CAT 2025 Lesson : Ranking - Introduction

1. Introduction

As the name suggests, this is a group of people or items ranked in a certain order. This can be based on physical characteristics (height,weight), performance (rank in class, amount of sales achieved, top speeds of cars), statistical characteristics (states ranked in ascending rainfall or per-capita GDP) or the outcome of races (F1 drivers or racehorses ranked in the order of the result, class ranking of students).

These questions are fairly common in all MBA entrance tests. We will be able to answer these questions based on the details given in the case.

In order to solve such questions, we can make use of symbols such as dashes (for placing a person or item at a certain point in the sequence), greater than and less than symbols (to show that one person is ranked ahead of or behind another).We need to read the question properly. For instance, Ram is taller than either Hari or Shyam is different from Ram is taller than Hari and Shyam. Similarly, Ram is taller than Hari implies that there can be other people with a height less than Ram but more than Hari (Ram > ________ > Hari).

Let us solve some questions to understand how to tackle them in entrance tests.

Concept Case 1

A class has 7 students - A, B, C, D, E, F and G - who took a test and were assigned ranks from 1 to 7, with 1 being assigned to the highest scorer and 7 being assigned to the lowest scorer. No two students got the same mark. The following additional information is known.

1) The marks of 3 of the students was less than C's mark but more than B's mark.
2) F had a numerically higher rank than D and at least one person's mark was between the marks secured by F and D.
3) The person who got the last rank was either E or A.
4) There was at least 1 person whose mark was between that of F and E.
5) G got the third lowest score.

Solution :

Ranks assigned are 1 for the highest scorer and 7 for the lowest scorer.

- From statement (5), G's rank is 5.

- From statement (1), if C = 1 then B ≠ 5. So C is ranked 2 and B is ranked 6.

- From statement (2), D ≠ 3, 4 (At least one student has to be in between D and F). This means that D = 1.

From statement (4), there has to be at least one person between F & E. E is ranked 7. So A/F is ranked either 3 or 4 from the above statement.

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