📌 Section 1 is Logical reasoning specially designed for CAT

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In a company, five employees – Angus, Billy, Charlie, David and Eric – were ranked from 1 to 5 based on two parameters – Sincerity and Approachability – such that in any parameter, a numerically lower rank is considered better than a numerically higher rank.

For any employee, the sum of the ranks across the two parameters is referred to as the Overall Rank, and it is known that the Overall Rank of each employee was distinct.

Further, it is also known that:

i. No employee received the same rank across the two parameters.
ii. Angus was ranked better than Charlie in each of the two parameters.
iii. Billy, who was ranked third in Sincerity, had the numerically highest Overall Rank.
iv. The difference in ranks of Charlie and David in Approachability is one.

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We have five employees:

Angus, Billy, Charlie, David and Eric.

Each employee is ranked from 1 to 5 in:

A lower numerical rank is better.

Overall Rank = Sincerity Rank + Approachability Rank

The Overall Rank values of all five employees are distinct.

Therefore:

Sincerity of Angus < Sincerity of Charlie

Approachability of Angus < Approachability of Charlie

Billy is given as:

Sincerity = 3

So the remaining Sincerity ranks 1, 2, 4 and 5 must belong to Angus, Charlie, David and Eric.

Also:

Angus must be better than Charlie in Sincerity.

Billy must have the highest numerical Overall Rank.

Since:

Overall Rank = Sincerity + Approachability

and Billy already has Sincerity = 3, Billy needs a sufficiently poor Approachability rank to ensure that his total is higher than everyone else's.

Billy cannot be ranked 3rd in Approachability because no employee can have the same rank in both parameters.

On satisfying all the remaining conditions, Billy must be ranked:

Approachability = 5

Therefore:

Billy's Overall Rank = 3 + 5 = 8

Since Billy has the highest Overall Rank, every other person's total must be less than 8.

Angus must be better than Charlie in both parameters.

The final Sincerity positions that satisfy all the conditions are:

This satisfies:

4 < 5

So Angus is better than Charlie in Sincerity.

Charlie and David must differ by exactly one rank in Approachability.

Also, Angus must be better than Charlie in Approachability.

The arrangement that satisfies these conditions is:

Here:

Charlie and David differ by:

3 − 2 = 1

And Angus is better than Charlie:

1 < 2

Both conditions are satisfied.

We now have:

The only rank remaining is 4.

Therefore:

Eric = 4

So the complete Approachability order is:

We already know:

Therefore ranks 1 and 2 must go to David and Eric.

Because no employee can have the same rank in both parameters:

David has Approachability = 3, so either 1 or 2 is possible.

Eric has Approachability = 4, so either 1 or 2 is possible.

Checking the requirement that all Overall Ranks must be distinct determines:

Thus the Sincerity order is:

Final Table

Q1 → C. David
Q2 → 3
Q3 → A. Angus
Q4 → C. Eric

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