13 students are standing in a row. The mean age of first seven students is 18, and the mean age of last seven students is 20. If the mean age of all the students is 19, then what must be the age of the seventh student in the row?
Anonymous Quiz
7%
(a) 17
14%
(b) 18
73%
(c) 19
7%
(d) 20
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👆Ans. C
Explanation:
➡️ Mean age of the first seven students = 18
➡️ Then, sum of first seven students’ ages = 7 × 18 = 126
➡️ Mean age of last seven students = 20
➡️ Then, sum of last seven students’ ages = 7 × 20 = 140
➡️ Mean age of all 13 students = 19
➡️ Then, sum of all 13 students’ ages = 13 × 19 = 247
➡️ So, seventh student’s age = (126 + 140) – 247 = 19
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Explanation:
➡️ Mean age of the first seven students = 18
➡️ Then, sum of first seven students’ ages = 7 × 18 = 126
➡️ Mean age of last seven students = 20
➡️ Then, sum of last seven students’ ages = 7 × 20 = 140
➡️ Mean age of all 13 students = 19
➡️ Then, sum of all 13 students’ ages = 13 × 19 = 247
➡️ So, seventh student’s age = (126 + 140) – 247 = 19
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What number should come in place of the question mark (?) in the following series.
17, 23, 35, ?, 107, 203
17, 23, 35, ?, 107, 203
Anonymous Quiz
22%
(a) 53
16%
(b) 55
55%
(c) 59
7%
(d) 90
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👆Ans. C
Explanation:
➡️ 17 + 6 = 23
➡️ 23 + 6×2 = 23 + 12 = 35
➡️ ? = 35 + 12×2 = 35 + 24 = 59
➡️ 59 + 24×2 = 59 + 48 = 107
➡️ 107 + 48×2 = 107 + 96 = 203
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Explanation:
➡️ 17 + 6 = 23
➡️ 23 + 6×2 = 23 + 12 = 35
➡️ ? = 35 + 12×2 = 35 + 24 = 59
➡️ 59 + 24×2 = 59 + 48 = 107
➡️ 107 + 48×2 = 107 + 96 = 203
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In the series 905, 812, 911, 678, 351, 796, if all digits of the numbers are arranged in ascending order within the number, then which of the following would become the fourth smallest number?
Anonymous Quiz
8%
(a) 911
49%
(b) 351
31%
(c) 812
12%
(d) None of the above
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👆Ans. B
Explanation:
➡️ Given series: 905, 812, 911, 678, 351, 796
➡️ If all digits of the numbers are arranged in ascending order within the number, then we get: 059, 128, 119, 678, 135, 679
➡️ Arranging the above series in descending order, we get: 679, 678, 135, 128, 119, 059
➡️ Fourth smallest number is 135, i.e. number 351.
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Explanation:
➡️ Given series: 905, 812, 911, 678, 351, 796
➡️ If all digits of the numbers are arranged in ascending order within the number, then we get: 059, 128, 119, 678, 135, 679
➡️ Arranging the above series in descending order, we get: 679, 678, 135, 128, 119, 059
➡️ Fourth smallest number is 135, i.e. number 351.
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Forwarded from UPSC FIX 2026 - 27 - 28
WR-CSM-2023-081223-ENG (1).pdf
220.8 KB
A six-digit number N is formed using the digits 0, 3, 6 and 9 only. Each of the digits is used at least once. It was found that N is divisible by 18. What is the ten’s digit of the smallest possible such six-digit number?
Anonymous Quiz
12%
(a) 0
50%
(b) 9
26%
(c) 6
12%
(d) 3
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👆Ans. B
Explanation:
➡️ Given that a six-digit number N is formed using the digits 0, 3, 6 and 9 only, and each of the digits is used at least once.
➡️ The number is divisible by 18. Therefore, the number has to be divisible by both 2 and 9.
➡️ Sum of the digits of the number should be divisible by 9, and the unit’s digit of the number should be either 0 or 6.
➡️ Smallest possible such number is 300096.
➡️ Therefore, the digit at the ten’s place is 9.
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Explanation:
➡️ Given that a six-digit number N is formed using the digits 0, 3, 6 and 9 only, and each of the digits is used at least once.
➡️ The number is divisible by 18. Therefore, the number has to be divisible by both 2 and 9.
➡️ Sum of the digits of the number should be divisible by 9, and the unit’s digit of the number should be either 0 or 6.
➡️ Smallest possible such number is 300096.
➡️ Therefore, the digit at the ten’s place is 9.
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In a certain police station, 20 officers are in ATS and 14 officers are in cyber security. 8 officers belong to both ATS and cyber security. How many officers belong to cyber security only or ATS only?
Anonymous Quiz
11%
(a) 14
32%
(b) 12
52%
(c) 18
5%
(d) 9
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👆Ans. C
Explanation:
➡️ Number of Officers in ATS, n(A) = 20
➡️ Number of Officers in cyber security, n(C) = 14
➡️ Number of Officers in both ATS and cyber security = n(A ∩ C) = 8
➡️ So, Number of Officers only in ATS = 20 – 8 = 12
➡️ Number of Officers only in cyber security = 14 – 8 = 6
➡️ Hence, number of officers only in ATS or only in cyber security = 12 + 6 = 18
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Explanation:
➡️ Number of Officers in ATS, n(A) = 20
➡️ Number of Officers in cyber security, n(C) = 14
➡️ Number of Officers in both ATS and cyber security = n(A ∩ C) = 8
➡️ So, Number of Officers only in ATS = 20 – 8 = 12
➡️ Number of Officers only in cyber security = 14 – 8 = 6
➡️ Hence, number of officers only in ATS or only in cyber security = 12 + 6 = 18
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One evening Dinesh and Bhavesh were talking to each other at a crossing keeping their backs towards each other. If Bhavesh’s shadow was exactly to the left of Dinesh, then which direction were Bhavesh and Dinesh facing respectively?
Anonymous Quiz
53%
(a) North, South
22%
(b) East, West
17%
(c) South, West
9%
(d) South, North
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👆Ans. A
Explanation:
➡️ In the evening, the sun is in the west direction, and so the shadows are formed in the east direction.
➡️ One evening Dinesh and Bhavesh were talking to each other at a crossing keeping their backs towards each other. Bhavesh’s shadow was exactly to the left of Dinesh.
➡️ Thus, Bhavesh and Dinesh were facing North and South direction respectively.
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Explanation:
➡️ In the evening, the sun is in the west direction, and so the shadows are formed in the east direction.
➡️ One evening Dinesh and Bhavesh were talking to each other at a crossing keeping their backs towards each other. Bhavesh’s shadow was exactly to the left of Dinesh.
➡️ Thus, Bhavesh and Dinesh were facing North and South direction respectively.
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Forwarded from State PCS - Guidance IAS
BPSC 68th PCS Interview Schedule .pdf
199.5 KB
Ram’s salary is more than Shyam’s salary, but less than Mayank’s salary. On the other hand, Vijay’s salary is more than that of Ganesh. Mayank’s salary, however, is less than the salary of Ganesh. Whose salary is the lowest?
Anonymous Quiz
5%
(a) Vijay
21%
(b) Mayank
67%
(c) Shyam
8%
(d) Ram
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👆Ans. C
Explanation:
As per the question,
➡️ Ram’s salary is more than Shyam’s salary, but less than Mayank’s salary: Mayank > Ram > Shyam
➡️ Vijay’s salary is more than that of Ganesh: Vijay > Ganesh
➡️ However, Mayank’s salary is less than that of Ganesh, therefore overall order is: Vijay > Ganesh > Mayank > Ram > Shyam
➡️ Therefore, Shyam’s salary is the lowest.
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Explanation:
As per the question,
➡️ Ram’s salary is more than Shyam’s salary, but less than Mayank’s salary: Mayank > Ram > Shyam
➡️ Vijay’s salary is more than that of Ganesh: Vijay > Ganesh
➡️ However, Mayank’s salary is less than that of Ganesh, therefore overall order is: Vijay > Ganesh > Mayank > Ram > Shyam
➡️ Therefore, Shyam’s salary is the lowest.
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Ravi painted a cube leaving one face unpainted. If this cube is divided into 64 small cubes, how many cubes will be there having at least one face painted?
Anonymous Quiz
19%
(a) 52
39%
(b) 48
30%
(c) 62
13%
(d) 36
A cricket team of 11 is to be selected from 7 batsmen and 6 bowlers which are available. The team must have at least 5 bowlers. In how many ways can it be done?
Anonymous Quiz
12%
(a) 21
35%
(b) 42
19%
(c) 8
34%
(d) 63
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👆Ans. D
Explanation:
➡️ Here we have to select, i.e. it's a question of combination (and not permutation), as the order of the players do not matter. As the team must have at least 5 bowlers, two cases emerge:
➡️ Case I: Team has 5 bowlers and 6 batsmen. Number of ways of choosing such a team = Number of ways of choosing 5 bowlers out of 6 available and 6 batsmen out of 7 available = 6C5 × 7C6 = 6 × 7 = 42.
➡️ Case II: Team has 6 bowlers and 5 batsmen. Number of ways of choosing such a team = Number of ways of choosing 6 bowlers out of 6 available and 5 batsmen out of 7 available = 6C6 × 7C5 = 1 × 21 = 21.
➡️ Hence, total possible ways = 42 + 21 = 63.
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Explanation:
➡️ Here we have to select, i.e. it's a question of combination (and not permutation), as the order of the players do not matter. As the team must have at least 5 bowlers, two cases emerge:
➡️ Case I: Team has 5 bowlers and 6 batsmen. Number of ways of choosing such a team = Number of ways of choosing 5 bowlers out of 6 available and 6 batsmen out of 7 available = 6C5 × 7C6 = 6 × 7 = 42.
➡️ Case II: Team has 6 bowlers and 5 batsmen. Number of ways of choosing such a team = Number of ways of choosing 6 bowlers out of 6 available and 5 batsmen out of 7 available = 6C6 × 7C5 = 1 × 21 = 21.
➡️ Hence, total possible ways = 42 + 21 = 63.
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One evening Dinesh and Bhavesh were talking to each other at a crossing keeping their backs towards each other. If Bhavesh’s shadow was exactly to the left of Dinesh, then which direction were Bhavesh and Dinesh facing respectively?
Anonymous Quiz
32%
(a) North, South
38%
(b) East, West
22%
(c) South, West
8%
(d) South, North
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