Topic : Number Ranking & Sequence PYQ's
CFORMULA
Ranking Starting + Ranking Last= TOTAL NUMBER +1
Ranking top + Ranking Bottom= TOTAL NUMBER +1
Ranking Left + Ranking Right= TOTAL NUMBER +1
Q1. In a queue, Mr. X is fourteenth from the front and Mr. Y is seventeenth from the end, while Mr. Z is exactly in between Mr. X and Mr. Y. If Mr. X is ahead of Mr. Y and there are 48 persons in the queue, how many persons are there between Mr. X and Mr. Z? [CSAT 2011]
(a) 6
(b) 7
(c) 8
(d) 9
Solution:
Given that,
There are 48 persons in the queue
Now,
Mr. X is fourteenth from the front
So , number of persons before X = 13
Mr. Y is seventeenth from the end
So, number of persons after Y = 16
Persons between X and Y = 48 - [13 + 16 + 1(including X) + 1(including Y)] = 17
Z is exactly between X and Y , so Z is 9th from X
Thus total persons between X and Z = 8
Hence option (c) is correct
Q2. In a class of 45 students, a boy is ranked 20th. When two boys joined, his rank was dropped by one. What is his new rank from the end? [CSAT 2013]
(a) 25th
(b) 26th
(c) 27th
(d) 28th
Solution:
Given that,
Total students = 45
Rank of a boy = 20th
Considering 20th from one end
So, from another end = 45 - 20 + 1 = 26th
Also, two boys joined and the rank is dropped by 1
Thus the rank from other end = 26 + 1 = 27th
Hence option (c) is correct
Q3. In a row 'A' is the 11th position from the left and 'B' is in the 10th position from the right. If 'A' and 'B' interchange, then 'A' becomes 18th from the left. How many persons are there in the row other than 'A' and 'B'? [CSAT 2014]
(a) 27
(b) 26
(c) 25
(d) 24
Solution:
Given that,
'A' is the 11th position from the left, so 10 people are on left of A
'B' is in the 10th position from the right so 9 people are on right of B
Now,
If 'A' and 'B' interchange, then 'A' becomes 18th from the left.
From 11th to 18th there were 7 positions were shifted So, number of people between A and B = 6
Thus total persons excluding A and B = 10 (left) + 6 + 9 (right) = 25
Hence option (c) is correct
Q4. In a class of 60 students, where the number of girls is twice that of boys, Kamal, a boy, ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is [CSAT 2016]
(a) 13
(b) 12
(c) 7
(d) 3
Solution:
Given that,
Total students = 60
Number of girls = 2 x number of boys
So Girls = 40 and boys = 20
Kamal is 17th from top, thus 16 students are ahead of Kamal
9 girls are ahead of kamal
Number of boys = 16 - 9 = 7 are ahead of Kamal
Number of boys rank after him = 20 - 7 - 1 (including Kamal) = 12
Hence option (b) is correct
Q5. 15 students failed in a class of 52. After removing the names of failed students, a merit order list has been prepared in which the position of Ramesh is 22nd from the top. What is his position from the bottom? [CSAT 2017]
(a) 18th
(b) 17th
(c) 16th
(d) 15th
Solution:
Given that,
Total students = 52
Number of students failed = 15
So number of students passed = 52 - 15 = 37
Ramesh is 22nd from the top
So, from bottom rank is 37 - 22 + 1 = 16th
Hence option (c) is correct
Q6. In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7? [CSAT 2019]
(a) 1
(b) 2
(c) 3
(d) None
Solution:
Given that,
Sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7
Only one 5 is not preceded by 3
Hence option (a) is correct
Q7. A is 16th from the left end in a row of boys and V is 18th from the right end. G is 11th from A, towards the right and 3rd from V, towards the right ends. How many boys are there in the row? [CSAT 2020]
(a) 40
(b) 41
(c) 42
(d) Insufficient data
Solution:
Given that,
A is 16th from the left end in a row of boys = 15 boys in the left
V is 18th from the right end.
G is 11th from A, towards the right and 3rd from V, towards the right ends.
Now,
There are 7 boys between A and V
There are 2 boys between V and G
Right of G = 14 boys in the right
Total students including A, V and G = 15 + 7 + 2 + 14 + 1 + 1 + 1 = 41
Hence option (b) is correct
Q8. Consider the following sequence of numbers: 5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
How many odd numbers are followed by the odd number in the above sequence? [CSAT 2020]
(a) 5
(b) 6
(c) 7
(d) 8
Solution:
Given that,
sequence of numbers: 5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
odd numbers are followed by the odd number
There are exactly six numbers
5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
Hence option (b) is correct
Q9. Three Statements S1, S2 and S3 are given below followed by a Question: [CSAT 2021]
S1: C is younger than D, but older than A and B.
S2: D is the oldest.
S3: A is older than B.
Question: Who among A, B, C and D is the youngest?
Which one of the following is correct in respect of the above Statements and the Question?
(a) S1 alone is sufficient to answer the Question.
(b) S1 and S2 together are sufficient to answer the Question.
(c) S2 and S3 together are sufficient to answer the Question.
(d) S1 and S3 together are sufficient to answer the Question.
Solution:
Given that,
S1: C is younger than D, but older than A and B.
D > C > A > B or D > C > B > A
S2: D is the oldest.
D > _ > _ >_
cannot be determined
S3: A is older than B.
Thus combining S1 and S3
D > C > A > B
Hence option (d) is correct
Q10. Consider two Statements and a Question: [CSAT 2021]
Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom.
Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom.
Question: What is Seema's rank from the top in the class of 40 students?
Which one of the following is correct in respect of the Statements and the Question?
(a) Statement-1 alone is not sufficient to answer the Question.
(b) Statement-2 alone is not sufficient to answer the Question.
(c) Either Statement-1 alone or Statement-2 alone is sufficient to answer the Question.
(d) Both Statement-1 and Statement-2 are required to answer the Question.
Solution:
Given that,
Total students = 40
Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom.
Thus Priya is above 30 and below 9 in class of 40
Priya rank = 40 - 30 = 10th
Thus rank of Seema = 10 - 4 = 6th
Hence statement 1 alone is sufficient
Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom.
Thus Ena is above 36 and below 3 in class of 40
Ena rank = 40 - 36 = 4th
Therefore Seema rank = 6th
Hence statement 2 alone is sufficient
Q11. Consider two Statements and a Question: [CSAT 2021]
Statement-1: Each of A and D is heavier than each of B, E and F, but none of them is the heaviest.
Statement-2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A, B, C, D and E?
Which one of the following is correct in respect of the Statements and the Question?
(a) Statement-1 alone is sufficient to answer the Question
(b) Statement-2 alone is sufficient to answer the Question
(c) Both Statement-1 and Statement-2 are required to answer the Question
(d) Neither Statement-1 alone nor Statement-2 alone is sufficient to answer the Question
Solution:
Given that,
Statement-1: Each of A and D is heavier than each of B, E and F, but none of them is the heaviest.
As A, B, D, E and F are not heaviest, however there is no information on C
A and D > B, F, E
Hence statement 1 alone is not sufficient
Statement-2: A is heavier than D, but is lighter than C.
C > A > D, However who is the heaviest cannot be determined as there is no information on B, E and F
Hence statement 2 alone is not sufficient
Using both the statements
C > A > D > B, F, E
Hence both the statements are required to answer the question
Note: UPSC official answer key have both C and D
Q12. Three persons A, B and c are standing in a queue not necessarily in the same order. There are 4 person between A and B, and 7 persons between B and C. If there are 11 persons ahead of C and 13 behind A, what could be the minimum number of persons in the queue? [CSAT 2022]
(a) 22
(b) 28
(c) 32
(d) 38
Solution:
Given that,
Three persons A, B and c are standing in a queue not necessarily in the same order.
There are 4 person between A and B
7 persons between B and C.
If there are 11 persons ahead of C and 13 behind A
Now,
(+ 3) B (+ 4) A (+ 2) C (+ 10)
Total = 3 + 1 + 4 + 1 + 2 + 1 + 10 = 22
Hence option (a) is correct
Q13. Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 a.m. and 2:00 p.m.
Consider the Question and two Statements given below: [CSAT 2022]
Question: Which lecture is in the third period?
Statement-1: Lecture F is preceded by A and followed by C.
Statement-2: There is no lecture after lecture B
Which one of the following is correct in respect of the Question and the Statements?
(a) Statement-1 alone is sufficient to answer the Question
(b) Statement-2 alone is sufficient to answer the Question
(c) Both Statement-1 and Statement-2 are sufficient to answer Question the
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question
Solution:
Given that,
Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 a.m. and 2:00 p.m.
Statement-1: Lecture F is preceded by A and followed by C.
Only three lectures can be traced rest other lectures information is not provided
Hence statement 1 alone is not sufficient
Statement-2: There is no lecture after lecture B
There is no information on other lectures
Hence statement 2 alone is not sufficient
Combining both the statements still it is not sufficient to answer the question
Thus data is insufficient.
Q14. A Question is given followed by two Statements I and II. Consider the Question and the Statements.
A certain amount was distributed among X, Y and Z.
Question: Who received the least amount? [CSAT 2024]
Statement-I: X received 4/5 of what Y and Z together received.
Statement-II: Y received 2/7 of what X and Z together received.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the statements together
Solution:
Given that,
Statement I: X received 4/5 of what Y and Z together received.
Statement II: Y received 2/7 of what X and Z together received.
Also, amount is distributed among X, Y, Z
Now,
From statement I:
X = (4/5) x (Y + Z)......(i)
However, the values of X, Y and Z cannot be determined
Hence statement I is insufficient to answer the question
From statement II:
Y = (2/7) x (X + Z).....(ii)
However, the values of X, Y and Z cannot be determined
Hence statement II is insufficient to answer the question
Combining both the statements:
X = (4/5) x (Y + Z)......(i)
Y = (2/7) x (X + Z).....(ii)
Putting the value of (ii) in (i)
X = (4/5) x [(2X/7) + (2Z/7) + Z] = (4/5) x [(2X/7) + 9Z/7]
5X = (8X/7) + (36Z/7)
27X/7 = 36Z/7
X = (4/3) x Z .......(iii)
Y = (2/7) x ((4/3) x Z + Z) = (2/3) x Z
Thus, X > Z > Y
Least is Y
Hence option (c) is correct
Q15. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [CSAT 2024]
P, Q, R and S appeared in a test.
Question: Has P scored more marks than Q?
Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S
Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
Solution:
Given that,
Statement I: The sum of marks scored by P and Q is equal to the sum of the marks scored by R and S.
Statement II: The sum of marks scored by P and S is more than the sum of the marks scored by Q and R.
Now,
From statement I: The sum of marks scored by P and Q is equal to the sum of the marks scored by R and S.
P + Q = R + S....(i)
However, the relation between P and Q cannot be determined.
Hence statement I is insufficient to answer the question
From statement II: The sum of marks scored by P and S is more than the sum of the marks scored by Q and R.
P + S > Q + R......(ii)
However, the relation between P and Q cannot be determined.
Hence statement II is insufficient to answer the question
Combining both the statements:
P + Q = R + S....(i)
P + S > Q + R......(ii)
P = R + S - Q.....(iii)
R + S - Q + S > Q + R
2S -Q > Q
S > Q.......(iv)
From equation (i)
S = P + Q - R.....(v)
P + P + Q - R > Q + R
P > R ......(vi)
However, the relation between P and Q cannot be determined
Hence option (d) is correct
ANSWER KEY
- 1. C
- 2. C
- 3. C
- 4. B
- 5. C
- 6. A
- 7. B
- 8. B
- 9. D
- 10. C
- 11. C/D
- 12. A
- 13. D
- 14. C
- 15. D
