# LR - Rank & Ordering - Previous Year CAT/MBA Questions

You can practice all previous year CAT questions from the topic LR - Rank & Ordering. This will help you understand the type of questions asked in CAT. It would be best if you clear your concepts before you practice previous year CAT questions.

**Answer the next 5 questions based on the information given below:**

All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade; others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained.

1. The numbers of non-CS students who took AI and ML were in the ratio 2 : 5.

2. The number of non-CS students who took either AI or ML was equal to the number of CS students.

3. The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.

4. In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3 : 2 for ML.

5. No CS student failed in AI, while no non-CS student got an A grade in AI.

6. The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4 : 5 : 2.

7. The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was 3 : 1.

8. 30 students failed in ML.

**CAT 2022 LRDI Slot 3 | LR - Rank & Ordering**

How many students took AI?

- A.
90

- B.
60

- C.
210

- D.
270

Answer: Option D

**Explanation** :

From (1) and (2): Let the number of non-CS students who took AI and ML are 2x and 5x respectively.

⇒ Number of CS students = 2x + 5x = 7x.

From (3): Let the number of non-CS students failing in two courses is ‘a’ each and CS students who got a C in ML = ‘2a’

From (6): Let number of CS students who got A, B and C grades respectively in AI are 3y, 5y, 2y.

While number of CS students who got A, B and C grades respectively in ML are 4a, 5a, 2a.

From (5): No CS student failed in AI, while no non-CS student got an A grade in AI.

From (4): The numbers of students who got A and C grades were the same for AI

⇒ 3y + 0 = 2y + non-CS students in AI with C grade

⇒ non-CS students in AI with C grade = 3y – 2y = y

From (8): 30 students failed in ML hence CS students failing in ML = 30 – a.

From (7):

⇒ $\frac{a+a}{30-a}$ = $\frac{3}{1}$

⇒ 2a = 90 – 3a

⇒ a = 18

⇒ 7x = 72 + 90 + 36 + 12 = 210

⇒ x = 30

⇒ 210 = 3y + 5y + 2y

⇒ y = 21

⇒ 60 = 0 + (non-CS student in AI getting B grade) + 21 + 18

∴ non-CS student in AI getting B grade = 60 – 39 = 21

From (4): In both the courses, 50% of the students who passed got a B grade

Number of students passing in ML = 72 + 90 + 36 + (150 - 18) = 330

⇒ Number of students receiving B grade in ML = 330/2 = 165.

⇒ non-CS students with B grade in ML = 165 – 90 = 75

Let number of non-CS students with A grade in ML = c, hence number of non-CS students with C grade in ML = 150 – 75 – 18 – c = 57 – c

From (4): the numbers of students who got A and C grades were in the ratio 3 : 2 for ML.

⇒ $\frac{72+c}{36+57-c}$ = $\frac{3}{2}$

⇒ 144 + 2c = 279 – 3c

⇒ 5c = 135

⇒ c = 27

∴ Number of students taking AI = 210 (CS students) + 60 (non-CS students) = 270.

Hence, option (d).

Workspace:

**CAT 2022 LRDI Slot 3 | LR - Rank & Ordering**

How many CS students failed in ML?

Answer: 12

**Explanation** :

Consider the solution to first question of this set.

Number of CS students failing in ML = 12.

Hence, 12.

Workspace:

**CAT 2022 LRDI Slot 3 | LR - Rank & Ordering**

How many non-CS students got A grade in ML?

Answer: 27

**Explanation** :

Consider the solution to first question of this set.

Number of non-CS students who got A grade in ML = 27.

Hence, 27.

Workspace:

**CAT 2022 LRDI Slot 3 | LR - Rank & Ordering**

How many students got A grade in AI?

- A.
84

- B.
63

- C.
99

- D.
42

Answer: Option B

**Explanation** :

Consider the solution to first question of this set.

Number of students who got A grade in AI = 63 + 0 = 63

Hence, option (b).

Workspace:

**CAT 2022 LRDI Slot 3 | LR - Rank & Ordering**

How many non-CS students got B grade in ML?

- A.
75

- B.
165

- C.
25

- D.
90

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

Number of non-CS students who got B grade in ML = 75

Hence, option (a).

Workspace:

**Study the following information carefully and answer the questions.**

Four houses Blue, Green, Red and Yellow are located in a row in the given order. Each of the houses is occupied by a person earning a fixed amount of a salary. The four persons are Paul, Krishna, Laxman, and Som.

Read the following instruction carefully:I. Paul lives between Som and Krishna

II. Laxman does not stay in Blue house

III. The person living in Red house earns more than that of person living in Blue

IV. Salary of Som is more than that of Paul but lesser than that of Krishna

V. One of the person earns Rs. 80, 000

VI. The person earning Rs. 110,000 is not Laxman

VII. The salary difference between Laxman and Son is Rs. 30,000

VIII. The House in which Krishna lives is located between houses with persons earning salaries of Rs. 30,000 and Rs. 50,000

IX. Krishna does not live in Yellow house, and the person living in yellow house is not earning lowest salary among the four persons.

**IIFT 2009 LRDI | LR - Rank & Ordering**

Who lives in Red house?

- A.
Paul

- B.
Krishna

- C.
Laxman

- D.
Som

Answer: Option B

**Explanation** :

It is given that the four houses Blue, Green, Red and Yellow are located in a row, From (VIII) we get that the house in which Krishna lives is located between houses with persons earning salaries of Rs. 30,000 and Rs. 50,000.

∴ Two cases are possible:

**Case 1:** Krishna lives in the Green house.

**Case 2:** Krishna lives in the Red house.

**Consider case 1:** Krishna lives in the Green house.

From (I) we get that Paul lives between Som and Krishna.

∴ Som lives in the Yellow house and Paul lives in the Red house.

∴ Laxman lives in the Blue house.

From (VIII) we get that Krishna lives in the house which is located between houses with persons earning salaries of Rs. 30,000 and Rs. 50,000.

And from (III) we get that the person living in the Red house earns more than the person living in the Blue house.

∴ Paul earns Rs. 50,000 and Laxman earns Rs. 30,000.

From (VII) we get that the salary difference between Laxman and Som is Rs. 30,000 which is not possible in this case as the four given salaries are Rs. 30,000, Rs. 50,000, Rs. 80,000 and Rs. 1,10,000.

∴ Case 1 is not possible.

**Consider case 2:** Krishna lives in the Red house.

From (I) we get that Paul lives between Som and Krishna.

∴ Som lives in the Blue house and Paul lives in the Green house.

∴ Laxman lives in the Yellow house.

In condition (VIII) it is given that Krishna lives in the house located between houses with persons earning Rs. 30,000 and Rs. 50,000.

And from (IX) we get that the person living in the Yellow house is not earning lowest salary among the four persons.

∴ Laxman earns Rs. 50,000 and Paul earns Rs. 30,000.

From (III) we get that the person living in the Red house earns more than the person living in the Blue house.

∴ Krishna earns Rs. 1,10,000 and Som earns Rs. 80,000.

This case satisfies all the given conditions.

∴ Krishna lives in the Red house.

Hence, option (b).

Workspace:

**Answer the following question based on the information given below.**

A Prime Minister is contemplating the expansion of his cabinet. There are four ministerial berths and there are eight probable candidates (C1-C8) to choose from. The selection should be in a manner that each selected person shares a liking with at least one of the other three selected members. Also, the selected must also hate at least one of the likings of any of the other three persons selected.

I. C1 likes travelling and sightseeing, but hates river rafting

II. C2 likes sightseeing and squash, but hates travelling

III. C3 likes river rafting, but hates sightseeing

IV. C4 likes trekking, but hates squash

V. C5 likes squash, but hates sightseeing and trekking

VI. C6 likes travelling, but hates sightseeing and trekking

VII. C7 likes river rafting and trekking, but hates travelling, and

VIII. C8 likes sightseeing and river rafting, but hates trekking

**IIFT 2009 LRDI | LR - Rank & Ordering**

Who are the four people selected by the Prime Minister?

- A.
C1, C2, C5, C6

- B.
C3, C4, C5, C6

- C.
C1, C2, C4, C7

- D.
None of the above

Answer: Option C

**Explanation** :

If the liking of a person is denoted by **√** and whatever a person hates is denoted by **×** then the data given can be represented in a tabular format as:

Now, each selected member should share a liking with at least one of the other three selected members and the selected member must also hate at least one of the likings of any of the other persons selected.

Consider option 1:

C1, C2, C5 and C6 cannot be the four people selected by the Prime Minister as C1 hates only River rafting which is not liked by any of the other three.

Consider option 2:

C3, C4, C5 and C6 cannot be the four people selected by the Prime Minister as none of them shares a liking with any other member, also C3 and C6 hate Sightseeing which is not liked by any of them.

Consider option 3:

C1, C2, C4 and C7 are the four people selected by the Prime Minister as all of them share at least one liking with at least one of the three selected members and all of them also hate at least one of the likings of at least one of the selected persons.

Hence, option (c).

Workspace:

**Answer the following question based on the information given below.**

Elle is three times older than Yogesh. Zaheer is half the age of Wahida. Yogesh is older than Zaheer.

**CAT 2001 LRDI | LR - Rank & Ordering**

Which of the following can be inferred?

- A.
Yogesh is older than Wahida.

- B.
Elle is older than Wahida.

- C.
Elle may be younger than Wahida.

- D.
None of the above

Answer: Option B

**Explanation** :

Let us assume that Zaheer is as old as Yogesh (which is the maximum possible age for Zaheer).

∴ Waheeda is twice older than Yogesh but Elle is three times older than Yogesh.

∴ Elle is the eldest.

Hence, option (b).

Workspace:

**CAT 2001 LRDI | LR - Rank & Ordering**

Which of the following information will be sufficient to estimate Elle's age?

- A.
Zaheer is 10 years old.

- B.
Both Yogesh and Wahida are older than Zaheer by the same number of years.

- C.
Both 1 and 2 above

- D.
None of the above

Answer: Option C

**Explanation** :

Using the information in options 1 and 2 together, we have,

Waheeda’s age = 2 × Zaheer’s age = 2 × 10 = 20

∴ Yogesh’s age must be equal to 20 years.

∴ Elle’s age = 3 × 20 = 60

Hence, option (c).

Workspace:

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