**> 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 based on the following information.**

**Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium or low.**

**1. Contamination levels at three pumps among P1 – P5 were recorded as high.**

**2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.**

**3. P7 and P8 are the only two consecutively numbered pumps, where the same levels of contamination were recorded.**

**4. High contamination levels were not recorded at any of the pumps P16 – P20.**

**5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.**

**1. **Which of the following must be true?

A. The contamination level at P10 was recorded as high.

B. The contamination level at P12 was recorded as high.

C. The contamination level at P13 was recorded as low.

D. The contamination level at P20 was recorded as medium.

**2. **What can be said about the number of pumps at which the contamination levels were recorded as medium?

A. More than 4

B. At most 9

C. Exactly 8

D. At least 8

**3. **If the contamination level at P11 was recorded as low, then which of the following must be true?

A. The contamination level at P18 was recorded as low

B. The contamination level at P12 was recorded as high

C. The contamination level at P14 was recorded as medium

D. The contamination level at P18 was recorded as medium

**4. **If the contamination level at P15 was recorded as medium, then which of the following must be false?

A. Contamination level at P11 and P16 were recorded as same

B. Contamination level at P10 and P14 were recorded as same

C. Contamination level at P13 and P17 were recorded as same

D. Contamination level at P14 was recorded to be higher than that of P15

**From clues (1), (2) and (3), we get the following possibilities for P1 – P10:**

**From clue (4), we get the following possibilities for P16 – P20:**

From clue (5), we can deduce that the total number of low contamination pumps and high contamination pumps should be a multiple of 3.

**Case 1:**

In this case, we already have 4 low contamination pumps, which implies there should be 8 high contamination pumps. For this, we need to add 4 high contamination pumps, which is not possible as no two consecutive pumps can have same levels of contamination except P7 and P8. So, we reject this case.

**Case 2:**

In this case, we have 3 low contamination pumps and 4 high contamination pumps. So, either we should add 2 high contamination pumps and 3 medium contamination pumps, or we should add 1 low contamination pump and 3 high contamination pumps. Both of which is not possible. So, we reject this case as well.

**Case 3:**

In this case, we have 4 low contamination pumps and 6 high contamination pumps. So, we should add 2 high contamination pumps and 3 medium contamination pumps.

**Case 4:**

In this case, we have 3 low contamination pumps and 6 high contamination pumps. So, we should add 1 low contamination pump, 2 high contamination pumps and 2 medium contamination pumps.

It can be done in 5 ways:

Now let’s answer the questions:

**1. **The contamination level at P10 was recorded high. **So, A is the correct option.**

**2. **The number of pumps at which contamination level is medium is exactly 8.** So, C is the correct option.**

**3. **We can see in the above possibilities that if the contamination level at P11 was recorded low, the contamination level at P14 was recorded as medium. **So, C is the correct option.**

**4. **If the contamination level in P15 was recorded as medium, the contamination level of P11 was recorded as medium and that of P16 as low. **So, A is the correct option.**

**Practice Exercise 2: Geeta is senior to Shilpa but not Kara. Sam is junior to Kara. No one is senior to Fatima. Who is the most junior?**

A. Shilpa

B. Geeta

C. Sam

D. Data Inadequate

E. None of the above

**> Geeta is senior to Shilpa but not Kara.**

Kara > Geeta > Shilpa

**> Sam is junior to Kara.**

Kara > Sam

**> No one is senior to Fatima.**

Fatima > Kara > Geeta > Shilpa

Fatima > Kara > Sam

We cannot determine who is junior among Sam and Shilpa. **So, D is the correct option.**

**Practice Exercise 3: Among A, B, C, D and E each having different height, B is shorter than only E and A is taller than only D. Who will be the third when they are arranged in descending order of their height?**

A. C

B. D

C. B

D. Data Inadequate

E. None of these

**> B is shorter than only E.**

This implies E is the tallest of all.

**> A is taller than only D.**

This implies D is the shortest of all.

Descending order of height: E > B > C > A > D

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

**Practice Exercise 4: In a row of children facing North, Steven is 12th from the left end. Virat who is twenty-second from the right end is fourth to the right of Steven. How many children in total are there in the row?**

A. 35

B. 36

C. 37

D. 34

E. None of these

Virat’s position from the left end = Steven’s position from the left end + 4 = 16th

Therefore, total number of children in the row = (Virat’s position from the left end) + (Virat’s position from the right end) – 1

= 16 + 22 – 1 = 37

**So, C is the correct option.**

**Practice Exercise 5: In a class of 40 students, Tim’s rank from the top is twelfth. Joe is eight ranks below Tim. What is Joe’s rank from the bottom?**

A. 20th

B. 21st

C. 22nd

D. 19th

E. None of these

Joe’s rank from the top = Tim’s rank from the top + 8 = 20th

Therefore, Joe’s rank from the bottom = (Total number of students in the class) – (Joe’s rank from the top) + 1

= 40 – 20 + 1 = 21st

**So, B is the correct option.**