**> 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: 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.**

Who among S, D, X, P, and R is shortest?

I. X is shorter than D and equal to P, R is not taller than S and D.

II. P is taller than R and equal to X. D and S are not shorter than X.

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 are not sufficient to answer the question.

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

**> Statement I:**

Height: D > X = P and S, D ≥ R

With this information, we can only infer that one of X and R is the shortest.

**> Statement II:**

Height: X = P > R and S, D ≥ X or we can write S, D ≥ X = P > R

Therefore, R is the shortest.

Hence, Data in statement II alone is sufficient to answer the question. **So, B is the correct option.**

**Practice Exercise 2: Study the information given below and answer the questions based on it.**

**Seven people A, B, C, D, E, F and G born in a different year, 1950, 1953, 1961, 1968, 1972, 1985, 1996. The base year is 2018. They like seven different fruits Mango, Guava, Pomegranate, Litchi, Apple, Fig, Banana. The Sum of ages of B and E is 90. B is elder than E. The difference between E and the one who like Fig is 11 years. The one who likes Pomegranate is younger to only two people. The sum of ages of the one who likes Pomegranate and G is 103 years. One who likes Banana is younger to G. As many people are elder to the person who likes Mango as younger to the person who likes Banana.**

**The sum of ages of A and D is 115 years. A is younger to D. The difference between the ages of A and the one who like Guava is 15. F is elder to C. The one who likes Litchi is elder to the one who likes Apple.**

**1.** Which of the following statements is **false** regarding the person born in 1972?

A. F was born in 1972.

B. G is 11 years older than the person born in 1972.

C. The person born in 1972 is 11 years older than the person who likes Litchi.

D. The person born in 1972 is 13 years older than the person who likes Fig.

E. All are incorrect

**2.** What is the difference between the age of the person who likes Apple and the one who likes Fig?

A. 14 years

B. 11 years

C. 15 years

D. 17 years

E. None of the above

**3.** What is the sum of the age of the person who likes Mango and the one who likes Banana?

A. 90 years

B. 103 years

C. 115 years

D. 112 years

E. 96 years

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

A. A – 1968 – Apple

B. C – 1985 – Fig

C. G – 1961 – Litchi

D. F – 1972 – Pomegranate

E. B – 1953 – Mango

**5.** Which of the following person was born in 1996?

A. A

B. D

C. C

D. E

E. F

**> The Sum of ages of B and E is 90. B is elder than E. The difference between E and the one who like Fig is 11 years. The one who likes Pomegranate is younger to only two people.**

There are two possibilities:

**> The sum of ages of the one who likes Pomegranate and G is 103 years. **

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

**> The sum of ages of A and D is 115 years. A is younger to D. ****The difference between the ages of A and the one who like Guava is 15.**

This implies A is 50 years old and D is 65 years old. The difference between D’s age and A’s age is 15 years. Therefore, D likes Guava.

**> One who likes Banana is younger to G. As many people are elder to the person who likes Mango as younger to the person who likes Banana. ****F is elder to C. The one who likes Litchi is elder to the one who likes Apple.**

Now let’s answer the questions:

**1. **The person who likes Litchi was born in 1961 and is 11 years older than the person who was born in 1972. **So, C is the correct option.**

**2. **The one who likes Apple is 50 years old and the one who like Fig is 33 years old. Therefore, the difference between their age is 17 years. **So, D is the correct option.**

**3. **The one who likes Mango is 68 years old and the one who likes Banana is 22 years old. The sum of their ages is 90 years.** So, A is the correct option.**

**4. ** B was born in 1950, not 1953. **So, E is the correct option.**

**5. **E was born in 1996. **So, D is the correct option.**

**Practice Exercise 3: Read the given information and answer the questions that follow.**

**In a bar, there are seven frequent visitors who visit the bar daily. On being asked about their visit to the bar last Sunday, the following were their answers.**

**Jai Chand: I came in first and the next two persons to enter were Sohan Singh and Shail Munshi, When I left the bar, Jai Prakash and Vinod Rai were present in the bar. Deepak Garg left with me.**

**Jai Prakash: When I entered the bar with Vinod Rai, Jai Chand was sitting there. There was someone else also, but I was not in the position to recognize him.**

**Shail Munshi: I went to the bar for a short while last Sunday and met Jai Chand, Sohan Singh and Deepak Garg there.**

**Sohan Singh: I left immediately after Shail Munshi left.**

**Deepak Garg: I met Jai Chand, Sohan Singh, Shail Munshi, Jai Prakash, and Vinod Rai during my first visit to the bar. But I got an urgent call and came out of the bar with Jai Chand. When I went to the bar for the second time, Jai Prakash and Vinod Rai were there.**

**Pradeep Kumar: I had some urgent work, so I did not sit in the bar for a long time. Jai Prakash and Deepak Garg were the only people in the bar while I was there.**

**Vinod Rai: I was drunk and I don’t remember anything.**

**1. **Who among Jai Prakash and Deepak Garg, entered the bar first?

A. Jai Prakash

B. Deepak Garg

C. Both entered together

D. Cannot be determined

**2. **Who was sitting with Jai Chand when Jai Prakash entered the bar?

A. Sohan Singh

B. Shail Munshi

C. Deepak Garg

D. Pradeep Kumar

**3. **How many of the seven members did Vinod Rai meet on Sunday in the bar?

A. 2

B. 3

C. 4

D. 5

**4. **Who were the last two persons to leave the bar?

A. Jai Chand and Deepak Garg

B. Pradeep Kumar and Deepak Garg

C. Jai Prakash and Pradeep Kumar

D. Jai Prakash and Deepak Garg

**Jai Chand: I came in first and the next two persons to enter were Sohan Singh and Shail Munshi, When I left the bar, Jai Prakash and Vinod Rai were present in the bar. Deepak Garg left with me.**

**>** Jai Prakash, Vinod Rai, and Deepak Garg entered the bar after Sohan Singh and Shail Munshi.

**>** Before Jai Chand left the bar with Deepak Garg, Sohan Singh and Shail Munshi had already left the bar.

**Jai Prakash: When I entered the bar with Vinod Rai, Jai Chand was sitting there. There was someone else also, but I was not in the position to recognize him.**

Only two persons were there when Jai Prakash entered the bar with Vinod Rai.

**Shail Munshi: I went to the bar for a short while last Sunday and met Jai Chand, Sohan Singh and Deepak Garg there.**

This implies Shail Munshi left after Deepak Garg entered the bar.

**Sohan Singh: I left immediately after Shail Munshi left.**

We can make the following table to represent these events.

When Jai Prakash entered with Vinod Rai, Jai Chand and Deepak Garg were there in the bar.

**Deepak Garg: I met Jai Chand, Sohan Singh, Shail Munshi, Jai Prakash, and Vinod Rai during my first visit to the bar. But I got an urgent call and came out of the bar with Jai Chand. When I went to the bar for the second time, Jai Prakash and Vinod Rai were there.**

**Pradeep Kumar: I had some urgent work, so I did not sit in the bar for a long time. Jai Prakash and Deepak Garg were the only people in the bar while I was there.**

This implies Vinod Rai left before Pradeep Kumar entered the bar. When Pradeep Kumar left, Deepak Garg and Jai Prakash were there in the bar.

Now let’s answer the questions:

**1. **Deepak Garg entered the bar before Jai Prakash. **So, B is the correct option.**

**2. **When Jai Prakash entered, Jai Chand and Deepak Garg were there in the bar. **So, C is the correct option.**

**3. **Vinod Rai met Jai Chand, Deepak Garg, and Jai Prakash. He enters after Shail Munshi and Sohan Singh had left the bar and leaves before Pradeep Kumar enters the bar. Therefore, he meets 3 members.** So, B is the correct option.**

**4. **Jai Prakash and Deepak Garg were the last two persons to leave the bar.** So, D is the correct option.**

**Practice Exercise 4: Read the information given below and answer the questions that follow.**

**A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam, and Himachal. ****These teas were placed in six cups, numbered 1 to 6, not necessarily in the same order. The tea taster was asked to rate these ****teas on the strength of their flavor on a scale of 1 to 10. He gave a unique integer rating to each tea. Some other information ****is given below:**

**1. Cup 6 contained tea from Himachal.**

**2. Tea from Ooty got the highest rating, but it was not in Cup 3.**

**3. The rating of tea in Cup 3 was double the rating of the tea in Cup 5.**

**4. Only two cups got ratings in even numbers.**

**5. Cup 2 got the minimum rating and this rating was an even number.**

**6. Tea in Cup 3 got a higher rating than that in Cup 1.**

**7. The rating of tea from Wayanad was more than the rating of tea from Munnar but less than that from Assam.**

**1. **What was the second-highest rating given?

A. 7

B. 5

C. 3

D. 2

**2. **What was the number of the cup that contained tea from Ooty?

A. 4

B. 6

C. 5

D. Cannot be determined

**3. **If the tea from Munnar did not get the minimum rating, what was the rating of the tea from Wayanad?

A. 3

B. 5

C. 1

D. 6

**4. **If cups containing teas from Wayanad and Ooty had consecutive numbers, which of the following statements may be true?

A. Cup 5 contains tea from Assam

B. Cup 1 contains tea from Darjeeling

C. Tea from Wayanad has got a rating of 6

D. Tea from Darjeeling got the minimum rating

**> Cup 6 contained tea from Himachal.**

**> Only two cups got ratings in even numbers. The rating of tea in Cup 3 was double the rating of the tea in Cup 5. Cup 2 got the minimum rating and this rating was an even number. Tea from Ooty got the highest rating, but it was not in Cup 3. Tea in Cup 3 got a higher rating than that in Cup 1.**

Rating of tea in cup 3 must be an even number. Since only two cups got ratings in even numbers, rating of cup 5 must be an odd number. Therefore, cup 3 can have a rating of 2, 6 and 10.

Also, the rating of tea in cup 3 is not the highest and it is greater than cup 1, cup 2 and cup 5. So, cup 3 can’t have a rating of 2 and 10. Therefore, it has a rating of 6. This implies cup 5 has a rating of 3.

Since cup 2 has got the minimum rating which is an even number, it must be 2.

Cup 1 has got the rating which is an odd number, and it should be greater than 2 and not less than 6. Therefore, it is 5.

The other two ratings must also be odd numbers greater than 2. Therefore, the other two ratings are 7 and 9. Remember that the tea from Ooty got the highest rating.

**> The rating of tea from Wayanad was more than the rating of tea from Munnar but less than that from Assam.**

Tea Rating: Assam > Wayanad > Munnar

We cannot determine whether the rating of tea from Darjeeling is more or less than that from Assam, Wayanad, and Munnar.

Now let’s answer the questions:

**1. **The second-highest rating given was 7. **So, A is the correct option.**

**2. **Cup number 4 contained the tea from Ooty. **So, A is the correct option.**

**3. **This implies that the tea from Darjeeling got the minimum rating.

The rating of tea from Wayanad is 5. **So, B is the correct option.**

**4. ****Cups containing teas from Wayanad and Ooty had consecutive numbers.**

Since the rating of tea from Wayanad is less than that from Assam, it must be in cup 5.

**Option (B) is correct.**

**Practice Exercise 5: The table below shows the number of goals scored by the top four international footballers in all International matches for each year from 2013-2016.**

**The goals scored by the four top goal scorers for each year between 2013 and 2016 have been represented as P, Q, R, and S in no particular order. It was the same set of four footballers – Lionel Messi, Neymar Jr., Wayne Rooney and Cristiano Ronaldo (in no particular order) who were the top goal scorers in each year.**

**The following additional information is provided too:**

**> Lionel Messi was the highest goal scorer in either 2015 or 2016.**

**> The total number of goals scored in the four years by Neymar Jr. and Cristiano Ronaldo differ by 9.**

**> The letter representing Wayne Rooney, was neither P nor S.**

**1. **If the difference in the number of goals scored by Cristiano Ronaldo and Lionel Messi is 3, in 2016, then in how many years did Wayne Rooney scored more than 60 goals?

A. 0

B. 1

C. 2

D. Cannot be determined

**2. **The highest possible number of goals scored by Wayne Rooney and Neymar Jr. together in any of these four years is?

A. 128

B. 130

C. 126

D. 127

**3. **Given the following two statements, what can be said regarding the goals scored by the footballers?

**Statement 1: **At least one of the other three footballers scored more goals than Cristiano Ronaldo, across the four years combined.

**Statement 2: **Wayne Rooney scored less goals than Lionel Messi in 2015.

A. If statement 1 is false, statement 2 is false

B. If statement 2 is true, statement 1 is false

C. If statement 2 is false, statement 1 is true

D. None of the above

Total number of goals scored by P in the four years = 229

Total number of goals scored by Q in the four years = 220

Total number of goals scored by R in the four years = 229

Total number of goals scored by S in the four years = 220

Based on the information given, there are two possibilities:

**1. **This is possible in case 2 if Q represents Cristiano Ronaldo. In this case, Wayne Rooney scored 61 goals in 2013 and 65 goals in 2015. Therefore, he scores more than 60 goals in 2 years. **So, C is the correct option.**

**2. **The highest possible number of goals scored by Wayne Rooney and Neymar Jr. together is 128. This happens in Case 1 in 2015 in which Wayne Rooney scores 62 goals and Neymar Jr. scores 66 goals. **So, A is the correct option.**

**3.**

**>** Statement 1 is false if Cristiano Ronaldo scores 229 goals. This is possible in Case 1 as well as Case 2. In Case 1, Wayne Rooney scores more goals than Lionel Messi in 2015, and in Case 2, Wayne Rooney scores less goals than Lionel Messi in 2015. So, we can’t say whether statement 2 is true or false.

**>** If Statement 2 is true, Case 2 holds, and if it is false, Case 1 holds. In both cases, there are further two possibilities, one in which Cristiano Ronaldo scores 220 goals, and the other in which he scores 229 goals. So, we can’t say whether statement 1 is true or false.

**Therefore, D is the correct option.**