Order and Ranking Practice Questions — State PSC Exam

Question 1Question →

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?

54^{\text{th}}

45^{\text{th}}

55^{\text{th}}

36^{\text{th}}

Show answer & explanation

Answer: $55^{\text{th}}$

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

1

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).

2

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.

3

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.

4

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.

5

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

Question 2Question →

A network administrator is establishing a 5-step automated security protocol. The five steps—Backup Creation, Database Sync, Malware Scan, System Initialization, and User Authentication—must be arranged in a specific sequence based on the following constraints:

1. The Database Sync must occur exactly two steps after User Authentication.
2. The Malware Scan must occur sometime after System Initialization, but before Backup Creation.
3. The Database Sync cannot be the final step, and User Authentication cannot be the first step.

Arrange the five security steps in the correct chronological order from first to last.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence is: System Initialization, User Authentication, Malware Scan, Database Sync, and Backup Creation.

The rules restrict the User Authentication and Database Sync pair strictly to steps 2 and 4. The remaining three steps (System Initialization, Malware Scan, Backup Creation) must maintain a strict relative order to satisfy the second rule, naturally falling into the remaining slots 1, 3, and 5.

Step-by-Step Solution

1

Determine the fixed positions for User Authentication and Database Sync based on constraints 1 and 3.

User Authentication must be step 2 and Database Sync must be step 4.

They have a fixed gap of one step between them. They cannot be steps 1 and 3 (User Authentication cannot be first), nor steps 3 and 5 (Database Sync cannot be last). Therefore, they must occupy steps 2 and 4.

2

Assign the remaining three steps (System Initialization, Malware Scan, and Backup Creation) to the empty slots.

System Initialization is step 1, Malware Scan is step 3, and Backup Creation is step 5.

Constraint 2 requires them to be in the strict relative order: System Initialization -> Malware Scan -> Backup Creation. The only remaining empty slots are 1, 3, and 5, so they must sequentially fill these slots.

Key Concept

Relative Positional Arrangement and Constraint Satisfaction

Estimated Time:1m 30s

Question 3Question →

In a single row of books on a library shelf, an Encyclopedia is $28^{\text{th}}$ from the left end and a Dictionary is $35^{\text{th}}$ from the right end. If there are exactly 12 books placed strictly between them, what is the minimum possible total number of books in this row?

Show answer & explanation

Answer: 49

Answer

The minimum possible total number of books is 49.

The minimum total is found using the overlapping queue formula:

L + R - M - 2

. Substituting the given values yields

28 + 35 - 12 - 2 = 49

.

Step-by-Step Solution

1

Identify the queue configuration for the minimum capacity.

The minimum possible number of books occurs in an overlapping scenario.

In an overlapping scenario, the item counted from the right (Dictionary) is placed to the left of the item counted from the left (Encyclopedia), yielding the smallest overall total length.

2

Apply the minimum capacity formula.

\text{Total} = L + R - M - 2

We add the rank from the left (

L

) and the rank from the right (

R

), then subtract the number of items strictly between them (

M

) and the 2 reference items to correct for double-counting.

3

Substitute the given values and calculate the final count.

\text{Total} = 28 + 35 - 12 - 2 = 49

This yields the exact minimum count of books on the shelf.

Key Concept

Overlapping Minimum Capacity in Ordering and Ranking

Estimated Time:1m 0s

Question 4Question →

A group of students is standing in a single straight row facing South. Arjun is $26^{\text{th}}$ from the left end of the row, and Bhavya is $19^{\text{th}}$ from the right end of the row. When Arjun shifts $7$ places towards his left, he exactly occupies the middle position of the row. What is Bhavya's position from the left end of the row?

47^{\text{th}}

19^{\text{th}}

46^{\text{th}}

18^{\text{th}}

Show answer & explanation

Answer: $47^{\text{th}}$

Answer

Bhavya is exactly

47^{\text{th}}

from the left end of the row.

By properly recognizing that facing South reverses anatomical left and right relative to the row's ends, we determine Arjun's new position is

26 + 7 = 33

. A middle position of

33

yields a total of

65

students. Bhavya's position from the left is then calculated by subtracting her right-end rank from the total and adding

1

(

65 - 19 + 1 = 47

).

Step-by-Step Solution

1

Determine Arjun's movement direction relative to the row.

Arjun shifts towards the right end of the row.

Since the row is facing South, a person's personal left hand points towards the right end (geographic East) from an external observer's perspective.

2

Calculate Arjun's new position from the left end.

Arjun's new position is

26 + 7 = 33^{\text{rd}}

from the left end.

He was initially

26^{\text{th}}

and moved

7

places further away from the left end.

3

Determine the total number of students in the row (

N

).

The total number of students is

65

.

Since the

33^{\text{rd}}

position is exactly in the middle, the total is calculated as

N = (33 \times 2) - 1 = 65

.

4

Calculate Bhavya's position from the left end.

Bhavya is

47^{\text{th}}

from the left end.

Using the formula: Left Position = Total (

N

) - Right Position +

1

. Thus,

65 - 19 + 1 = 47

.

Key Concept

Directional awareness in linear arrangements and position reversal formulas.

Estimated Time:1m 15s

Question 5Question →

Five startup companies—Solaris, Terra, Umbra, Vesta, and Wyvern—are being ranked by their market valuation from highest to lowest. Based on the following information, arrange the companies in the correct order from highest valuation (top) to lowest valuation (bottom):

1. Umbra is valued higher than both Vesta and Wyvern.
2. Terra is valued lower than Solaris but higher than Umbra.
3. Wyvern is not the lowest valued company.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from highest to lowest valuation is: Solaris, Terra, Umbra, Wyvern, and Vesta.

Based on the provided clues, Solaris has the highest valuation, followed directly by Terra, and then Umbra. Since Umbra is valued higher than both Vesta and Wyvern, those two must occupy the fourth and fifth spots. Because Wyvern cannot be the lowest valued company, it must take the fourth position, leaving Vesta as the fifth and lowest valued company.

Step-by-Step Solution

1

Analyze the relationship between Terra, Solaris, and Umbra.

Solaris > Terra > Umbra

The second clue explicitly states that Terra is valued lower than Solaris but higher than Umbra.

2

Analyze the relationship between Umbra, Vesta, and Wyvern.

Umbra > Vesta and Umbra > Wyvern

The first clue states that Umbra is valued higher than both Vesta and Wyvern.

3

Combine the findings from Step 1 and Step 2 to form a partial sequence.

Solaris > Terra > Umbra > (Vesta and Wyvern)

Applying the transitive property, Solaris and Terra occupy the first and second positions, Umbra is third, leaving Vesta and Wyvern for the bottom two spots.

4

Determine the exact final positions of Vesta and Wyvern.

Wyvern > Vesta

The third clue states that Wyvern is not the lowest valued company. Therefore, between the remaining two spots, Wyvern must be fourth and Vesta must be fifth.

Key Concept

Relative position ordering using transitive logic and negative constraints.

Question 6Question →

A solar energy farm has a continuous linear array of $105$ solar panels. Panel Sigma is currently positioned $43^{\text{rd}}$ from the left end of the array. Due to a localized upgrade project, the first $18$ panels from the left end and the last $24$ panels from the right end are temporarily removed from the array. In the newly formed, shorter array of remaining panels, what is the position of Panel Sigma from the right end?

Show answer & explanation

Answer: 39

Answer

39

Panel Sigma's original position from the left is

43^{\text{rd}}

. When

18

panels are removed from the front, its new position from the left becomes

43 - 18 = 25^{\text{th}}

. The initial total was

105

panels. After removing

18

from the left and

24

from the right, the new total is

105 - 18 - 24 = 63

panels. Using the standard ranking formula (

Total = Left + Right - 1

), the position from the right is calculated as

63 - 25 + 1 = 39^{\text{th}}

.

Step-by-Step Solution

1

Calculate the new total number of panels in the array.

105 - 18 - 24 = 63

panels

Removing panels from both ends reduces the overall length of the array.

2

Determine Panel Sigma's new position from the left end.

43 - 18 = 25^{\text{th}}

from the left

Removing 18 panels from the left shifts Panel Sigma 18 positions closer to the left end.

3

Calculate Panel Sigma's new position from the right end.

Position from right =

63 - 25 + 1 = 39^{\text{th}}

Using the standard ranking formula (Total = Left Position + Right Position - 1), we find the right-side position.

Key Concept

Positional shift and total rank calculation in a truncated linear arrangement

Alternative Method

Instead of calculating the new total, you can determine how many panels are strictly to the right of Panel Sigma. Initially, there are

105 - 43 = 62

panels to its right. Removing

24

panels from the right end leaves

62 - 24 = 38

panels to its right. Since there are

38

panels after it, Panel Sigma must be the

39^{\text{th}}

panel from the right end.

Estimated Time:1m 0s

Question 7Question →

In a processing queue of a mainframe computer, Job Alpha is positioned $28^{\text{th}}$ from the front of the queue, and Job Beta is positioned $34^{\text{th}}$ from the back of the queue. If there are exactly $12$ jobs currently waiting between Job Alpha and Job Beta, what is the minimum possible total number of jobs in this queue?

Show answer & explanation

Answer: 48

Answer

48

To find the minimum possible number of jobs, we assume an overlapping sequence. The formula for the minimum total in a ranking problem is: Total = (Rank from Front) + (Rank from Back) - (Number of items in between) - 2. Substituting the values gives: 28 + 34 - 12 - 2 = 62 - 14 = 48.

Step-by-Step Solution

1

Identify the queue configuration required for a minimum total.

The configuration must be overlapping, meaning Job Beta is ahead of Job Alpha in the queue.

An overlapping configuration results in the smallest possible total number of items because the counted items from both ends overlap.

2

Apply the minimum total formula for overlapping cases.

Total = Rank of Alpha from front + Rank of Beta from back - Jobs between them - 2

This formula deducts the overlapping region (the jobs between them and the two jobs themselves) which were counted twice.

3

Substitute the provided numerical values into the formula.

Total = 28 + 34 - 12 - 2

Job Alpha is 28th, Job Beta is 34th, and there are 12 jobs in between.

4

Calculate the final value.

Total = 62 - 14 = 48

Basic arithmetic yields the minimum possible number of jobs in the queue.

Key Concept

Order and Ranking (Overlapping/Minimum Capacity Queue)

Question 8Question →

In a straight row of cadets facing North for a morning assembly, Cadet Marcus is standing $15^{\text{th}}$ from the left end and Cadet Victor is standing $28^{\text{th}}$ from the right end. If they interchange their positions, Cadet Marcus becomes $35^{\text{th}}$ from the left end. What is Cadet Victor's new position from the right end?

47^{\text{th}}

48^{\text{th}}

49^{\text{th}}

62^{\text{nd}}

Show answer & explanation

Answer: $48^{\text{th}}$

Answer

48^{\text{th}}

The correct answer accurately calculates the total number of cadets as

62

and correctly applies the formula to find the rank from the opposite end (

62 - 15 + 1 = 48

).

Step-by-Step Solution

1

Calculate the total number of cadets in the row.

Total =

62

cadets.

After the interchange, Marcus occupies Victor's original position. This physical spot is

35^{\text{th}}

from the left and

28^{\text{th}}

from the right. The total number of cadets is

L + R - 1 = 35 + 28 - 1 = 62

.

2

Determine Victor's new position from the left.

Victor is now

15^{\text{th}}

from the left.

During the interchange, Victor takes Marcus's original spot, which was given as

15^{\text{th}}

from the left.

3

Calculate Victor's new position from the right end.

Victor is

48^{\text{th}}

from the right.

Using the position conversion formula (Total - Position from left + 1), Victor's position from the right is

62 - 15 + 1 = 48

.

Key Concept

Position Interchange and Total Calculation in Linear Arrangements

Alternative Method

Since Marcus's position shifted by

20

places (

35 - 15 = 20

) during the interchange, Victor's position must also shift by the exact same number of places relative to his starting end. Therefore, Victor's new position from the right end is simply

28 + 20 = 48^{\text{th}}

.

Estimated Time:1m 0s

Question 9Question →

In a single row of students facing North, Akash is ranked $18^{\text{th}}$ from the left end, while Banya is ranked $24^{\text{th}}$ from the right end. Chetan is sitting $6^{\text{th}}$ to the right of Akash and $4^{\text{th}}$ to the left of Banya. If Akash and Banya interchange their positions while Chetan remains in his place, and then Deepa sits exactly midway between Akash's new position and Chetan's position, what is Deepa's rank from the left end of the row?

26^{\text{th}}

21^{\text{st}}

25^{\text{th}}

27^{\text{th}}

Show answer & explanation

Answer: $26^{\text{th}}$

Answer

The rank of Deepa from the left end of the row is

26^{\text{th}}

.

By following the relative linear placements, Chetan's left rank is

18 + 6 = 24

, and Banya's left rank is

24 + 4 = 28

. After Akash swaps positions with Banya, Akash's new position from the left becomes

28

. Deepa sits directly midway between Chetan (

24^{\text{th}}

) and Akash's new position (

28^{\text{th}}

), which corresponds to the rank

\frac{24 + 28}{2} = 26^{\text{th}}

.

Step-by-Step Solution

1

Determine Chetan's position from the left end.

Since Akash is

18^{\text{th}}

from the left and Chetan is

6^{\text{th}}

to his right, Chetan's left-rank

= 18 + 6 = 24^{\text{th}}

.

Moving right along a row facing North increases the positional index from the left.

2

Determine Banya's position from the left end.

Chetan is

4^{\text{th}}

to the left of Banya, so Banya's left-rank

= 24 + 4 = 28^{\text{th}}

.

Since Chetan is to the left of Banya, adding

4

to Chetan's position gives Banya's position from the left.

3

Find Akash's position after interchanging with Banya.

Akash takes Banya's original place, making Akash's new left-rank

= 28^{\text{th}}

.

Interchanging positions swaps their exact ranks from the left end.

4

Calculate Deepa's position midway between Chetan's position (

24^{\text{th}}

) and Akash's new position (

28^{\text{th}}

).

Midpoint

= \frac{24 + 28}{2} = 26^{\text{th}}

from the left end.

The exact midway index between two positions

p_1

and

p_2

is their arithmetic mean

(p_1 + p_2) / 2

.

Key Concept

Order and Ranking involving multi-person relative placement and position interchange

Estimated Time:2m 0s

Question 10Question →

In a class merit list, Rahul is ranked $15^{\text{th}}$ from the top and $21^{\text{st}}$ from the bottom. What is the total number of students in the class?

Show answer & explanation

Answer: 35

Answer

The total number of students in the class is

35

.

When the position of a single person is given from both ends of a line, the total count is calculated using the formula

\text{Total} = \text{Position from Left/Top} + \text{Position from Right/Bottom} - 1

. Substituting the values gives

15 + 21 - 1 = 35

.

Step-by-Step Solution

1

Identify the given ranks from both ends for the same person.

Rank from top = 15, Rank from bottom = 21.

The position of Rahul is provided relative to both the start and end of the queue.

2

Apply the single-person dual rank total calculation formula.

\text{Total} = \text{Rank}_{\text{top}} + \text{Rank}_{\text{bottom}} - 1

Since Rahul is included in both rank counts, adding the ranks counts him twice, requiring a subtraction of 1.

3

Perform the computation.

15 + 21 - 1 = 35

Simplifying the arithmetic yields the exact total headcount of the class.

Key Concept

Single-Person Dual Rank Total Calculation

Question 11Question →

In a straight row of parked vehicles, a red car is positioned $14^{\text{th}}$ from the left end and $19^{\text{th}}$ from the right end. What is the total number of vehicles parked in the row?

32

33

31

34

Show answer & explanation

Answer: 32

Answer

The total number of vehicles parked in the row is 32.

When the rank of a single item is given from both ends of a row, the total number of items is calculated using

N = \text{Rank from Left} + \text{Rank from Right} - 1

. Adding

14

and

19

gives

33

, and subtracting

1

to correct for double-counting gives

32

.

Step-by-Step Solution

1

Identify the given position values for the object.

Position from left (

L

) = 14, Position from right (

R

) = 19.

The rank of a single object is provided from both ends of a single linear row.

2

Apply the dual-rank single-person total formula.

Total (

N

) =

L + R - 1 = 14 + 19 - 1 = 32

.

The specified car is counted twice (once from the left and once from the right), so

1

must be subtracted from the sum of ranks.

Key Concept

Single-person dual rank total calculation

Question 12Question →

In a published civil services merit list, Rohan is ranked $14^{\text{th}}$ from the top, while Seema is ranked $33^{\text{rd}}$ from the bottom. After a re-evaluation of marks, Rohan and Seema interchange their positions, resulting in Rohan becoming $48^{\text{th}}$ from the top. A third candidate, Amit, holds a rank exactly halfway between Rohan's new position and Seema's new position. If $6$ candidates ranked above Amit withdraw their candidature and $4$ new candidates are placed below Amit in the updated list, what is Amit's final rank from the bottom of the modified merit list?

Show answer & explanation

Answer: 54

Answer

Amit's final rank from the bottom of the modified merit list is 54.

Seema's dual information (

48^{\text{th}}

from top and

33^{\text{rd}}

from bottom) gives an initial total of 80 candidates. Amit's midpoint position between

14^{\text{th}}

and

48^{\text{th}}

is

31^{\text{st}}

from top, placing 49 candidates below him. Accounting for 6 withdrawals above and 4 additions below leaves 53 candidates below Amit, establishing his final rank as

54^{\text{th}}

from the bottom.

Step-by-Step Solution

1

Find total candidates in the original merit list using the interchange data.

Total candidates N = 80

When Rohan and Seema interchange positions, Rohan occupies Seema's original spot (

48^{\text{th}}

from top). Since Seema was

33^{\text{rd}}

from bottom,

N = 48 + 33 - 1 = 80

.

2

Calculate Amit's initial rank from the top.

Amit's initial top rank = 31st

Amit is positioned halfway between Seema's new position (

14^{\text{th}}

from top) and Rohan's new position (

48^{\text{th}}

from top), so rank =

(14 + 48) / 2 = 31^{\text{st}}

.

3

Find initial counts of candidates ranked above and below Amit.

30 candidates above, 49 candidates below

With a top rank of

31^{\text{st}}

out of 80, there are

31 - 1 = 30

candidates above Amit and

80 - 31 = 49

candidates below Amit.

4

Adjust counts based on candidate withdrawals and additions.

24 candidates above, 53 candidates below

Subtract 6 from candidates above (

30 - 6 = 24

) and add 4 to candidates below (

49 + 4 = 53

).

5

Calculate Amit's revised rank from the bottom.

54th from the bottom

The rank from the bottom equals (candidates below + 1), which gives

53 + 1 = 54

.

Key Concept

Dual Rank Position Interchange, Midpoint Computation, and Dynamic List Adjustment

Estimated Time:2m 30s

Question 13Question →

In a single line of applicants waiting for an interview, Oliver is positioned $34^{\text{th}}$ from the front and Maya is positioned $41^{\text{st}}$ from the back. There are exactly $15$ applicants standing between them. If the total number of applicants in the line is the absolute minimum possible to satisfy these conditions, what is the position of the applicant standing exactly halfway between Oliver and Maya, counting from the front of the line?

26^{\text{th}}

27^{\text{th}}

33^{\text{rd}}

42^{\text{nd}}

Show answer & explanation

Answer: $26^{\text{th}}$

Answer

The applicant standing exactly halfway between them is in the

26^{\text{th}}

position from the front.

To find the minimum possible number of people in the line, the positions of Oliver and Maya must overlap (Maya is closer to the front than Oliver). Since Oliver is

34^{\text{th}}

from the front and there are

15

people between them, Maya's position from the front is

34 - 15 - 1 = 18^{\text{th}}

. The person exactly in the middle of the

15

people between them is the

8^{\text{th}}

person after Maya. Therefore, their position from the front is

18 + 8 = 26^{\text{th}}

.

Step-by-Step Solution

1

Identify the arrangement type required for the minimum total number of applicants.

An overlapping arrangement must be used, meaning Maya is standing ahead of Oliver in the line.

If Oliver is ahead of Maya, the total number of applicants maximizes. For the minimum capacity, they must cross over so their positional counts overlap.

2

Calculate Maya's exact position from the front of the line.

Maya is

18^{\text{th}}

from the front.

Oliver is

34^{\text{th}}

. Since Maya is ahead of him with

15

people in between, Maya's position is

34 - 15 \text{ (people between)} - 1 \text{ (Oliver)} = 18^{\text{th}}

from the front.

3

Determine the relative position of the middle applicant between Oliver and Maya.

The middle applicant is exactly

8

positions after Maya.

There are

15

applicants between them. The exact middle of a

15

-person gap is the

8^{\text{th}}

person (

7

people on one side, the middle person, and

7

people on the other side).

4

Calculate the middle applicant's absolute position from the front.

18 + 8 = 26^{\text{th}}

position from the front.

Adding the relative

8

-position offset to Maya's starting position of

18^{\text{th}}

from the front yields the final answer.

Key Concept

Overlapping Minimum Capacity in Linear Ranking

Estimated Time:2m 0s

Question 14Question →

A local theater has a single continuous row of 42 seats in its front balcony. A guest's assigned seat is the $12^{\text{th}}$ one when counting from the left side. What is the position of this exact same seat when counting from the right side?

30^{\text{th}}

12^{\text{th}}

31^{\text{st}}

32^{\text{nd}}

Show answer & explanation

Answer: $31^{\text{st}}$

Answer

31^{\text{st}}

To find the position of an item from one end when its position from the opposite end and the total count are known, we subtract the known position from the total number of items, and then add 1. Using the ranking formula

R = T - L + 1

, we get

42 - 12 + 1 = 31

. Thus, the seat is

31^{\text{st}}

from the right.

Step-by-Step Solution

1

Identify the total number of seats and the known position from the left.

Total = 42

,

Left = 12

These are the given values required to find the relative position from the opposite end of the row.

2

Apply the standard ranking formula to calculate the position from the right side.

Right = Total - Left + 1

When converting a rank from one end to the other, subtracting the known rank from the total excludes the item itself from the count, so we must add 1 back to include it.

3

Perform the mathematical calculation.

Right = 42 - 12 + 1 = 30 + 1 = 31

Completing the arithmetic yields the final rank from the right side.

Key Concept

Position Calculation from Opposite Ends in a Linear Sequence

Question 15Question →

During a corporate seminar, 60 employees are seated in a single straight row facing the stage. If David is seated in the $38^{\text{th}}$ position when counting from the left end of the row, what is his position when counting from the right end?

22^{\text{nd}}

23^{\text{rd}}

24^{\text{th}}

38^{\text{th}}

Show answer & explanation

Answer: $23^{\text{rd}}$

Answer

23^{\text{rd}}

To find a person's position from one end when the total and the position from the other end are known, use the formula: Position = Total - Known Position + 1. Here, 60 - 38 + 1 equals 23.

Step-by-Step Solution

1

Identify the total number of employees and David's position from the left.

Total = 60, Left position = 38.

These are the known variables needed for the ranking formula.

2

Apply the single-person dual rank formula to find the position from the right.

Right position = Total - Left position + 1.

Subtracting the left position removes everyone up to and including David. Adding 1 back includes David in the count from the right.

3

Calculate the final value.

60 - 38 + 1 = 22 + 1 = 23.

Basic arithmetic completion yields the correct rank.

Key Concept

Single-person dual rank calculation in a linear arrangement.

Question 16Question →

At a busy immigration checkpoint, a single line of passengers is waiting to be processed. Fatima is standing $22^{\text{nd}}$ from the front of the line, while Diego is $32^{\text{nd}}$ from the back.

Due to a lane reassignment, Fatima and Diego completely swap their positions in the line. After the swap, Fatima becomes $40^{\text{th}}$ from the front.

A third passenger, Haruki, is standing exactly halfway between Diego's new position and Fatima's new position.

If $5$ passengers at the very back of the line give up and leave, what is Haruki's new position counting from the back of the line?

35^{\text{th}}

36^{\text{th}}

37^{\text{th}}

41^{\text{st}}

Show answer & explanation

Answer: $35^{\text{th}}$

Answer

The correct answer is the

36^{\text{th}}

position.

By determining the initial total number of passengers (

40 + 32 - 1 = 71

) and identifying Haruki's position from the front (the midpoint of

22

and

40

, which is

31

), we can find Haruki's final position from the back after

5

people leave. The new total is

66

, making Haruki's position from the back

66 - 31 + 1 = 36

.

Step-by-Step Solution

1

Calculate the initial total number of passengers in the line.

Total =

40 + 32 - 1 = 71

passengers.

After the swap, Fatima moves to Diego's old position. Since her new rank is

40^{\text{th}}

from the front and Diego's old rank was

32^{\text{nd}}

from the back, this single position's front and back ranks sum to the total plus one.

2

Determine Diego's new position from the front.

Diego is now

22^{\text{nd}}

from the front.

Because Fatima and Diego completely swapped places, Diego assumes Fatima's original position.

3

Find Haruki's position from the front of the line.

Haruki's position =

\frac{22 + 40}{2} = 31^{\text{st}}

from the front.

Haruki is exactly halfway between Diego's new position (

22^{\text{nd}}

) and Fatima's new position (

40^{\text{th}}

).

4

Calculate the new total number of passengers and Haruki's position from the back.

New total =

71 - 5 = 66

. Haruki's back rank =

66 - 31 + 1 = 36

.

Since

5

people left from the very back, Haruki's front rank (

31^{\text{st}}

) remains unchanged, but the overall line length shrinks to

66

. The standard formula for finding a back rank is (Total - Front Rank + 1).

Key Concept

Position Interchange and Midpoint Ranking

Estimated Time:2m 30s

Question 17Question →

In a vertical stack of passport applications, Amit's folder is placed $8^{\text{th}}$ from the top and $16^{\text{th}}$ from the bottom. What is the total number of passport applications in this stack?

22

23

24

25

Show answer & explanation

Answer: 23

Answer

The total number of passport applications in the stack is 23.

To find the total number of items in a linear arrangement when one item's position is given from both ends, you add the two position numbers and subtract 1. Adding the top rank (8) and the bottom rank (16) gives 24. We must then subtract 1 because Amit's folder is included in both the '8' and the '16'. Therefore,

8 + 16 - 1 = 23

.

Step-by-Step Solution

1

Identify the top and bottom rank of the specific item.

Top position = 8, Bottom position = 16.

Both positions of the same object are required to determine the overall length of the sequence.

2

Apply the dual rank formula for a single item: Total = Top + Bottom - 1.

8 + 16 - 1 = 23.

Subtracting 1 is necessary because Amit's folder is counted twice—once when counting from the top, and once when counting from the bottom.

Key Concept

Single-person dual rank total calculation

Question 18Question →

Four runners participated in a 100-meter sprint. Based on the information provided, arrange the runners in order of their finishing positions, starting from 1st place (fastest) to 4th place (slowest).

- David finished ahead of Michael but behind John.
- Robert finished behind Michael.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from fastest to slowest is John, David, Michael, and Robert.

Based on the provided statements, John is faster than David, who is faster than Michael, who is faster than Robert. Therefore, the continuous sequence from 1st place to 4th place is John, David, Michael, and Robert.

Step-by-Step Solution

1

Analyze the first statement regarding David, Michael, and John.

John > David > Michael

David finished ahead of Michael (David is faster than Michael) but behind John (John is faster than David).

2

Analyze the second statement regarding Robert and Michael.

Michael > Robert

Robert finished behind Michael, meaning Michael is faster than Robert.

3

Combine the relative rankings.

John > David > Michael > Robert

Using transitive logic on the established sequences determines the final absolute order.

Key Concept

Relative position and transitive ranking

Question 19Question →

In a straight row of cadets facing North, Vikram is positioned $13^{\text{th}}$ from the left end and Rahul is positioned $31^{\text{st}}$ from the right end. If they interchange their positions, Vikram becomes $39^{\text{th}}$ from the left end. Another cadet, Sanjay, is standing exactly in the middle of Vikram and Rahul's new positions. What is Sanjay's position from the right end?

44^{\text{th}}

26^{\text{th}}

43^{\text{rd}}

45^{\text{th}}

Show answer & explanation

Answer: $44^{\text{th}}$

Answer

Sanjay's position is

44^{\text{th}}

from the right end.

The correct answer accurately determines the total number of cadets as

69

by combining the left and right ranks of the intersection seat. It identifies Sanjay's position as

26^{\text{th}}

from the left by averaging

13

and

39

, and finally correctly converts this to the

44^{\text{th}}

position from the right using the formula

N - L + 1

.

Step-by-Step Solution

1

Calculate the total number of cadets in the row.

Total =

39 + 31 - 1 = 69

cadets.

After the swap, Vikram is

39^{\text{th}}

from the left. This physical seat is the same as Rahul's original seat, which was

31^{\text{st}}

from the right. The formula for total is

L + R - 1

.

2

Determine the new positions of Vikram and Rahul from the left end.

Vikram's new position =

39^{\text{th}}

from the left. Rahul's new position =

13^{\text{th}}

from the left.

Since they swapped, Rahul occupies Vikram's original seat, which is

13^{\text{th}}

from the left.

3

Calculate Sanjay's position from the left end.

Sanjay's position =

(13 + 39) \div 2 = 26^{\text{th}}

from the left.

Sanjay is exactly in the middle of

13

and

39

, so we average the two positions.

4

Convert Sanjay's position from the left end to the right end.

Sanjay's position from the right =

69 - 26 + 1 = 44^{\text{th}}

.

The formula to find the rank from the opposite end is

\text{Total} - \text{Current Rank} + 1

.

Key Concept

Position Interchange and Midpoint Calculations

Question 20Question →

On a straight railway track, a sequence of freight carriages is standing in a single line. Carriage $X$ is the $38^{\text{th}}$ carriage from the front end, and Carriage $Y$ is the $47^{\text{th}}$ carriage from the rear end. Carriage $Z$ is positioned exactly halfway between Carriage $X$ and Carriage $Y$ . If Carriage $Z$ is the $62^{\text{nd}}$ carriage from the rear end, what is the total number of freight carriages on the track?

Show answer & explanation

Answer: 114

Answer

114

The positional distance between Carriage

Y

and Carriage

Z

from the rear is 15. Since

Z

is the midpoint, Carriage

X

is another 15 positions ahead, making

X

the

77^{\text{th}}

carriage from the rear. Since

X

is also

38^{\text{th}}

from the front, the total number of carriages is calculated as

38 + 77 - 1 = 114

.

Step-by-Step Solution

1

Calculate the positional difference between Carriage

Y

and Carriage

Z

from the rear.

62 - 47 = 15

positions.

To find the distance from one end of the segment to its exact midpoint.

2

Determine Carriage

X

's position from the rear.

Carriage

X

is the

77^{\text{th}}

carriage from the rear.

Since

Z

is exactly halfway between

X

and

Y

, the positional difference between

Z

and

X

must also be 15. Thus,

62 + 15 = 77

.

3

Calculate the total number of carriages.

38 + 77 - 1 = 114

carriages.

The total number of items in a row equals (Position from front) + (Position from rear) - 1.

Key Concept

Calculating total count using dual positional ranks and midpoint symmetry in a sequence.

Order and Ranking

Answer

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