In a consolidated merit list of 90 applicants for a university fellowship, Marcus is ranke… — State PSC Exam

In a consolidated merit list of 90 applicants for a university fellowship, Marcus is ranked $25^{\text{th}}$ from the top, while Elena is ranked $44^{\text{th}}$ from the bottom. If David is positioned exactly in the middle of Marcus and Elena in this merit list, what is David's rank from the bottom?

A
$54^{\text{th}}$
B
$45^{\text{th}}$
$55^{\text{th}}$ Answer
D
$36^{\text{th}}$

Answer

David's rank from the bottom is the

55^{\text{th}}

position.

To find David's position, we first standardise the reference points. Elena's

44^{\text{th}}

position from the bottom corresponds to the

47^{\text{th}}

position from the top (calculated as

90 - 44 + 1

). The exact midpoint between the

25^{\text{th}}

and

47^{\text{th}}

ranks is the

36^{\text{th}}

rank from the top (calculated as the average:

(25 + 47) / 2 = 36

). Finally, converting David's

36^{\text{th}}

top rank to a bottom rank yields

90 - 36 + 1 = 55^{\text{th}}

Step-by-Step Solution

Convert Elena's bottom rank to a top rank to establish a common directional reference.

Elena's rank from the top is

90 - 44 + 1 = 47^{\text{th}}

To calculate the number of people strictly between Marcus and Elena, both ranks must be measured from the same end (the top).

Calculate the number of applicants positioned strictly between Marcus and Elena.

There are

47 - 25 - 1 = 21

applicants between them.

Subtracting the top ranks and deducting 1 excludes both Marcus and Elena from the middle count.

Determine David's exact relative position starting from Marcus.

David is the

11^{\text{th}}

person after Marcus.

The exact midpoint of 21 people is

(21 + 1) / 2 = 11

positions away from the starting person.

Calculate David's overall absolute rank from the top.

David's top rank is

25 + 11 = 36^{\text{th}}

Adding David's relative interval to Marcus's top rank yields David's absolute top rank.

Convert David's top rank back to a bottom rank to answer the final question.

David's rank from the bottom is

90 - 36 + 1 = 55^{\text{th}}

Applying the standard linear ranking formula:

\text{Total} = \text{Top Rank} + \text{Bottom Rank} - 1

Key Concept

Positional overlap calculation and dual-rank directional conversion

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