**> 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: Answer the questions on the basis of the information given below.**

**A tournament was organized among five teams, Red Backs, Warriors, Royals, Daredevils, and Chargers. This was a round-robin league tournament where each team has to play every other team exactly once. For any team, three points are awarded for a win, one point for a draw and no point for a loss.**

**The following table was still incomplete even after the end of the tournament.**

**where W = Number of matches won**

**D = Number of matches drawn**

**L = Number of matches lost**

**P = Total Points**

**It is known that the match between Red Backs and Chargers resulted in a draw. **

**1. **Which teams did Red Backs beat?

A. Only Daredevils and Chargers

B. Only Daredevils

C. Only Warriors and Royals

D. Only Warriors and Chargers

**2. **Which team(s) drew the match with Warriors?

A. Only Red Backs

B. Only Royals and Daredevils

C. Only Daredevils and Chargers

D. Only Chargers

**3. **Which team has the highest number of draws?

A. Warriors

B. Red Backs

C. Royals

D. Daredevils

The points table would be as follows:

Matches Drawn:

**>** Since Warriors and Royals didn’t win any match, the match between them must have resulted in a draw.

**>** It is given that one match was drawn between Red Backs and Chargers. Therefore, Daredevils must have drawn one match with Warriors.

Now let’s answer the questions:

**1. **Red Backs lost one match to Daredevils and won against Warriors and Royals. **So, C is the correct option.**

**2. **Royals and Daredevils drew the match with Warriors. **So, B is the correct option.**

**3. **Warriors has the highest number of draws.** So, A is the correct option.**

**Practice Exercise 2: A question and two statements numbered I and II are given below. You have to decide whether the data provided in which of the statements are sufficient to answer the question or not.**

**Eight persons A, B, C, D, E, F, G, and H are staying on an eight-storey building. Lowermost floor is numbered 1 and the topmost floor is numbered 8. Who among the following lives on the top floor?**

**I. ‘A’ lives on an even-numbered floor but not on the top floor. Three floors are between A and H. The number of the persons above H is same as below E. C lives just above E but not on the top floor. **

**II. Two floors are between A and D. One floor is between D and F. G lives two floors above E. A live just above G.**

A. Data in statement I alone is sufficient to answer the question.

B. Data in statement II alone is sufficient to answer the question.

C. Data either in statement I alone or statement II alone is sufficient to answer the question.

D. Data given in both I and II together is not sufficient to answer the question.

E. Data in both the statements I and II together is necessary to answer the question.

**Statement I:**

**> ‘A’ lives on an even-numbered floor but not on the top floor. Three floors are between A and H. The number of the persons above H is same as below E.**

There are three possibilities:

**> C lives just above E but not on the top floor.**

This is not possible in Case 3. So, we reject this case.

So, based on Statement I alone we can’t figure out who lives on the top floor.

**Statement II:**

Going through the hints given in Statement II, we can see that this statement alone wouldn’t be sufficient to figure out who lives on the top floor. So, let’s use it along with the Statement I.

**> Two floors are between A and D. One floor is between D and F.**

**> G lives two floors above E. ****A live just above G.**

This is possible only in Case 2. So, we reject Case 1.

Therefore, H lives on the top floor. Hence, data given in both statements is necessary to figure out who lives on the top floor. **So, E is the correct option.**

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

**In a recently held test series consisting of three matches – 1st, 2nd, and 3rd, five players – Sehwag, Ganguly, Tendulkar, Dravid, and Laxman, are the top five scoring batsmen, not necessarily in the same order.**

**(i) No two players scored the same number of runs in any match.**

**(ii) Sehwag scored more runs than Ganguly in the 1st and 2nd matches.**

**(iii) The player who scored highest runs in the 3rd match scored the least runs in the 1st match.**

**(iv) Dravid scored more runs than Laxman but less runs than Tendulkar in the 2nd match. Tendulkar scored more runs than Laxman in the 1st match.**

**Laxman scored more runs than Ganguly but less runs than Dravid in the 3rd match.**

**(v) Tendulkar scored lowest runs in one match and in two matches his position in the decreasing order of the runs scored by the batsmen is same. He was not the top scorer in any of the three matches.**

**1. **Among the given five players, who scored the least number of runs in the 3rd match?

A. Sehwag

B. Ganguly

C. Tendulkar

D. Cannot be determined

**2. **If Tendulkar scored more runs than Ganguly in the 2nd match, then who is the second-highest scorer in the 1st match?

A. Sehwag

B. Laxman

C. Dravid

D. None of these

From the given information, decreasing order of batsmen in terms of runs scored by them in the three matches is:

1st match: Sehwag > Ganguly and Tendulkar > Laxman

2nd match: Sehwag > Ganguly and Tendulkar > Dravid > Laxman

3rd match: Dravid > Laxman > Ganguly

**1. **It is given that Tendulkar scored lowest runs in one match. Clearly, it must be the third match.** So, C is the correct option.**

**2. **It is given that Tendulkar was not the top scorer in any of the three matches. So, he must have scored less runs than Sehwag in the 2nd match.

2nd match: Sehwag > Tendulkar > Ganguly, Dravid, and Laxman

Also, it is given that Tendulkar’s position in the decreasing order of runs scored by the batsmen is same in two matches.

Therefore, he must be the second-highest scorer in the 1st match as well. **So, D is the correct option.**

**Practice Exercise 4: The question given below consists of three statements. You have to decide whether the data provided in the statements is sufficient to answer the question.**

**Who earns most among A, B, C, D, and E?**

**I. A earns less than C but not less than E**

**II. D earns more than A but not equal to B**

**III. B earns more than A and E**

A. Data in statement I alone is sufficient to answer the question.

B. Data in statement II alone is sufficient to answer the question.

C. Data in statement III alone is sufficient to answer the question.

D. Data in all the statements together is necessary to answer the question.

E. Data in all the statements together is not sufficient to answer the question.

**Statement I: A earns less than C but not less than E**

Earnings: C > A ≥ E

**Statement II: D earns more than A but not equal to B**

Earnings: D > A and D ≠ B

**Statement III: B earns more than A and E**

Earnings: B > A ≥ E

Clearly, even with all the statements together, we cannot determine who among A, B, C, D, and E earns the most. **So, E is the correct option.**

**Practice Exercise 5: Answer the following questions based on the statements given below.**

**(i) There are three houses on each side of the road.**

**(ii) These six houses are labeled as P, Q, R, S, T, and U.**

**(iii) These houses are of different colors, namely, Red, Blue, Green, Orange, Yellow, and White.**

**(iv) These houses are of different heights.**

**(v) T, the tallest house, is exactly opposite to the Red house.**

**(vi) The shortest house is exactly opposite to the Green-colored house.**

**(vii) U, the Orange colored house, is located between P and S.**

**(viii) R, the Yellow-colored house, is exactly opposite to P.**

**(ix) Q, the Green colored house, is exactly opposite to U.**

**(x) P, the White-colored house, is taller than R, but shorter than S and Q.**

**1. **What is the color of the house diagonally opposite to the Yellow-colored house?

A. White

B. Blue

C. Green

D. Red

E. None of these

**2. **Which is the second tallest house?

A. P

B. S

C. Q

D. R

E. Cannot be determined

**3. **What is the color of the tallest house?

A. Red

B. Blue

C. Green

D. Yellow

E. None of these

**> Clue (vii): U, the Orange colored house, is located between P and S.**

There are two possibilities:

**> Clue (viii), (ix) and (x): R, the Yellow-colored house, is exactly opposite to P. Q, the Green colored house, is exactly opposite to U. P, the White-colored house, is taller than R, but shorter than S and Q.**

**Height: S, Q > P > R**

**> Clue (v) and (vi): ****T, the tallest house, is exactly opposite to the Red house.**** The shortest house is exactly opposite to the Green-colored house.**

**Height: T > S, Q > P > R > U**

Now let’s answer the questions:

**1. **Red-colored house is diagonally opposite to the Yellow-colored house.** So, D is the correct option.**

**2. **The second tallest house is either S or Q.** So, E is the correct option.**

**3. **T is the tallest house, and it is blue in color. **So, B is the correct option.**