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Series, Clocks, Calendar & Miscellaneous — UPSC CSAT Paper II Quantitative Aptitude previous year questions
20 free solved previous year questions on Series, Clocks, Calendar & Miscellaneous, papers from 2019 to 2026, drawn from UPSC CSAT, covering questions of the kind UPSC asks in CSAT Paper II. Every answer key has been checked again against published sources and solved independently, and each explanation is written fresh.
Read all 20 questions with answers
- #1UPSC CSAT 2026In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is
- A29
- B37
- C43
- D47
Answer: (D) 47Explanation
The first two numbers are 4 and 7.
3rd = 4 + 7 = 11.
4th = 7 + 11 = 18.
5th = 11 + 18 = 29.
6th = 18 + 29 = 47.
Answer: 47, option (d).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #2UPSC CSAT 2025Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct?I. The result of the match between P and Q is a draw with the score 0-0.II. The number of goals scored by R against Q is 1.
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Answer: (C) Both I and IIExplanation
Checking all possible scorelines by computer, only one fits the points and goals: P-Q 0-0, Q-R 1-1, R-P 0-1.
So the P-Q match is a 0-0 draw and R scored 1 goal against Q.
Both statements hold.
Answer: option (c).Source: UPSC CSAT 2025 question; answer key checked by independent computation
- #3UPSC CSAT 2024In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, -, x each at most two times. Which is the smallest non-negative value of the expression?
- A3
- B2
- C1
- D0
Answer: (D) 0Explanation
Trying every allowed operator combination by computer, 5 - 4 - 3 + 2 x 1 = 0 is achievable and no negative value counts.
So the smallest non-negative value is 0.
Answer: option (d).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #4UPSC CSAT 2024How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?
- A3 times
- B4 times
- C5 times
- D6 times
Answer: (A) 3 timesExplanation
The hands coincide every 12/11 hours, i.e. 11 times in 12 hours, at about 12:00, 1:05 and 2:11 and so on.
In the window 10:00 to 14:00 the meetings are near 10:54, at 12:00 and near 1:05.
The next one (about 2:11) is outside the window, so 3 times. Answer: option (a).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #5UPSC CSAT 2024What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?
- A12.5°
- B15°
- C17.5°
- D20°
Answer: (C) 17.5°Explanation
At 4:25 the hour hand is at 4 x 30 + 25 x 0.5 = 132.5 degrees.
The minute hand is at 25 x 6 = 150 degrees.
Difference = 17.5 degrees. Answer: option (c).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #6UPSC CSAT 2024What is the sum of the first 28 terms in the following sequence?1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,...
- A83
- B84
- C85
- D86
Answer: (B) 84Explanation
The sequence is built in blocks: 1 | 1,2 | 1,3,2 | 1,4,3,2 | ... with block k having k terms.
28 terms = 1+2+...+7, so seven full blocks.
Block sums are 1, 3, 6, 10, 15, 21, 28, which total 84. Answer: option (b).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #7UPSC CSAT 2023There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:1. To buy 78 gm of coins one must buy at least 7 coins.2. To weigh 78 gm using these coins one can use less than 7 coins.Which of the statements given above is/are correct?
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Answer: (C) Both 1 and 2Explanation
A minimum-coin search for a total of 78 gm gives 7 coins (for example 50 + 10 + 10 + 2 + 2 + 2 + 2), so statement 1 is true.
On a balance with coins on both pans, 78 = 50 + 25 + 5 - 2 uses only 4 coins.
So statement 2 is also true.
Answer: option (c).Source: UPSC CSAT 2023 question; answer key checked by independent computation
- #8UPSC CSAT 202340 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again?
- A14
- B15
- C16
- D17
Answer: (B) 15Explanation
The k-th pass moves the ring k places ahead, so after k passes it is at child number 1 + k(k+1)/2 (mod 40).
We need k(k+1)/2 to be a multiple of 40; the first k that works is 15 (15 x 16 / 2 = 120 = 3 x 40).
So the ring is back with child-1 after 15 passes.
Answer: option (b).Source: UPSC CSAT 2023 question; answer key checked by independent computation
- #9UPSC CSAT 2022Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40 m. Then X turns left and runs 50 m and stops, while Y turns right and runs 50 m and then stops. How far are the two friends from each other now?
- A100 m
- B90 m
- C60 m
- D50 m
Answer: (A) 100 mExplanation
Take the common start as origin facing east. After 50 m both are at (50,0).
X goes right (south) 60 m then left (east) 50 m: (100,-60). Y goes left (north) 40 m then right (east) 50 m: (100,40).
Both are on the same vertical line, 60+40 = 100 m apart.
Answer: option (a).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #10UPSC CSAT 2022In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?
- A151
- B150
- C149
- D148
Answer: (C) 149Explanation
Every match eliminates exactly one player.
To end with one winner, 149 of the 150 entrants must be eliminated.
So 149 matches are played.
Answer: option (c).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #11UPSC CSAT 2022Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons 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?
- A22
- B28
- C32
- D38
Answer: (A) 22Explanation
C is at position 12 from the front. B is 8 places from C: position 4 or 20.
A is 5 places from B. With B at 4, A is at 9, and 13 behind A gives 22 in all (checks: 4 between A and B, 7 between B and C).
B at 20 gives 28 or 38. The minimum is 22.
Answer: option (a).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #12UPSC CSAT 2022Consider the following statements:1. Between 3:16 p.m. and 3:17 p.m. both hour hand and minute hand coincide.2. Between 4:58 p.m. and 4:59 p.m. both minute hand and second hand coincide.Which of the above statements is/are correct?
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Answer: (C) Both 1 and 2Explanation
Statement 1: hands coincide at 3 + 180/11 minutes = 3:16 4/11, i.e. about 3:16:22, inside the interval.
Statement 2: at 4:58 and s seconds the minute hand is at 58 + s/60 minute marks; it equals the second hand at s when s = 58 x 60/59, about 58.98 s, inside the interval.
Both are correct.
Answer: option (c).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #13UPSC CSAT 2021Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
- AMonday
- BWednesday
- CThursday
- DSunday
Answer: (B) WednesdayExplanation
They meet again after LCM(5, 24, 9) = 360 days.
360 = 7 x 51 + 3, so the day is 3 days after Sunday.
That is Wednesday.
Answer: option (b).Source: UPSC CSAT 2021 question; answer key checked by independent computation
- #14UPSC CSAT 2021At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other?
- AAt 7:00 hours
- BBetween 7:00 hours and 7:05 hours
- CAt 7:05 hours
- DBetween 7:05 hours and 7:10 hours
Answer: (D) Between 7:05 hours and 7:10 hoursExplanation
After 7:00 the hour hand is at 210 degrees; minute hand moves 6 deg/min, hour hand 0.5 deg/min.
Opposite when 6m = 30 + 0.5m, so m = 60/11 = 5.45 minutes.
This lies between 7:05 and 7:10.
Answer: option (d).Source: UPSC CSAT 2021 question; answer key checked by independent computation
- #15UPSC CSAT 2021Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct?
- AAll the villagers who have their own houses are literate.
- BSome villagers under 25 years of age are literate.
- COnly half of the villagers who cultivate paddy are literate.
- DNo villager under 25 years of age has his own house.
Answer: (B) Some villagers under 25 years of age are literate.Explanation
Under-25s (4/5) and literates (1/3) add to more than the whole village (4/5+1/3 = 17/15 > 1), so the two groups must overlap.
Hence some under-25 villagers are literate.
The other statements are not forced: house owners need not be literate, paddy growers may all be literate, and under-25s (80%) must overlap with house owners (50%) by at least 30%.
Answer: option (b).Source: UPSC CSAT 2021 question; answer key checked by independent computation
- #16UPSC CSAT 2020A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ..... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?
- A34
- B36
- C38
- D40
Answer: (C) 38Explanation
Subtract 1 from each term: 13, 17, 19, 23, 29, 31 - consecutive primes.
The next prime is 37, so the next term is 37+1 = 38.
Answer: option (c).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #17UPSC CSAT 2020Two Statements are given followed by two Conclusions:Statements:All numbers are divisible by 2.All numbers are divisible by 3.Conclusion-I: All numbers are divisible by 6.Conclusion-II: All numbers are divisible by 4.Which of the above Conclusions logically follows/follow from the two given Statements?
- AOnly Conclusion-I
- BOnly Conclusion-II
- CNeither Conclusion-I nor Conclusion-II
- DBoth Conclusions-I and Conclusion-II
Answer: (A) Only Conclusion-IExplanation
A number divisible by both 2 and 3 is divisible by LCM(2,3) = 6, so Conclusion-I follows.
Divisibility by 4 is not implied (6 and 18 are divisible by 2 and 3 but not 4).
Answer: option (a).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #18UPSC CSAT 2020A frog tries to come out of a dried well 4.5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. what is the number of jumps required for the frog to come out of the well?
- A28
- B29
- C30
- D31
Answer: (B) 29Explanation
Well depth = 450 cm; net gain per jump-and-slide is 15 cm.
The frog escapes on the jump that starts at 420 cm or higher, since 420 + 30 = 450.
Reaching 420 cm needs 28 jumps, so the 29th jump takes it out (no slide after exit).
Answer: option (b).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #19UPSC CSAT 2019In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct?1. At least 30 Indian participants are vegetarian.2. At least 10 Indian participants are non-vegetarian.Select the correct answer using the codes given below:
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Answer: (C) Both 1 and 2Explanation
There are only 30 non-Indians, so at least 60 - 30 = 30 vegetarians are Indian: statement 1 holds.
At most 60 Indians are vegetarian, so at least 70 - 60 = 10 Indians are non-vegetarian: statement 2 holds.
Answer: option (c).Source: UPSC CSAT 2019 question; answer key checked by independent computation
- #20UPSC CSAT 2019All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data?1. 40% members went for shopping as well as sightseeing.2. 20% members went for only shopping.Select the correct answer using the code given below:
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Answer: (A) 1 onlyExplanation
Those who went out = 100 - 10 = 90%.
Both = 80 + 50 - 90 = 40%, so statement 1 is true.
Only shopping = 80 - 40 = 40%, not 20%, so statement 2 is false.
Answer: option (a).Source: UPSC CSAT 2019 question; answer key checked by independent computation
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