Order And Ranking: Reasoning Questions, Mock Test, Types

Order and Ranking is one of the most important topics of the Reasoning aptitude section. Questions based on this topic are often seen in many competitive exams.In order and ranking questions, the information related to objects or persons would be given based on height, weight, length, marks, time, etc. The aspirants need to arrange the persons or objects based on the given information in ascending and descending order.
In some of the questions, the rank of the person from top or bottom, left or right would be given. The following formula can help to get the rank of the person from either end or to calculate the total number of persons in that arrangement -

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This Story also Contains

1. Approach to Solve the Questions Based on Order and Ranking
2. Types of Order and Ranking Questions
3. Practice and Resources on order and ranking
4. Question Weightage of Order and Ranking in Competitive Exams
5. Practice Questions For Time and sequence-based order and ranking
6. Practice Questions For Height/weight/length or marks based on order and ranking
7. Practice Questions For Ranking from top or bottom
8. Practice Questions For Ranking from left or right
9. Order and Ranking Questions for TANCET/ SRMJEE
10. Order and Ranking Questions for SSC/ RRB exams
11. Order and Ranking Questions for Banking/ Insurance exams

Total number = Position from the left or the bottom + Position from the right or the top - 1

Approach to Solve the Questions Based on Order and Ranking

1. Read the given information carefully and then decide whether you want to arrange in ascending or descending order.

2. Consider drawing all the possibilities that can be drawn based on the given information.

3. Keep eliminating those possibilities in which all the given cases cannot be satisfied.

4. Use the formula, if required to calculate the position or rank of the person.

Types of Order and Ranking Questions

Following are the types of questions asked from the order and ranking concept -

1. Time and sequence-based order and ranking

2. Height/weight/length or marks based on order and ranking

3. Ranking from top or bottom

4. Ranking from left or right

Now let’s understand all of the types of Order and Ranking questions in detail -

1. Time and sequence-based order and ranking

In this type of order and ranking questions, information related to the time or numbers would be given. Compare the given information and arrange them in ascending or descending order and accordingly answer the question that follows.

Example:

Directions: The number of letters in six words B1, B2, B3, B4, B5, and B6 are compared. The number of letters in B1 is the least. The number of letters in B4 is more than B1 but less than B2. The number of letters in B6 is more than B3 and B5. The number of letters in B3 is more than B2. If the number of letters in B5 is more than B3, then the number of letters in B4 is less than the number of letters in how many words?

(a) 4 (b) 2 (c) 1 (d) 3

Solution:
I. The number of letters in B1 are least.
B2, B3, B4, B5, B6 > B1
II. The number of letters in B4 is more than B1 but less than B2.
B2 > B4 > B1
III. The number of letters in B6 is more than B3 and B5.
B6 > B3, B5
IV. The number of letters in B3 is more than in B2.
B3 > B2
V. The number of letters in B5 is more than in B3.
B5 > B3
Therefore, from the above statements, the order is –
B6 > B5 > B3 > B2 > B4 > B1

So, the number of letters in B4 is less than the number of letters in four words. Hence, the first option is correct.

2. Height/weight/length or marks based on order and ranking

In this type of order and ranking questions, information related to the height, length, weight or marks of the persons would be given. Compare the given information and arrange them in ascending or descending order and accordingly answer the question that follows.

Example:

Directions: Marks obtained by the seven students of a tuition class, Panchi, Qazi, Ricky, Sweta,

Tiya, Urusha, and Vinay, are mentioned. Panchi scored the second-highest marks in the class.

The marks scored by Vinay were higher than only one of the people. Sweta's score was more

than Tiya's but less than Panchi's. Three people got higher than Tiya and three got less than

Tiya. Neither Ricky nor Qazi received the lowest marks.

Given that no two students have the same marks, whose marks were the lowest?

(a) Ricky (b) Urusha (c) Vinay (d) Tiya
Solution:
1. Panchi scored the second-highest marks in the class. The marks scored by Vinay were higher than only one of the people.

2. Sweta's score was more than Tiya's but less than Panchi's. Three people got higher than Tiya and three got lesser than Tiya. Neither Ricky nor Qazi received the lowest marks.

Ricky/Qazi > Panchi > Sweta > Tiya > Ricky/Qazi > Vinay > Urusha

So, Urusha has scored the lowest marks. Hence, the second option is correct.

3. Ranking from top or bottom

In this type of order and ranking questions, information related to the rank of the person from top and bottom would be given, the aspirant needs to calculate the total number of persons, or the rank from one end and the total number of persons would be given the aspirant needs to calculate the rank of the person from the other end.

Example:

Directions: Amit ranked 7th from the top and 26th from the bottom in his class. How many students are there in the class?

(a) 31 (b) 33 (c) 27 (d) 32
Solution:

Amit ranked 7th from the top and 26th from the bottom in his class.

Total number of students in the class = (Position from top) + (Position from bottom) – 1
= 7 + 26 – 1
= 32

Therefore, 32 students are there in the class. Hence, the fourth option is correct.

4. Ranking from left or right

In this type of order and ranking questions, information related to the rank of the person from left and right would be given, the aspirant needs to calculate the total number of persons, or the rank from one end and the total number of persons would be given the aspirant needs to calculate the rank of the person from the other end.

Example:
Directions: All 32 students in a class are standing in a row facing north. Akash is 12th from the right end while Priya is 18th from the left end. How many people are standing between Akash and Priya?

(a) Two (b) Four (c) Three (d) Five
Solution:

There are a total of 32 students in the class.
Akash is 12th from the right end while Priya is 18th from the left end.

⇒ If Aakash is 12th from the right end, this means that 11 students are standing after Aakash.
Thus, the position of Aakash from the left end will be→32 – 11 = 21st
⇒ Priya is 18th from the left end and Aakash is 21st from the left end, then the number of students standing between both of them is→21 – 18 = 2

So, 2 people are standing between Akash and Priya. Hence, the first option is correct.

Practice and Resources on order and ranking

Following are the recommended sources for the practice of the questions of order and ranking -
a) A Modern Approach to Verbal & Non-Verbal Reasoning by R.S. Aggarwal

b) Analytical Reasoning by M.K. Pandey

c) Logical and Analytical Reasoning by A.K. Gupta

d) Test of Reasoning by Edgar Thorpe

Question Weightage of Order and Ranking in Competitive Exams

The number of questions based on order and ranking varies from exam to exam -

1) In SSC and various Banking competitive exams like SBI, IBPS, and RRB, 3 to 4 questions are asked from this topic.
2) In the Railways exam i.e. Group D, NTPC, JE, ALP etc - 1 to 2 questions are asked.

3) In CUET, NPAT and other college entrance exams - 1 to 2 questions are asked.

Practice Questions For Time and sequence-based order and ranking

Q1. Directions: Speed of five cars C1, C2, C3, C4, and C5 are compared. The speed of C1 is more than only one car. The speed of C5 is more than four cars. The speed of C4 is more than C1 but less than C3 and C5. Speed of how many cars is less than the speed of C3?

1. 0

2. 1

3. 3 (correct)

4. 2

Solution-

Given:
(I) Speed of five cars C1, C2, C3, C4, and C5 are compared.
_, _, _, _, _
(II) Speed of C1 is more than only one car.
_ > _ > _ > C1 > _
(III) Speed of C5 is more than four cars.
C5 > _ > _ > C1 > _
(IV) Speed of C4 is more than C1 but less than C3 and C5.
C5 > C3 > C4 > C1 > C2

So, the speed of three cars is less than the speed of C3. Hence, the third option is correct.

Q2. Directions: The number of wickets taken by six bowlers Anil, Kamal, Laxman, Mohan, Bittu and Rahul are compared. The number of wickets taken by Kamal is more than only the number of wickets taken by Anil. The number of wickets taken by Bittu is less than only two bowlers. The number of wickets taken by Mohan is not more than Bittu. Who among the following has taken more wickets than Bittu?

1. Rahul (correct)

2. Kamal

3. Anil

4. Mohan

Solution-

Given:
1. The number of wickets taken by Kamal is more than only the number of wickets taken by Anil; Kamal > Anil
2. The number of wickets taken by Bittu is less than only two bowlers; _ > _ > Bittu
3. The number of wickets taken by Mohan is not more than Bittu; Bittu > Mohan

So, combining the above statements, the final arrangement is –
(Laxman, Rahul) > Bittu > Mohan > Kamal > Anil
The position of Laxman and Rahul cannot be determined. They can either be in 1st or 2nd place.

Since Laxman is not mentioned in the options so, according to the options given, Rahul has taken more wickets than Bittu. Hence, the first option is correct.

Q3. Directions: The prices of five cars B, M, J, N, and U are compared. The price of J is less than U, M, and N. The price of B is the lowest. No two cars have the same price. The price of U is less than M. The price of neither U nor M is the highest. The price of how many cars is less than the price of M?

1. 3 (correct)

2. 2

3. 4

4. 1

Solution-

Given:
I. The price of J is less than U, M and N→J < (U, M, N)
II. The price of B is the lowest→B < J < (U, M, N)
III. The price of U is less than M→B < J < U < (M, N)
IV. The price of neither U nor M is the highest ⇒ N has the highest price.
By concluding all the given information we have – B < J < U < M < N

So, three cars have a price less than the price of M. Hence, the first option is correct.

Q4. Directions: Seven brothers Subham, Sourav, Sehwag, Sachin, Sam, Shoaib, and Surya have different ages. Subham is the eldest brother. Surya is older than only two brothers. Sourav is older than Sam but younger than Shoaib. Sehwag is older than Sachin only. How many brothers are younger than Sourav?

1. 2

2. 3

3. 5

4. 4 (correct)

Solution-

Given:
1. Subham is the eldest brother.
Subham > _ > _ > _ > _ > _ > _
2. Surya is older than only two brothers.
Subham > _ > _ > _ > Surya > _ > _
3. Sourav is older than Sam but younger than Shoaib.
Shoaib > Sourav > Sam
4. Sehwag is older than Sachin only.
Subham > _ > _ > _ > Surya > Sehwag > Sachin

Therefore, the correct order of age is –
Shubham > Shoaib > Sourav > Sam > Surya > Sehwag > Sachin

So, Sourav has 4 younger brothers. Hence, the fourth option is correct.

Q5. Directions: Five girls Anjali, Beena, Chintu, Diksha, and Saruti are of different ages. Anjali is younger than only Diksha and Shruti. Shruti is younger than Diksha. Chintu is the youngest. Who is the fourth oldest?

1. Beena (correct)

2. Chintu

3. Diksha

4. Shruti

Solution-

Given:
1. Anjali is younger than only Diksha and Shruti.
Anjali < Diksha, Shruti
2. Shuti is younger than Diksha.
Anjali < Shruti < Diksha
3. Chintu is youngest.
Chintu < Beena < Anjali < Shruti < Diksha

So, Beena is the fourth oldest. Hence, the first option is correct.

Practice Questions For Height/weight/length or marks based on order and ranking

Q1. Directions: Among seven sisters, T, U, V, W, X, Y, and Z. U is older than only four other sisters. V is older than W. T is older than Y. X is older than one person only that is Z who is the youngest among all sisters. U is older than T. Given that no two sisters are of the same age, find who is the eldest sister.

1. X

2. V (correct)

3. U

4. W

Solution-

Given:
I. U is older than only four other sisters.
_ > _ > U > _ > _ > _ > _
II. X is older than one person only that is Z who is the youngest among all sisters.
_ > _ > U > _ > _ > X > Z
III. T is older than Y. U is older than T.
_ > _ > U > T > Y > X > Z
IV. V is older than W.
V > W > U > T > Y > X > Z

So, it is clear that V is the eldest. Hence, the second option is correct.

Q2. Directions: Amongst six friends Uday, Vikrant, William, Xena, Yasir and Ziya, each has a different height. Vikrant is taller than only three other friends. Ziya is only taller than Xena and William is only shorter than Uday. Given that no two friends have the same height, find who is the third shortest among all the friends.

1. Uday

2. Ziya

3. Yasir (correct)

4. William

Solution-
Given:
I. Vikrant is taller than only three other friends.
_ > _ > Vikrant > _ > _ > _
II. Ziya is only taller than Xena.
_ > _ > Vikrant > _ > Ziya > Xena
III. William is only shorter than Uday.
Uday > William > Vikrant > Yasir > Ziya > Xena

So, Yasir is the third shortest among all the friends. Hence, the third option is correct.

Q3. Directions: Seven students of a coaching centre Param, Qazi, Ravi, Suresh, Tanvir, Uday, and Varsha have obtained different percentages. Param scored the second-highest percentage in the centre. The percentage scored by Varsha was more than only one person. Suresh's percentage was more than Tanvir's but less than Param's. Three people got more percentage than Tanvir and three got lesser than Tanvir. Neither Ravi nor Qazi received the lowest percentage. Whose percentage was the lowest?

1. Tanvir

2. Param

3. Uday (Correct)

4. Qazi

Solution-
Given:
(I) Param scored the second-highest percentage in the centre. The percentage scored by Varsha was more than only one person.
__ > Param > __ > __ > __ > Varsha > __
(II) Suresh's percentage was more than Tanvir's but less than Param's. Three people got more percentage than Tanvir and three got lesser than Tanvir.
__ > Param > Suresh > Tanvir > __ > Varsha > __
(III) Neither Ravi nor Qazi received the lowest percentage.
Ravi / Qazi > Param > Suresh > Tanvir > Ravi / Qazi > Varsha > Uday

So, Uday got the lowest percentage. Hence, the third option is correct.

Q4. Directions: Seven students P, Q, R, S, T, U, and V are the top rankers in the class. No two people got the same rank. The student with the highest marks is given rank 1 and the student with the lowest mark gets rank 7. Q got fewer marks than R but more than T. V got more marks than S. U got more marks than P but less than S. Q got the second least rank and S got the second highest rank. R got fewer marks than P. Who got the lowest marks?

1. T (Correct)

2. R

3. U

4. P

Solution-
Given:
1. Q got the second lowest rank and S got the second highest rank. Q got fewer marks than R but more than T.
_ > S > _ > _ > R > Q > T
2. V got more marks than S. U got more marks than P but less than S. R got fewer marks than P.
V > S > U > P > R > Q > T

So, T got the lowest marks. Hence, the first option is correct.

Q5. Directions: Seven friends M, N, O, P, Q, R, and S having different heights are standing in ascending order of their heights. The tallest person stands on the right and the shortest on the left. Only three friends are taller than O. R is shorter than only Q. N is taller than both P and M but shorter than S. Who is the third tallest?

1. P

2. N

3. S (Correct)

4. O

Solution-
Given:
(I) The tallest person stands on the right and the shortest on the left.
_ < _ < _ < _ < _ < _ < _
(II) Only three friends are taller than O.
_ < _ < _ < O < _ < _ < _
(III) R is shorter than only Q.
_ < _ < _ < O < _ < R < Q
(IV) N is taller than both P and M but shorter than S.
P/M < P/M < N < O < S < R < Q

So, S is the third tallest. Hence, the third option is correct.

Practice Questions For Ranking from top or bottom

Q1. Directions: Four children, Akram, Bopsi, Priya, and Tulsi are sitting on a ladder. Akram is further up on the ladder than Bopsi. Bopsi is in between Akram and Priya. If Tulsi is still further up than Akram, who is the second person from the bottom?

1. Tulsi

2. Akram

3. Priya

4. Bopsi (Correct)

Solution-

Given:
1. Akram is further up the ladder than Bopsi.
2. Bopsi is in between Akram and Priya.
3. Tulsi is still further up than Akram.

So, the second person from the bottom is Bopsi. Hence, the fourth option is correct.

Q2. Directions: Raju ranks 10th from the top and Ravi ranks 21st from the bottom. If there are 3 students between them, how many students are there in the class?

1. 34 (Correct)

2. 33

3. 31

4. 32

Solution-

Given:
Raju ranks 10th from the top and Ravi ranks 21st from the bottom. There are 3 students between Raju and Ravi.

Total number of students = 10 (Raju's rank) + 21 (Ravi's rank) + 3 (students between them)
Total number of students = 34

Therefore, the total number of students in a class is 34. Hence, the first option is correct.

Q3. Directions: In an examination, Rahul got the 11th rank and he was 47th from the bottom among those who passed, 3 students could not appear for the exam. 1 student failed. What is the total number of students in the class?

1. 60

2. 62

3. 59

4. 61 (Correct)

Solution-

Rahul's rank from the top = 11
Rahul's rank from the bottom = 47
Total number of passed students = Rahul's rank from the top + Rahul's rank from the bottom – 1
= 11 + 47 – 1 = 57
So, the total number of passed students = 57
Number of students who didn't appear for the exam = 3
Number of failed students = 1

Total number of students = Number of passed students + number of failed students + Number of students who didn't appear for the exam
= 57 + 3 + 1 = 61

So, the total number of students is 61. Hence, the fourth option is correct.

Q4. Directions: Priyank ranks 6th from the bottom and 28th from the top in a class. How many students are there in the class?

1. 31

2. 32

3. 33 (Correct)

4. 34

Solution-

Given:
Priyank ranks 6th from the bottom and 28th from the top in a class.

In the class, the total no. of students = Rank from top + Rank from bottom – 1
= (28 + 6) – 1
= 34 – 1
= 33

So, the total number of students in the class is 33. Hence, the third option is correct.

Q5. Directions: In a row of people, Manu is 7th from the bottom end of the row. Shrey is 10 ranks above Manu. If Shrey is 8th from the top, then how many people are there in this row?

1. 25

2. 26

3. 24 (Correct)

4. 23

Solution

Given:
Manu is 7th from the bottom end of the row. Shrey is 10 ranks above Manu and is 8th from the top.

The rank of Shrey from the top = 8
The rank of Shrey from the bottom = 10 + 7 = 17 ( Since Shrey is 10 ranks above Manu)
Total number of people in a row = Rank from top + Rank from bottom – 1
Total number of people in a row = 8 + 17 – 1 = 24

So, the total number of people in the row is 24. Hence, the third option is correct.

Practice Questions For Ranking from left or right

Q1. Directions: In a row of cars, Maruti is 20th from the left end of the row. Honda is 10th to the right from Maruti and is at the exact centre of the row. How many cars are there in the row?

1. 54

2. 59 (Correct)

3. 57

4. 56

Solution-

Given:
Maruti is 20th from the left end of the row. Honda is 10th to the right from Maruti and is at the exact centre of the row.

Maruti = 20th from the left end of the row.
Honda = 10th to the right from Maruti means it is 30th from the left end of the row = At the exact centre of the row.
If the 30th car is at the exact centre, then the total number of cars will be –
29(cars in the left to the centre car) + 29(cars in the right to the centre car) + 1(30th car) = 59

So, the total number of cars is 59. Hence, the second option is correct.

Q2. Directions: In a row of children, Ravi is fourth from right and Sham is second from left. When they interchange positions, Ravi is ninth from right. What will be Sham's position from the left?

1. Fifth

2. Sixth

3. Seventh (Correct)

4. Eighth

Solution-

Given:
Ravi is fourth from right and Sham is second from left. When they interchange positions, Ravi is ninth from right.
After interchanging Ravi is ninth from right.
So, the total number of students in the row = 9 + 1 = 10
Sham’s new position from left = 10 − 3 = 7th

So, Sham's position is seventh from the left. Hence, the third option is correct.

Q3. Directions: In a row at a bus stop, A is 7th from the left, and B is 9th from the right. They both interchange their positions. Now A becomes 11th from the left. How many people are there in the row?

1. 10

2. 20

3. 19 (Correct)

4. 18

Solution-

Given:
A is 7th from the left, and B is 9th from the right. They both interchange their positions. Now A becomes 11th from the left.

After interchanging the new position of A = 11th from the left
Total number of persons = New position of A from left + B's position from right – 1
Total number of persons = 11 + 9 – 1
Total number of persons = 19

So, the total number of people at a bus stop is 19. Hence, the third option is correct.

Q4. Directions: In a row of children, Rashi is fifteenth from left. If Ramesh who is twenty-ninth from the right interchanges his position, Rashi becomes twenty-sixth from the left. How many children are there in the row?

1. 56

2. 64

3. 54 (Correct)

4. 45

Solution-

Given:
Rashi is the fifteenth from the left.
If Ramesh who is twenty-ninth from the right interchanges his position, Rashi becomes twenty-sixth from the left.

Total number of children in a row = New position of Rashi from the left + Position of Ramesh from the right – 1
Total number of children in a row = 26 + 29 – 1
Total number of children in a row = 54

Total number of children in a row is 54. Hence, the third option is correct.

Q5. Directions: In a row of trees, one tree is the 7th from either end of the row. How many trees are there in the row?

1. 11

2. 13 (Correct)

3. 15

4. 14

Solution-

Given:
One tree is the 7th from either end of the row.

This means that there are 6 six trees ahead of that tree and 6 six trees behind that tree.
Then, the total number of trees in a row including that one tree is = 6 + 6 + 1 = 13

So, the total number of trees is 13. Hence, the second option is correct.

Order and Ranking Questions for TANCET/ SRMJEE

1) Directions: Paresh is 14th from the left and Dileep is 16th from the right in a line of students. When both Paresh and Dileep interchange their positions, the position of Dileep becomes 21st from the right. How many students are there in the line?

1) 33

2) 35

3) 36

4) 34

Hint: Observe the position of the persons from both sides and subtract 1 from the sum of the positions from the left and right sides.

Solution

Paresh is 14th from the left and Dileep is 16th from the right in a line of students. The position of Dileep becomes 21st from the right when both interchange their positions.

So, we can say that –

Paresh position of 14th from the left end = Paresh position of 21st from the right end.

The total number of students in that row = (Position from left) + (Position from right) – 1

= (14 + 21) – 1 = 35 – 1 = 34

So, the total number of people in the line is 34. Hence, the fourth option is correct.

2) Directions: Among seven friends A, B, C, D, E, F, and G, G is older than A and C. C is older than D. F is older than one friend only. A is the third eldest. E is the youngest. G is younger than B. Who is the eldest?

1) G

2) F

3) B

4) C

Hint: Follow the instructions and arrange them in descending order according to their age.

Solution

I. G is older than A and C. C is older than D. A is the third eldest.

_ > G > A > C > D

II. F is older than one friend only. E is the youngest. G is younger than B. After combining all the statements –

B > G > A > C > D > F > E

So, B is the eldest person. Hence, the third option is correct.

Order and Ranking Questions for SSC/ RRB exams

1) Directions: O, P, Q, R, S, and T are six sisters who are good at knitting. T is better than S. Q is better than R. O is better than P. Q is not as good as P. S is better than O. Who among the six is the best at knitting?

1) P

2) O

3) T

4) S

Hint: Arrange the sisters according to their knitting skills as per the instructions.

Solution

I. T is better than S. S is better than O. O is better than P.

T > S > O > P

II. Q is better than R. Q is not as good as P.

P > Q > R

After combining all the statements, the order is –

T > S > O > P > Q > R

So, T is best at knitting. Hence, the third option is correct.

2) Directions: In a class, 24 students have scored more marks than Vineet, whereas 19 students have scored fewer marks than Surbhi. Arti has scored more marks than Surbhi, but lesser marks than Vineet. Arti has scored fewer marks than 29 students and more marks than 26 students. How many total students are there in the class?

1) 54

2) 57

3) 56

4) 55

Hint: Find the rank of Arti from top and bottom to find the number of students in the class.

Solution

This means Arti has the 30th rank from the top and the 27th rank from the bottom.

So, the number of students in the class = (rank from top) + (rank from bottom) – 1

Number of students in the class = 30 + 27 – 1

= 56

So, the total number of students in the class is 56. Hence, the third option is correct.

Order and Ranking Questions for Banking/ Insurance exams

1) Directions: A group of 10 students are sitting in a row according to their age. Rohan is sixth from the beginning and his friend Shomya is ninth from the end of the row. How many students are sitting between them?

1) 3

2) 4

3) 2

4) 5

Hint: Calculate the position of both persons from the same end.

Solution

Rohan is 6th from the beginning.

Shomya is ninth from the end of the row, which means Shomya is 2nd place from the beginning.

The number of people sitting between Shomya and Rohan = (Position from the left of Rohan – Position from the left of Shomya + 1)

= 6 – 2 + 1 = 3.

So, 3 persons sit between Shomya and Rohan. Hence, the first option is correct.

2) Directions: In a class, Sheena's roll number is 8th from the top and Sushmit's roll number is 11th from the bottom. If there are nine students between them, what is the total number of students in the class?

1) 29

2) 28

3) 24

4) 26

Hint: The total number of students in the class is equal to the sum of the position from the top, the position from the bottom, and the total number of students in between.

Solution

The total number of students in the class = (Position from top) + (position from bottom) + (total students in between)

= 8 + 11 + 9

= 28

So, the total number of students in the class is 28. Hence, the second option is correct.

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Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.