Solving Number Ranking and Time Sequence Problems

The 3 Types of Number Ranking and Sequence Problems:
1. Number Type Test
2. Ranking Type Test
3. Number Type Test

Two type of symbols:
greater than(>)
less than(<).

To solve these questions we only know the three things:

Symbol of Greater Than and Less than means if A>B IMPLIES THAT (A is greater than B)or B < A(B is smaller than A)

These are for the same person:

TOTAL={(TOP+BOTTOM)-1}

TOTAL={(LEFT+RIGHT)-1}

In numbering and ranking arrangement questions, position/rank of a person from left-right/top-bottom of a row/class is to be determined or rank/position is given & total no. of persons is to be calculated.

You may also be asked to determine, using data given, which floor which person lives on.

Tips:

1) Read the statement line by line and apply the cases as explained below.

2) Position can be from either sides of row and rank is always from top or bottom of the row

Number Ranking Problem Type 1
Total number of persons = {(sum of positions of same person from both sides i.e. left and right side) – 1}

OR

2) Position of a person from opposite side = {(Total no. of persons – Position of same person from given side) +1}

Example 1: In a row of persons, position of A from left side of the row is 27th and position of A from right side of the row is 34th. Find total no. of persons in the row?

Solution: Total no. of students = (Position of A from left + Position of A from right) -1
?Total no. of students = (27 + 34) – 1 = 61 – 1 = 60

Example 2: In a row of 16 persons, position of A from left side of the row is 12th. Find the position of A from right side of the row?

Solution: Position of A from right side = {(Total no. of persons – Position of A from left side) + 1}

?Position of A from right side = (16 – 12) + 1 = 4 + 1 = 5th


Number Ranking Problem Type 2
1) Total no. of persons = No. of persons after or before the given person in a row + Position of same person from the other side

OR

2) No. of persons after or before the given person in a row = Total no. of persons – Position of same person from other side

Example 1: In a row of persons, position of A from left side of the row is 27th and there are 5 persons after A in the row. Find total no. of persons in the row?

Solution:No. of persons in the row = Position of A from left + No. of persons after A

? Total no. of persons = 27 + 5 = 32

Example 2: In a row of 18 persons, position of A from left side of the row is 6th. Find the no. of persons after A in the row?

Solution: No. of persons after A = Total no. of persons – Position of A from left

? No. of persons after A in the row = 18 – 6 = 12


Number Ranking Problem Type 3
When the positions of two persons are given from opposite ends and we know the total number of persons, then two cases arise when trying to determine the number of persons between these two persons –

When there is no overlapping: i.e. the sum of positions of the two persons from opposite ends < total number of persons

When there is overlapping: i.e. the sum of positions of the two persons from opposite ends > total number of persons

Case 1: No. of students between two different persons = Total no. of students – (Sum of positions of two different persons from opposite sides)

Example 1: In a row of 54 persons, A is 15th from the left side of the row and B is 20th from the right side of the row. Find the no. of persons sitting between A and B?

Solution: Here Sum of positions of A & B from opposite ends = 15 + 20 = 35 < Total no. of persons

? No. of persons between A & B = Total no. of students – (Position of A from left + Position of B from right)

? No. of persons between A & B = 54 – (15+20) = 54 – 35 = 19

Case 2: No. of students between two different persons = (Sum of positions of two different persons from opposite sides) – Total no. of students – 2

Example 1 In a row of 54 persons, A is 35th from the left side of the row and B is 22nd from the right side of the row. Find the no. of persons sitting between A and B?

Solution: Here Sum of positions of A & B from opposite ends = 35 + 22 = 57 > Total no. of persons

? No. of persons between A & B = (Position of A from left + Position of B from right) – Total no. of students – 2

? No. of persons between A & B = (35+22) – 54 – 2 = 57 – 54 – 2 = 1


Number Ranking Problem Type 4
If total no. of students is to be calculated and positions of different persons from any side are given then it is always a case of ‘cannot be determined’ or ‘data inadequate’ or ‘can’t say’. This is because we do not know if there is overlapping or not.

Example 1 In a row Position of A from left side of the row is 18th and position of B from right side of the row is 25th. Find the total no. of students in the row?

Solution: Cannot be determined as position of different persons is given from the same side.


Number Ranking Problem Type 5
Positions of two persons is given and their positions are interchanged and after interchanging position of 1st person is given from same side as before interchanging

Position of 2nd person from the same side as before interchanging = Position of 2nd person from same side before interchanging + (Position of 1st person after interchanging – position of 1st person before interchanging from same side)

To find total no. of students Þ Find the person whose position from both sides can be depicted from the statement. Add both his positions from opposite ends and subtract 1.

To find no. of persons between them Þ Difference in the position of common person whose position from same side before and after interchanging is given then subtract 1

Example 1 A and B are standing in a row of persons. A is 18th from left side of the row and B is 24th from right side of the row. If they interchange their positions A becomes 31st from left. Find

i) New position of B from right side

ii) Total no. of persons

iii) No. of persons between A & B

Explanation:
i) New position of B from right side = Position of B from right side before interchanging + (Position of A from left side after interchanging – Position of A from left side before interchanging)

? New position of B from right side = 24 + (31 – 18) = 24 + 13 = 37th

ii) Total no. of persons = (A’s position from right before interchanging + A’s position from left before interchanging) – 1

? Total no. of persons = (B’s position from right after interchanging + A’s position from left before interchanging) – 1

? Total no. of persons = (24 + 31) – 1 = 55 – 1 = 54

iii) No. of persons between A & B = (Position of A from left after interchanging– Position of A from left before interchanging) – 1

? No. of persons between A & B = (31 – 18) – 1 = 13 – 1 = 12


Number Ranking Problem Type 6
If positions of two different persons are given from opposite sides of the row and a third person is sitting exactly in middle of the two and total no. of persons in the row is to be calculated as

i) When position of third person sitting is given from either side of row
ii) When position of third person is given from either of the two persons between whom he/she is sitting
Then find the position of the 3rd person from both sides of the row and hence find total no. of persons according to type 1

Example 1 In a row of persons, position of A from left side of the row is 9th & position of B from right side of the row is 8th.If C is sitting just in middle of A & B and position of C from left side of the row is 15th. Find the total no. of persons in the row?

Explanation: Position of C from left is 15th and A from left is 9th so there are (15 – 9 – 1 = 5) persons are sitting between A and C. As C is sitting in middle of A and B so there must also be 5 persons sitting between B and C.

Thus position of C from right = Position of B from right + 5 + 1 = 8 + 6 = 14th

Total no. of students = (Sum of positions of C from both sides – 1)

? Total no. of students = (15 + 14) – 1 = 29 – 1 = 28

Example 2 In a row of persons, Position of A from left side of the row is 11th and B from right side of the row is 19th. If C is sitting just in middle of A & B and position of C from A is 7th. Find total no. of persons in the row?

Explanation: Position of C from Left = Position of A from left + Position of C from A = 11 + 7 = 18th

Given C is 7th from A and C is sitting in middle of A and B then also C is at 7th position from B

Position of C from right = Position of B from right + Position of C from B = 19 + 7 = 26th

Total no. of students = (Sum of position of C from both sides – 1)

? Total no. of students = (18 + 26) – 1 = 44 – 1 = 43

Number Ranking Problem Type 7
In the questions where it is asked to find minimum no. of persons in a row then it is always a case of overlapping i.e. given positions of persons from either sides overlap each other.

Then

Minimum no. of persons = Sum of positions of persons from both sides – Persons between them – 2

Example 2 If position of A from left side of a row is 15th and position of B from right side of a row is 19th and only 1 person is sitting in middle of A & B. Find the minimum number of persons that can be seated in this row?

Explanation: Total no. of persons = 15 + 19 – 1 – 2 = 31

Number Ranking Problem Type 8
These are numbering type questions. In this type of question, it is given that there are several people living in an n-storey building. Some information will be given about the relative positions of one above or below the other. You need to find which floor each person lives on. These are almost similar to seating arrangement questions. However, you may be required to apply the rules you learnt above, in these problems.


Ranking And Direction Short Cut:

Ranking Test:

In this type, generally a set, group or series of numerals is given and the candidates is asked to trace out numerals following certain given conditions or lying at specific mentioned positions after shuffling according to a certain given pattern.

Examples:

Here is a table.

No. Rank from top Rank from bottom
A 1 6
B 2 5
C 3 4
D 4 3
E 5 2
F 6 1


Let take the case of‘D’

D’s rank from top = 4 and from bottom = 3

Now total rank = 6

Means total rank = (rank from top + rank from bottom) – 1

Now rank from top = (total rank + 1) – rank from both

Rank from bottom = (total rank + 1) – rank from top


Example 1: How many 1’s are there in number sequence that immediately followed by 3 and not immediate preceded by 1.
2 3 4 1 3 9 5 6 8 4 1 3 9 4 1 3 3 2 5 4 8 4 1 3 9 4 3 2
Solution: Four in number sequence that immediately followed by 3 and not immediate preceded by 1.
2 3 [ 4 1 3 ] 9 5 6 8 [ 4 1 3 ] 9 [ 4 1 3 ] 3 2 5 4 8 [ 4 1 3 ] 9 4 3 2

Example 2: How many odd number are there in sequence which is followed by even number and immediately preceded by odd number ?
2 4 7 2 8 7 2 2 9 1 7 4 2 2 4 4 8 8 3 7 6 9 9 7 3 7 1 3 7 7 7 8
Solution: There are three which is followed by even number and immediately preceded by odd number .
2 4 7 2 8 7 2 2 9 [ 1 7 4 ] 2 2 4 4 8 8 [ 3 7 6 ] 9 9 7 3 7 1 3 7 [ 7 7 8 ]

Example 3: How many even number are there in sequence which is followed by even number and immediately preceded by odd number ?
3 4 7 5 3 2 8 9 5 8 7 1 3 9 4 1 2 3 2 8 3 4 5 5 6 3 2 8 9 4 3
Solution: There are three which is followed by even number and immediately preceded by odd number .
3 4 7 5 [ 3 2 8 ] 9 5 8 7 1 3 9 4 1 2 [ 3 2 8 ] 3 4 5 5 6 [ 3 2 8 ] 9 4 3

Example 4: Find the number 6’s there in the following numbers sequence that is exactly divisible by its immediate preceded number and also followed numbers ?
1 7 2 6 7 7 2 6 3 7 8 5 4 5 8 8 9 7 1 3 2 6 3 1 3 9 7 1 3 2 6 3
Solution: Here three 6’s are present which exactly divisible by its immediate preceded number and also followed numbers.
1 7 2 6 7 7 [ 2 6 3 ] 7 8 5 4 5 8 8 9 7 1 3 [ 2 6 3 ] 1 3 9 7 1 3 [ 2 6 3 ] 1

Example 5: Count 9 in the numbers sequence which is followed by 7 and preceded by either 4 or 5. How many 9 are there in the sequence ?
1 2 3 7 8 9 1 4 9 7 3 6 9 8 1 5 3 5 9 7
Solution: Two 9 are present which is followed by 7 and preceded by either 4 or 5.
1 2 3 7 8 1 [ 4 9 7 ] 3 6 9 8 1 5 3 [ 5 9 7 ] 1 1 2 7

Example 6: Count the numbers in the given sequence numbers, which have equal frequency ?
1 5 4 8 9 7 1 5 4 7 8 9 1 6 5 7 8 9 2 4 7 5 6 8 9 2 6 5 4 7 9 2 4 5 8 7 4 6 9 8 3 9 5 4 6 9 7 3 4 5 8 3
Solution: 1’s has three times and 2 has three times and 3 has three times present in this number sequence.
[ 1 ] 5 4 8 9 7 [ 1 ] 5 4 7 8 9 [ 1 ] 6 5 7 8 9 [ 2 ] 4 7 5 6 8 9 [ 2 ] 6 5 4 7 9 [ 2 ] 4 5 8 7 4 6 9 8 [ 3 ] 9 5 4 6 9 7 [ 3 ] 4 5 8 [ 3 ]

Example 7: Find out how many times 2, 3, and 7 have present together, and always 3 in middle and 2 and 7 places either side of 3 ?
1 1 1 1 3 3 2 2 2 3 7 7 3 3 3 6 6 4 7 3 2 4 9 8 7 7 3 2 3 3 3 4 4 2 3 7
Solution: Four times 3 present together with 2 and 7, where 2 and 7 present either side of 3.
1 1 1 1 3 3 2 2 [ 2 3 7 ] 7 3 3 3 6 6 4 [ 7 3 2 ] 4 9 8 7 [ 7 3 2 ] 3 3 3 4 4 [ 2 3 7 ]

Example 8: How many even number are there in sequence which is followed by odd number and not immediately preceded by odd number ?
6 8 6 4 8 7 1 4 4 5 8 2 4 4 4 1 8 8 6 6 8 6 8 6 4 8 8 6 7
Solution: Three number are there in sequence which is followed by odd number and not immediately preceded by even number 487, 445, 441, 867
6 8 6 [ 4 8 7 ] 1 [ 4 4 5 ] 8 2 4 [ 4 4 1 ] 8 8 6 6 8 6 8 6 4 8 [ 8 6 7 ]

Example 9: Find out how many numbers from 1 to 25 which are exactly divisible 3, and arranged in ascending order ?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Solution: 3 6 9 12 15 18 21 24 divisible by 3 in ascending order.
1 2 [ 3 ] 4 5 [ 6 ] 7 8 [ 9 ] 10 11 [ 12 ] 13 14 [ 15 ] 16 17 [ 18 ] 19 20 [ 21 ] 22 23 [ 24 ] 25

Example 10: How many 3 are there in the following list in which followed by 9 and preceded 2, 3, or 4 ?
1 1 2 3 9 4 4 5 5 5 5 3 3 9 8 7 7 7 8 8 8 5 5 4 3 9 6 6 6 6
Solution: Three numbers in which followed by 9 and preceded 2, 3, or 4
1 1 [ 2 3 9 ] 4 4 5 5 5 5 [ 3 3 9 ] 8 7 7 7 8 8 8 5 5 [ 4 3 9 ] 6 6 6 6


Ranking Type Problems

Example 1: In a row of boys, one boy is seventh from either end of the row. Find how many boys are present in the row ?
Solution: Number of boys are in the row is 6+ 1 + 6 = 13.

Example 2: Subir is tenth from the left and fifteenth from right in a row. How many student are present in the row ?
Solution: 10 + 15 – 1 = 24

Example 3: Vinit ranks seventeenth in a math class of thirty-five student’s. What would be his rank from last ?
Solution: Student’s behind Vinit in class = 35 – 17 = 18.
Vinit rank from last is = 18 + 1 = 19.

Example 4: Arin is sixth from right he is fifth to the right of Rakesh who is sixth from left. How many boy’s in a row ?
Solution: 6 +6 + 4 = 16 boys.

Example 5: Jonny ranked twelve from top and forty-five from bottom in a class. Find how many students present in the class ?
Solution: 12 + 45 = 57 – 1 = 56.

Example 6: In a row of a class has 31 girls, When Ritu was shifted by six places towards the left, she became 16th from the right end. What was her position before from the left end of the row?
Solution: 31 – (16 – 6) = 21 + 1 = 22. Ritu before position was 10th from right end and 22 from left end.

Example 7: Joy is sixth from right and jack is fifth from left, if there is seven boy’s between them. How many boy’s are in the row ?
Solution: 6 + 7 + 5 = 18 boy’s.

Example 8: Raj is fifteenth from the top and Suresh is thirty-one from the bottom, there are nine students in between them. How many boy’s are in this row ?
Solution: 15 + 9 + 31 = 55 boy’s.

Example 9 In a row of forty girls Rita is seventeenth from left and Renuka is twelfth from right. How many girls are in between them ?
Solution: 40 – ( 17 + 12 ) = 40 – 29 = 11.

Example 10: In a row of girls, Dipika is fifth from the left and Dolly is eleventh from right, they interchange their positions and Dipika becomes twenty-fifth from left. Find how many girls are in row ?
Solution: New position is 25th from left,
In a row = 24 + 1 + 10 + 35 girls.