**> 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: ****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.**

**What is Sunita’s rank from the top in the class of 40 students?**

**(a) Rani is 4 ranks below Sunita and is thirty first from the bottom.**

**(b) Amit is two ranks above Sunita and is thirty-seventh from the bottom.**

A. 1

B. 2

C. 3

D. 4

**Statement (a): Rani is 4 ranks below Sunita and is thirty first from the bottom.**

Rani’s rank from the top = (Total number of students) – (Rani’s rank from the bottom) + 1

= 40 – 31 + 1 = 10

Therefore, Sunita’s rank from the top = Rani’s rank from the top – 4

= 10 – 4 = 6

**Statement (b): Amit is two ranks above Sunita and is thirty-seventh from the bottom.**

This implies Sunita’s rank is thirty-fifth from the bottom.

Therefore, Sunita’s rank from the top = (Total number of students) – (Sunita’s rank from the top) + 1

= 40 – 35 + 1 = 6

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

**Practice Exercise 2: ****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.**

**Who is tallest among the five boys Samar, Ramesh, Rakesh, Karan, and Vishwas?**

**(a) Rakesh is taller than Karan and Ramesh, but not as tall as Samar.**

**(b) Samar is not the tallest.**

A. 1

B. 2

C. 3

D. 4

**Statement (a): Rakesh is taller than Karan and Ramesh, but not as tall as Samar.**

Height: Samar > Rakesh > Karan, Ramesh

We cannot determine if Samar is taller or shorter than Vishwas.

**Statement (b): Samar is not the tallest.**

Clearly, this statement alone does not tell who is the tallest among the five boys.

With the help of the statement (a), we know that Samar is taller than Rakesh, Karan, and Ramesh. Using the information given in statement (b), we can infer that Vishwas is the tallest.

Therefore, the question can be answered by using both the statements together but not by either statement. **So, D is the correct option.**

**Practice Exercise 3: Study the following information carefully and answer the questions given below.**

**A building has eight floors numbered one to eight, in such a way that the ground floor is numbered one, the floor above it, numbered two and so on such that the top floor is numbered eight. One out of eight persons viz, J, K, L, M, V, W, X, and Y lives on one of these floors.**

**L lives on floor number 6. Only one person lives between L and X. Only two persons live between V and W. V lives on a floor above W’s floor. V lives on an even-numbered floor. Only one person lives between W and K. Only two persons live between Y and J. J lives on one of the floors above Y.**

**1. **Who lives on the topmost floor?

A. X

B. V

C. M

D. W

E. K

**2. **Who lives exactly between the floors on which Y and J live?

A. V, W

B. W, X

C. L, V

D. M, W

E. V, K

**3. **Who lives on floor number 5?

A. X

B. K

C. M

D. J

E. W

**4. **Who amongst the following lives on the floor immediately above the floor on which Y lives?

A. M

B. K

C. L

D. No one as Y lives on the topmost floor

E. J

**5. **Which of the following statements is true with respect to the given arrangement?

A. Y lives on floor number 7.

B. W lives on a floor immediately above Y’s floor.

C. None of the given options is true.

D. M lives on the lowermost floor.

E. V lives on floor number 4.

**1. **X lives on the topmost floor. **So, A is the correct option.**

**2. **V, K lives exactly between the floors on which Y and J live. **So, E is the correct option.**

**3. **J lives on floor number 5. **So, D is the correct option.**

**4. **K lives on the floor immediately above the floor on which Y lives. **So, B is the correct option.**

**5. **V lives on floor number 4. **So, E is the correct option.**

**Practice Exercise 4:**** ****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.**

**Among M, N, D, P, and K, who earns more than only the least earner among them?**

**(a) N earns more than M and P but less than only D.**

**(b) M earns more than P who earns more than K.**

A. 1

B. 2

C. 3

D. 4

**Statement (a): N earns more than M and P but less than only D.**

N earns less than only D. This implies D earns the highest.

Earnings: D > N > M, P and K

Based on this statement alone, we can’t tell who earns more than only the least earner among M, N, D, P, and K.

**Statement (b): M earns more than P, who earns more than K.**

Earnings: M > P > K

Using this statement alone, we can’t decide who is the least earner as we don’t know about the earnings of N and D.

Using both the statements, we get this order of earnings: D > N > M > P > K

Therefore, P earns more than only the least earner, who is K. Hence, both the statements are necessary to answer the given question. **So, D 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 5. If the question cannot be answered by using either or both the statements together.**

**Who among P, Q, R, S, and T is the lightest?**

**(a) R is heavier than Q and T but lighter than S.**

**(b) S is not the heaviest.**

A. 1

B. 2

C. 3

D. 4

E. 5

**Statement (a): R is heavier than Q and T but lighter than S.**

Weight: S > R > Q, T

**Statement (b): S is not the heaviest.**

Clearly, the given question cannot be answered by using either statement alone.

Let’s use both the statements together.

Since S is not the heaviest, P must be heavier than S.

Weight: P > S > R > Q, T

Still, we cannot determine who among Q and T is lighter. Therefore, the given question cannot be answered using these two statements.** So, E is the correct option.**

**Practice Exercise 6: Six boys A, B, C, D, E, and F play a game of cards. Each has a pack of 10 cards. F borrows 2 cards from A and gives away 5 to C who in turn gives 3 to B while B gives 6 to D who passes on 1 to E. Then the number of cards possessed by D and E is equal to the number of cards possessed by**

A. A, B and C

B. B, C and F

C. A, B and F

D. A, C and F

**> F borrows 2 cards from A and gives away 5 to C.**

Number of cards with F = 10 + 2 – 5 = 7

Number of cards with A = 10 – 2 = 8

Number of cards with C = 10 + 5 = 15

**> C gives 3 cards to B while B gives 6 to D who passes on 1 to E**

Number of cards with C = 15 – 3 = 12

Number of cards with B = 10 + 3 – 6 = 7

Number of cards with D = 10 + 6 – 1 = 15

Number of cards with E = 10 + 1 = 11

Number of cards possessed by D and E = 15 + 11 = 26

Number of cards possessed by A, B and C = 8 + 7 + 12 = 27

Number of cards possessed by B, C and F = 7 + 12 + 7 = 26

Number of cards possessed by A, B and F = 8 + 7 + 7 = 22

Number of cards possessed by A, C and F = 8 + 15 + 7 = 30

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