correct option.**

**Practice Exercise 4: Study the given information carefully to answer the given questions.**

**Seven persons – E, F, G, H, S, T, and U buy seven different items viz. Tie, Coat, Ring, Nail paint, Shirt, Diary and Goggles on different days. One person buys one item in a day.**

**Four persons buy items between E and the one who buys Tie. The one who buys a coat buys immediately after the one who buys Tie. Two persons buy items between H and the one who buys Tie. T buys immediately after H. F buys his item immediately after the one who buys Diary. Two persons buy items between the one who buys a coat and the one who buys Shirt. S buys Ring. Goggles were bought immediately after E. Two persons buy an item between the one who buys Ring and the one who buys Diary. U buys his item before G.**

**1. **Who among the following buys Nail paint?

A. U

B. G

C. H

D. T

E. None of these

**2. **Which item was bought immediately after Shirt?

A. Diary

B. Googles

C. Tie

D. Coat

E. None of these

**3. **How many persons buy items between S and F?

A. One

B. Two

C. Three

D. Four

E. None of these

**4. **Which of the following combination is true?

A. G – Tie

B. H – Diary

C. T – Goggles

D. E – Diary

E. None is true

**5. **Who among the following buys an item immediately before ring?

A. U

B. G

C. H

D. T

E. None of these

**> Four persons buy items between E and the one who buys Tie.**

There are four possibilities:

**> The one who buys a coat buys immediately after the one who buys Tie. Two persons buy items between H and the one who buys Tie. T buys immediately after H.**

This is not possible in Case 2. So, we reject this case.

**> F buys his item immediately after the one who buys Diary. ****Two persons buy items between the one who buys a coat and the one who buys Shirt. S buys Ring.**

**> Goggles were bought immediately after E. Two persons buy an item between the one who buys Ring and the one who buys Diary. U buys his item before G.**

This is possible only in Case 3.

Now let’s answer the questions:

**1. **H buys Nail paint. **So, C is the correct option.**

**2. **Diary was bought immediately after Shirt. **So, A is the correct option.**

**3. **Three persons buy items between S and F. **So, C is the correct option.**

**4. **E buys Diary. **So, D is the correct option.**

**5. **G buys coat immediately before S buys a ring. **So, B is the correct option.**

**Practice Exercise 5: The question below is followed by two statements (a) and (b).**

**Choose 1. If the question can be answered by using statement (a) alone but not by using (b) alone.**

**Choose 2. If the question can be answered by using statement (b) alone but not by using (a) alone.**

**Choose 3. If the question can be answered by using either statement alone.**

**Choose 4. If the question can be answered by using both the statements together but not by either statement.**

**Four friends, A, B, C, and D got the top four ranks in a competitive examination, but A did not get the first, B did not get the second, C did not get the third and D did not get the fourth rank. Who secured which rank?**

**(a) Neither A nor D were among the first 2.**

**(b) Neither B nor C was third or fourth.**

A. 1

B. 2

C. 3

D. 4

**> A did not get the first, B did not get the second, C did not get the third and D did not get the fourth rank.**

**Statement (a): Neither A nor D were among the first 2.**

This implies B and C were among the first two. Since B did not get the second rank, he must have secured the first rank. Therefore, C secured the second rank.

Also, since D did not get the fourth rank, he must have secured the third rank and hence, A must have secured the fourth rank.

Therefore, the given question can be answered by using the statement (a) alone.

**Statement (b): Neither B nor C was third or fourth.**

We know that B did not get the second rank. This implies B secured the first rank and C secured the second rank. Also, D did not get the fourth rank. Therefore, D secured the third rank and A secured the fourth rank.

Therefore, the given question can be answered by using either statement alone. **So, C is the correct option.**