**> Ranking and Ordering: Introduction**

**> Ranking and Ordering: Solved Examples**

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

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

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

**Ranking and Ordering Question 1: Study the information given below and answer the questions based on it.**

**A. Nine boxes A, B, C, D, E, F, G, H and I are kept one above another not necessarily in the same order.**

**B. There are three boxes between H and G and neither of them is at the top or the bottom position.**

**C. There are two boxes between F and C and box F is above box C.**

**D. Box C is above box G. Two boxes are there between G and C.**

**E. The number of boxes between A and H is the same as that of A and G.**

**F. Box D is above box E and there is more than one box in between D and E.**

**G. Box E is not at the bottom position. Two boxes are there between E and I.**

**1. **Which of the following boxes is at the top?

A. Box C

B. Box F

C. Box D

D. Box E

E. Box B

**2. **How many boxes are there between box C and box E?

A. None

B. 1

C. 2

D. 3

E. 4

**3. **What is the position of box H from the top?

A.1st

B. 2nd

C. 3rd

D. 4th

E. 5th

**4. **Which of the following boxes is not below C?

A. Box A

B. Box E

C. Box G

D. Box D

E. Box B

**5. **Which of the following boxes is just above box B?

A. Box G

B. Box E

C. Box A

D. Box H

E. Box D

To begin with, we can draw this table:

**> From Clues (B), (C), and (D): There are two boxes between F and C, and two between C and G. Box F is above box C, and box C is above box G. There are three boxes between H and G. Neither of H and G are at the top or the bottom position.**

**Possibility 1:** Box G is at 2nd position. Then Box C would be at 5th position, and box F at 8th position.

**Possibility 2:** Box G is at 3rd position. Then Box C would be at 6th position, and box F at 9th position.

So, there are two possibilities:

**> Clue (E): The number of boxes between A and H is same as that of A and G.**

**> Clue (G): Box E is not at the bottom position. Two boxes are between E and I.**

This is possible only in Case II if we place E at 4th position and I at 1st position. So, we reject Case I.

**> Clue (F): Box D is above box E and there is more than one box D and E.**

This implies that box D is at 8th position and therefore, box B is at 2nd position.

Now let’s answer the questions:

**1. **Box F is at the top. **So, B is the correct option.**

**2. **There is 1 box between C and E. **So, B is the correct option.**

**3. **Box H is at 3rd position from the top. **So, C is the correct option.**

**4. **Box D is above box C. **So, D is the correct option.**

**5. **Box G is just above Box B. **So, A is the correct option.**

**Ranking and Ordering Question 2: In a school, there are five teachers A, B, C, D and E. A and B teach Hindi and English. C and B teach English and Geography. D and A teach Mathematics and Hindi. E and B teach History and French. Who teaches the maximum number of subjects?**

**a. A**

**b. B**

**c. C**

**d. D**

**e. E**

**> Subject taught by A: Hindi, English, Mathematics**

**> Subject taught by B: Hindi, English, Geography, History, French**

**> Subject taught by C: English, Geography**

**> Subject taught by D: Hindi, Mathematics**

**> Subject taught by E: History, French**

Clearly, B teaches the maximum number of subjects. **So, (b) is the correct option.**

**Ranking and Ordering Question 3: Refer to the following statements and answer the questions:**

**A. Seven students Pepper, James, Raman, Harry, Tony, Deepak, and David take a series of tests.**

**B. No two students get similar marks.**

**C. David always scores more than Pepper.**

**D. Pepper always scores more than James.**

**E. Each time either Raman scores the highest and Tony gets the least, or alternatively Harry scores the highest and Deepak or James scores the least.**

**1. **If Harry is ranked 6th and James is ranked 5th, which of the following can be true?

A. David is ranked first or fourth

B. Raman is ranked second or third

C. Tony is ranked fourth or fifth

D. Deepak is ranked third or fourth

**2. **If Raman gets the highest, David should be ranked not lower than:

A. Second

B. Third

C. Fourth

D. Fifth

**3. **If Raman is ranked second and James is ranked first, which of the following must be true?

A. Harry is ranked third

B. Tony is ranked third

C. Pepper is ranked sixth

D. None of these

**4. **If Harry is ranked second, which of the following can be true?

A. Deepak gets more than David

B. David gets more than Harry

C. Pepper gets more than Raman

D. Pepper gets more than David

**5. **If David is ranked fifth, which of the following must be true?

A. Harry scores the highest

B. Raman is ranked second

C. Tony is ranked third

D. James is ranked second

**Clue E: Each time either Raman scores the highest and Tony gets the least, or Harry scores the highest and Deepak or James scores the least.**

There are two possibilities:

**1.** If Harry is ranked 6th and James is ranked 5th, then Raman’s rank would be 1st, and Tony’s rank would be 7th.

From Clues (C) and (D), we know that David always scores more than Pepper, who always scores more than James. So, we have:

**> **If Pepper’s rank is 4th, then David’s rank could be 2nd or 3rd. If David’s rank is 2nd, then Deepak’s rank would be 3rd and vice-versa.

**> **If Pepper’s rank is 3rd, then David’s rank would be 2nd, and therefore Deepak’s rank would be 4th.

Thus, Raman is ranked first, Tony is ranked seventh, David is ranked second or third, and Deepak is ranked second, third or fourth.** So, D is the correct option.**

**2. **If Raman is ranked 1st, then Tony’s rank would be 7th. David always scores more than Pepper and James. This implies if James’ rank is 6th and Pepper’s rank is 5th, then David’s rank would be 4th. So, David’s rank would not be lower than 4th. **Therefore, C is the correct option.**

**3. **It is given that Pepper always scores more than James. So, James can’t be ranked first and hence, this case is not possible. **Therefore, D is the correct option.**

**4. **If Harry is ranked 2nd, then Raman’s would be 1st and Tony’s rank would be 7th. In this case, David cannot get more marks than Harry and Pepper cannot get more marks than Raman. Also, we know that David always scores more than Pepper. So, options (B), (C) and (D) are not correct.

Deepak can get more marks than David. In that case, David’s rank would 4th, and Deepak’s rank would be 3rd.** So, option A is correct.**

**5. **If David’s rank is 5th, then Pepper’s rank would be 6th, James’ rank would be 7th and Harry’s rank would be 1st. **So, A is the correct option.**

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