Lessons / Logical reasoning
Logical reasoning · Day 10

Ranking

Position from left + position from right = total + 1. Everything in this topic is that one line.

Practise (6 questions) Present as slides

Why this topic matters

Ravi is 7th from the left and 12th from the right in a row. How many people are there? 7 + 12 - 1 = 18: Ravi was counted twice.

Ranking questions all come from one identity: position from left + position from right = total + 1.

Left + right - 1 = total

A person counted from both ends is counted twice, so subtract 1.

Between two people: if A is p-th from the left and B is q-th from the left, there are |p - q| - 1 people between them.

123456Ravi789101112131415161718leftright
7th from the left and 12th from the right: 18 people
Total = left rank + right rank - 1
Right rank = total - left rank + 1
Example 1In a class of 40, Priya is 15th from the top. What is her rank from the bottom?
  1. Bottom rank = 40 - 15 + 1.Rearranged identity.
  2. = 26.
Example 2In a row, A is 10th from the left and B is 15th from the right. If they swap places, A becomes 18th from the left. How many people are in the row?
  1. After the swap A is where B was: 18th from the left and 15th from the right.The swap tells us B's left position.
  2. 18 + 15 - 1 = 32.

Formula summary

Total
Left rank + right rank - 1.
Swap two people
The change in one's rank equals the change in the other's.
Between two people
Total - (sum of their ranks from opposite ends) ... draw it when overlap is possible.

Shortcuts and tricks

Total from both ends

Use it when: '15th from the top and 20th from the bottom'.

  1. 15 + 20 - 1 = 34.
ExampleTotal students?
  1. 34.

Before you move on, you should be able to...

  • use left + right - 1 = total
  • count people between two positions
  • solve swap questions

Practice questions (6)

Try each one before opening the solution. Or practise them one by one so your score is saved.

easy Ram is 12th from the left and 18th from the right in a row. How many are in the row?
  1. 12 + 18 - 1.

Answer: 29

easy In a class of 40, Sita is 15th from the top. Rank from the bottom?
  1. 40 - 15 + 1.

Answer: 26

easy A and B are 10th and 25th from the left in a row of 40. How many between them?
  1. 25 - 10 - 1.

Answer: 14

medium A is 14th from the left, B is 17th from the right, and there are 5 people between them (A to the left of B). Total?
  1. 14 + 5 + 17 = 36.

Answer: 36

medium A and B swap places. A was 8th from the left and moves to 15th from the left; B was 12th from the right. B's new rank from the right?
  1. A moved 7 places right, so B moved 7 places left.
  2. 12 + 7 = 19.

Answer: 19

hard Rita is 12th from the left, Mona 4th from the right. They swap, and Rita is now 15th from the left. How many are in the row?
  1. Rita now sits where Mona was: 15th from left and 4th from right.
  2. 15 + 4 - 1.

Answer: 18

Class plan (2 hours, for trainers)

A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.

10 minWarm-up.
30 minThe identity with a real row of students.
25 minPeople between two positions.
15 minSwaps.
35 minPractice set.
5 minRecap.
← AnalogySyllogisms →
RankingPractise now