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UPSC CSE Prelims 2026 — Logical Reasoning Questions with Answers
All 46 Logical Reasoning previous-year questions from UPSC CSE Prelims 2026, each with the correct answer and a full explanation. Practise them as a free, timed mock test with instant scoring.
Practice Logical Reasoning as a timed test →- Q1.Algebra
The weight of X, in kg, is denoted by X. The weights of A, B, C, D, P, Q, R and S are measured. Given: A + B + C + D = 17 A + C = 6 P + Q + S + D = 15 P + Q + R + B = 17 P = R and Q = S Which one of the following statements is correct?
- a)B and D together weigh less than the total weight of P and Q.
- b)P and Q together weigh more than the total weight of A and C.
- c)P weighs more than Q.
- d)Q weighs more than P.
- Q2.Permutations & Combinations
How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning.
- a)6
- b)8
- c)10
- d)12
- Q3.Sequences & Series
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?
- a)11
- b)12
- c)13
- d)14
- Q4.Algebra
A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?
- a)6
- b)7
- c)8
- d)9
- Q5.Seating Arrangement
Eight persons P, Q, R, S, T, U, V and W sit around a round table in eight different seats placed with equal distance between any two consecutive seats. Both P and R are adjacent to Q. Both T and R are adjacent to S. Both U and W are adjacent to V. S and W are on opposite chairs. If while going in the clockwise direction around the table from P, one meets R before T, then how many persons shall Q cross while moving in the clockwise direction around the table before meeting W?
- a)5
- b)4
- c)2
- d)1
- Q6.Mensuration
The top of a table is rectangular and its dimensions are 6' × 10'. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2.5' × 8' and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?
- a)2
- b)4
- c)6
- d)8
- Q7.Statements & Conclusions
Which of the following statements is/are correct? 1. Real value should not change in the instance of static output cost and unchanged quantities against falling oil prices. 2. Deflators are to be used separately for inputs and outputs, and this is a practice universally adopted by all economies.
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
- Q8.Statements & Conclusions
Which of the following assumptions is/are valid? 1. Deflation strategies can be used to make manufacturers appear to be doing better than they actually are. 2. When input and output prices are both deflated against a single input price, it is referred to as 'double deflation'.
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
- Q9.Pattern Recognition
A pattern formed by two characters a and b is repeated more than once in the following string : x b x a x a x x a x a b What is x x in the 7th and 8th positions from the left in the above string?
- a)aa
- b)ab
- c)ba
- d)bb
- Q10.Algebra
If 10^m × 100 × n = 75^25 × 25^32 × 32^75, where n is not divisible by 10, then the value of m is
- a)101
- b)111
- c)121
- d)131
- Q11.Time Speed & Distance
The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
- a)13.51
- b)13.65
- c)13.85
- d)14.05
- Q12.Algebra
For 1/3 < x < y < 2, which of the following statements is/are always correct? I. x + 1/x < y + 1/y II. sqrt(1+y^2)/y < sqrt(1+x^2)/x Select the answer using the code given below.
- a)I only
- b)II only
- c)Both I and II
- d)Neither I nor II
- Q13.Measurement Strategy
What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?
- a)4
- b)5
- c)9
- d)13
- Q14.Permutations & Combinations
There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?
- a)7
- b)8
- c)9
- d)10
- Q15.Cubes & Dice
A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted by x_n. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x_4?
- a)16
- b)12
- c)8
- d)5
- Q16.Averages
The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y, then y - x is
- a)2
- b)3
- c)5
- d)6
- Q17.Algebra
29. Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression (x × y) + z; then M – N is
- a)11
- b)12
- c)13
- d)14
- Q18.Algebra
30. Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
- a)1/7
- b)1/5
- c)5/7
- d)1
- Q19.Statements & Conclusions
Which of the following assumptions is/are valid? 1. Agricultural productivity has marched ahead in the West because of the economies of scale facilitated by the adoption of AI tools. 2. Affordable AI tools rendered available in local languages can help AI-based solutions reach more and more small farmers. 3. Though penetration is as yet low, critical application areas deploying AI tools are already in use in India.
- a)1, 2 and 3
- b)2 only
- c)1 and 3 only
- d)2 and 3 only
- Q20.Seating Arrangement
P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct? I. If the rank of S is 3, then that of T is 2. II. If the rank of Q is 3, then that of T is 5.
- a)I only
- b)II only
- c)Both I and II
- d)Neither I nor II
- Q21.Permutations & Combinations
Two identical straight rods are painted in five distinct colours so that each of them gets divided into five equal parts along the length. In one of them, the portions are marked P1, P2, P3, P4 and P5 (not necessarily in that order) whereas in the other, they are marked Q1, Q2, Q3, Q4 and Q5 (not necessarily in that order). When the rods are kept parallel to each other side by side, P1 and Q3 match, P4 matches Q1 or Q2, and Q4 matches P3 or P5. If Q3 and Q5 are adjacent, which of the following is/are possible? I. Q3 is marked at the middle portion of the straight rod. II. P2 is marked at one of the extreme portions of the straight rod. Select the answer using the code given below.
- a)I only
- b)II only
- c)Both I and II
- d)Neither I nor II
- Q22.Seating Arrangement
Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Y, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct? I. No one travels alone. II. Only D travels with F. III. Only C travels with B. Select the answer using the code given below.
- a)I and II only
- b)I and III only
- c)II and III only
- d)All the three
- Q23.Statements & Conclusions
There are four statements X, Y, Z and W. Their relations are as follows: If X is incorrect, then so is Z; if Y is incorrect, then W is correct; if W is incorrect, then X is incorrect. Which of the following is/are correct? I. If X is correct, then so is Y. II. If Z is correct, then it is not necessary that Y is correct. Select the answer using the code given below.
- a)I only
- b)II only
- c)Both I and II
- d)Neither I nor II
- Q24.Time Speed & Distance
X and Y are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When X completed 7 rounds, Y did exactly 5. After completing 5 rounds, Y changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, X continued to run with the same speed. They stopped running when X completed exactly 21 rounds. How many times did X and Y meet after they had started and before they finally stopped?
- a)35
- b)34
- c)31
- d)29
- Q25.Algebra
In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?
- a)99
- b)81
- c)84
- d)79
- Q26.Time Speed & Distance
An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30 m/s, at what time did the explosion take place? Assume that the speed of sound is 300 m/s.
- a)4:59:00 PM
- b)4:59:02 PM
- c)4:58:42 PM
- d)4:56:32 PM
- Q27.Percentages
A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?
- a)20% increase
- b)30% increase
- c)03% decrease
- d)02% decrease
- Q28.Blood Relations
P has a son and a daughter. S is the mother of T. S is R's spouse. Q and R are children of P. Then how is Q related to S?
- a)Q is a sister of S
- b)Q is a daughter of S
- c)Q is the mother of S
- d)Q is a sister of the husband of S
- Q29.Number System
How many three-digit numbers can be expressed as an integral power of 2?
- a)1
- b)2
- c)3
- d)4
- Q30.Syllogisms
Consider the following statements : Every red is blue. Every blue is green. Every green is yellow. Which of the following statements denoted by P, Q and R are correct? P. Every blue is yellow. Q. Every red is green. R. Every red is yellow.
- a)P and Q only
- b)Q and R only
- c)P and R only
- d)P, Q and R
- Q31.Number System
How many times does 5 appear in all two-digit positive integers?
- a)18
- b)19
- c)20
- d)21
- Q32.Time Speed & Distance
X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?
- a)3
- b)4
- c)5
- d)6
- Q33.Logical Puzzles
Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty?
- a)2
- b)3
- c)4
- d)1
- Q34.Direction Sense
A person facing the East travels 4 km straight and then turns right and travels 3 km, then further turns left and travels 2 km and finally turns left and travels 3 km. The minimum distance between the final point and the initial point, and the direction in which the person is facing at the final point are, respectively
- a)12 km, East
- b)6 km, East
- c)8 km, North
- d)6 km, North
- Q35.Sequences & Series
In 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
- a)29
- b)37
- c)43
- d)47
- Q36.Ratio & Proportion
The ratio of male to female workers in two companies A and B is 13 : 10 and 7 : 5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?
- a)24 : 23
- b)23 : 24
- c)18 : 17
- d)27 : 18
- Q37.Number System
If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?
- a)1
- b)3
- c)5
- d)7
- Q38.Ratio & Proportion
An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?
- a)1 : 3
- b)3 : 1
- c)2 : 3
- d)3 : 2
- Q39.Number System
A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A – B is a multiple of 27, where A > B, how many such different A's are possible?
- a)6
- b)9
- c)12
- d)18
- Q40.Coding-Decoding
If ZERO is encoded as ADSN, then how do you encode STOP?
- a)SPOT
- b)TSPO
- c)TSOP
- d)POST
- Q41.Mensuration
There are three types of rectangular tiles : 3'× 3', 3'× 7' and 3'× 11'. An area of rectangular shape of dimensions 3'× 100' is to be covered using these tiles without breaking the tiles. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x – y is
- a)20
- b)12
- c)10
- d)7
- Q42.Time Speed & Distance
A train has to complete a journey of 800 km. If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing speed. On its way, the train meets with a minor accident after 200 km; and 400 km thereafter, it develops a mechanical defect. Had the train developed the mechanical defect after 200 km and met the minor accident 400 km thereafter, it would have taken 4 more hours to reach its destination. What was the original speed of the train in km per hour?
- a)200
- b)190
- c)150
- d)100
- Q43.Averages
In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are 0·2, 0·3 and 0·5, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected :
- a)5·1
- b)5·2
- c)5·3
- d)5·4
- Q44.Ratio & Proportion
Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹ 17,000, how much profit will C get?
- a)₹ 12,000
- b)₹ 10,000
- c)₹ 12,500
- d)₹ 10,750
- Q45.Ratio & Proportion
There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?
- a)25
- b)27
- c)29
- d)31
- Q46.Algebra
A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹ 5. At the end of the day, he also gets ₹ 2 for every kilometre of the distance covered in the day. The boy wants to earn more than ₹ 500 a day, but does not want to travel more than 100 km. Which of the following numbers of deliveries would definitely meet his target?
- a)80
- b)85
- c)90
- d)The question cannot be answered due to insufficient data
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