UPSC CSE Prelims CSAT (Paper II) previous year questions on LCM and HCF (Quantitative Ability), asked from 2013–2026, with answers. There are 16 questions in this post. Attempt each question, then click Show Answer to check.
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1] X, Y and Z jump forward 4′, 6′ and 5′ respectively. At 8 AM, they all land on mark 199′. How many times will they all land on the same mark (need not be at the same moment) between mark 195′ and 1000′, if all of them cross mark 1000′ by 9 AM? [2026/10]
(a) 11
(b) 12
(c) 13
(d) 14
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Ans: (d) 14
2] If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?
I. The difference of the numbers is an even number.
II. One of the numbers is a perfect square.
Select the answer using the code given below. [2026/59]
(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II
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Ans: (c) Both I and II
3] A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N? [2025/18]
(a) 1068
(b) 1072
(c) 1078
(d) 1082
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Ans: (c) 1078
4] There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n? [2025/28]
(a) 6
(b) 7
(c) 8
(d) More than 8
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Ans: (d) More than 8
5] Let P = QQQ be a 3-digit number. What is the HCF of P and 481? [2025/47]
(a) 1
(b) 13
(c) 37
(d) 481
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Ans: (c) 37
6] A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible? [2024/19]
(a) (a) 3
(b) (b) 4
(c) (c) 5
(d) (d) 6
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Ans: (b) (b) 4
7] There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m., they together turn green. At what time will they change to green next, simultaneously? [2023/50]
(a) 4:00 p.m.
(b) 4:10 p.m.
(c) 4:20 p.m.
(d) 4:30 p.m.
Show Answer
Ans: (b) 4:10 p.m.
8] 40 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? [2023/54]
(a) 14
(b) 15
(c) 16
(d) 17
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Ans: (b) 15
9] X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)? [2022/15]
(a) 2
(b) 3
(c) 4
(d) 5
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Ans: (b) 3
10] Joseph 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? [2021/75]
(a) Monday
(b) Wednesday
(c) Thursday
(d) Sunday
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Ans: (b) Wednesday
11] 1f you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure? [2020/12]
(a) 0.05 foot
(b) 0.25 foot
(c) 1 foot
(d) 3.25 feet
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Ans: (b) 0.25 foot
12] Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds? [2018/40]
(a) 6: 5
(b) 4: 3
(c) 6: 1
(d) 4: 2
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Ans: (a) 6: 5
13] A and B walk around a circular park. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 8 00 a.m. and before 9.30. a.m.? [2016/75]
(a) 7
(b) 6
(c) 5
(d) 8
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Ans: (a) 7
14] Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of times they would fire the bullets together at the target in an hour is [2014/6]
(a) 6
(b) 7
(c) 8
(d) 9
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Ans: (bc)
15] A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o’clock in the morning, at what other time will they all ring together? [2014/46]
(a) 12 : 40 hrs
(b) 12 : 48 hrs
(c) 12 : 56 hrs
(d) 13 : 04 hrs
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Ans: (b) 12 : 48 hrs
16] There are five hobby clubs in a college viz. photography, yachting, chess, electronics, and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days? [2013/28]
(a) 3
(b) 5
(c) 10
(d) 18
Show Answer
Ans: (a) 3
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