Introduction

In reasoning based on ranking, we are required to arrange or order a certain number of people or objects in increasing or decreasing order of their particular attribute. This attribute can be height, weight, performance (in a game, exam, etc.), age, position in a row, etc.

There is no particular method to solve these problems. But there are a few tips that can help solve these questions:

1. Use the direct hints/clues (the ones that tell the position or rank directly) first.

2. As you go through the clues, make their visual representation so that you don’t have to read again.

Let’s see some examples.

Ranking and Ordering Question 1: Read the following information carefully and answer the questions.

> A, B, C, and D live on floors 3 to 6 of the same storeyed building.

> A lives on the fourth floor.

> Only one person lives on the floor between A and B.

> C does not live on a floor between A and B

1. Who lives on the floor immediately above B’s floor?

2. Who lives on the 5th floor?

Answer and Explanation:

The first step to solve these problems is to make a table as shown below:

Ranking and Order Example 1: Table 1

> A lives on the fourth floor.

Ranking and Order Example 1 Table (Part - 2)

> Only one person lives on the floor between A and B

This implies B lives on the 6th floor.

Ranking and Order Example 1 Table (Part - 3)

> C does not live on a floor between A and B

This implies C lives on the 3rd floor and therefore, D lives on the 5th floor.

Ranking and Order Example 1 Table (Part - 4)

Now let’s answer the questions:

1. B lives on the top floor. So, no one among C, A, and D lives on the floor immediately above B’s floor.

2. D lives on the 5th floor.

Ranking and Ordering Question 2: Read the following information and answer the questions.

> A, B, C, D, E, and F are six students in a class.

> B and C are shorter than F but heavier than A.

> D is heavier than B and taller than C.

> E is shorter than D but taller than F.

> F is heavier than D.

> A is shorter than E but taller than F.

1. Who among them is the tallest?

A. B

B. A

C. D

D. E

E. None of these

2. Who is third from the top when they are arranged in descending order of their height?

A. A

B. E

C. B

D. C

E. None of these

3. Which of the following is true for F as regarding height and weight?

A. He is heavier than B but shorter than D.

B. He is lighter than B and C but taller than D.

C. He is heavier than B and taller than E.

D. He is lighter than E and also shorter than E.

E. He is lighter than E and taller than E.

Answer and Explanation:

> B and C are shorter than F but heavier than A.

Height: F > B, C

Weight: B,C > A

> D is heavier than B and taller than C.

Height: D > C

Weight: D > B > A

> E is shorter than D but taller than F.

Height: D > E > F > B, C

> F is heavier than D.

Weight: F > D > B > A

> A is shorter than E but taller than F.

Height: D > E > A > F > B, C

> We don’t know who among B and C is taller.

> Also, we don’t know the position of C and E in weight. The only information we have is that C is heavier than A.

Now let’s answer the questions:

1. D is the tallest. So, C is the correct option.

2. A is third from the top when the students are arranged in descending order of their height. So, A is the correct option.

3. F is heavier than B but shorter than D. So, A is the correct option.

Ranking and Ordering Question 3: In a class of 64 students Senorita ranks 19th from the top. What would be her rank from the bottom?

A. 45th

B. 46th

C. 44th

D. Data inadequate

E. None of these

Answer and Explanation:

Senorita’s rank from the bottom = Total number of students – Senorita’s rank from the bottom + 1

= 64 – 19 + 1 = 46th

Therefore, B is the correct option.

Ranking and Ordering Question 4: Laura is five ranks below top student Tommy in a class of 40 students. What is Laura’s rank from the bottom in the class?

A. 34th

B. 36th

C. 33rd

D. 35th

E. None of these

Answer and Explanation:

Laura’s rank from the top = 5 + 1 = 6th

Her rank from the bottom = Total number of students – her rank from the top + 1

= 40 – 6 + 1 = 35th

Therefore, D is the correct option.

Your Turn:

Let’s practice what we have learned. Read the following information and answer the questions.

i. Five boxes E, F, G, H and I are placed above one another.

ii. Each box is of different color viz. Pink, Blue, Grey, White, and Black.

iii. The grey box is kept immediately above H.

iv. Only two boxes are kept between the pink and the blue boxes. The pink box is kept at one of the positions above the blue box as well as H.

v. More than one box is kept between the blue box and the E. E is not pink in color.

vi. As many boxes are kept between E and the grey box as between G and the white box.

vii. H is not white in color.

viii. F is kept at one of the positions below the pink box but not immediately below it.

1. How many boxes are kept between I and the black box?

A. Cannot be determined

B. Three

C. None

D. One

E. Two

2. Which of the following is/are true with respect to the given arrangement?

a. There are only two boxes between E and the blue box.

b. F is placed at the bottom-most position.

c. There is only one box between E and the grey box.

A. a and b

B. b and c

C. only a

D. only b

E. only c

3. Which of the following boxes is black in color?

A. H

B. I

C. E

D. G

E. Cannot be determined

4. Which of the following represents the color of I?

A. Grey

B. White

C. Black

D. Blue

E. Pink

To begin with, we can draw this table:

Ranking and Order Practice Exercise 1 Table (Part - 1)

> We can visually represent clue (iii) as:

Visual Representation 1

> Clue (iv): Only two boxes are kept between the pink and the blue boxes. The pink box is kept at one of the positions above the blue box as well as H.

There are two possible cases for which there are two boxes between the pink and the blue box, and the pink box is kept above the blue box.

Practice Exercise 1 (Table - 2)

Since we don’t know the position of H with respect to the pink box, we have drawn a visual representation. The arrow donates that the pink box is kept above the H box, while the question mark donates that we do not know the number of boxes between them.

> Clue (v): More than one box is kept between the blue box and the E. E is not pink in color.

This information rejects Case I.

Practice Exercise 1 Table (Part- 3)

> Clue (vi) and (vii): As many boxes are kept between E and the grey box as between G and the white box. H is not white in color.

There are two possible positions for the Grey box. Also, remember that the Grey box is kept immediately above H.

Practice Exercise 1 Table (Part- 4)

In Case II (a), the number of boxes between G and the white box should be 1.

In Case II (b), the number of boxes between G and the white box should be 2.

Practice Exercise 1 Table (Part- 5)

> Clue (viii): F is kept at one of the positions below the pink box but not immediately below it.

This is possible only in Case II (a). Hence, we reject Case II (b).

Practice Exercise 1 Table (Part- 6)

Now let’s answer the questions:

1. There is one box between I and the black box. So, D is the correct option.

2. Both (b) and (c) are true statements. So, B is the correct option.

3. Box H is black. So, A is the correct option.

4. Box I is pink. So, E is the correct option.

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