UPSC quantitative aptitude Previous Year Questions

Q39. 39. Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had Team Y's average run rate ...

Quantitative Aptitude - Ratio & Proportion / Time & Work (Cricket context)

Q40. 40. The price (p) of a commodity is first increased by k%, then decreased by k%; again increased by k%, and again decrea...

Quantitative Aptitude - Percentage

Q45. 45. In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X ...

Quantitative Aptitude - Ratio & Proportion

Q46. 46. Let p + q = 10, where p, q are integers. Value-I = Maximum value of p × q when p, q are positive integers. Value-II ...

Quantitative Aptitude - Number Properties / Maxima-Minima

Q47. 47. Consider a set of 11 numbers: Value-I = Minimum value of the average of the numbers of the set when they are consecu...

Quantitative Aptitude - Average / Number Properties

Q48. 48. The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What...

Quantitative Aptitude - Average

Q69. 69. X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can ...

Quantitative Aptitude - Time & Work

Q75. A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 min...

Work and Time (Pipes and Cisterns)

Q76. If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4?...

Number System (Remainders)

Q77. Let P = QQQ be a 3-digit number. What is the HCF of P and 481?...

Number System (HCF/LCM)

Q78. What is the 489th digit in the number 123456789101112...?...

Number System (Digit Counting)

Q5. 5. What is the least possible number of cuts required to cut a cube into 64 identical pieces?...

Geometry (Cuts on Cube)

Q6. 6. In the expression 5 * 4* 3* 2* 1, * is chosen from +, -, × each at most two times. What is the smallest non-negative ...

Number Operations

Q7. 7. A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should ...

Time and Work

Q8. 8. X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one ...

Time and Work

Q9. 9. How many consecutive zeros are there at the end of the integer obtained in the product 1^2 × 2^4 × 3^6 × 4^8 ×.... × ...

Number System (Trailing Zeros)

Q10. 10. On January 1st, 2023, a person saved Rs 1. On January 2nd, 2023, he saved Rs. 2 more than that on the previous day. ...

Number System (Perfect Squares and Cubes)

Q15. 15. 222^333 + 333^222 is divisible by which of the following numbers ?...

Number System (Divisibility)

Q16. 16. What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey ?...

Profit and Loss / Mixtures

Q17. 17. What is the rightmost digit preceding the zeros in the value of 30^30 ?...

Number System (Unit Digit)

Q18. 18. 421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the diviso...

Number System (HCF/LCM)

Q19. 19. A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles o...

Number System (HCF/LCM)

Q20. 20. Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers e...

Number System (Prime Numbers)

Q25. 25. Two persons P and Q enter into a business. P puts ₹ 14,000 more than Q, but P has invested for 8 months and Q has in...

Partnership

Q26. 26. P’s salary is 20% lower than Q’s salary which is 20% lower than R’s salary. By how much percent is R’s salary more t...

Percentages

Q27. 27. A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to ...

Percentages

Q28. 28. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the sub...

Set Theory / Percentages

Q29. 29. A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years b...

Ages

Q30. 30. Consider the following : 1. 1000 litres = 1m^3 2. 1 metric ton = 1000 kg 3. 1 hectare = 10000 m^2 Which of the above...

Units and Conversions

Q35. 35. Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X + Y) is...

Number System (Two-Digit Numbers)

Q36. 36. Consider the following : Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women If the average w...

Averages and Ratios

Q39. 39. Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements...

Number System (Parity)

Q6. A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider...

Permutations and Combinations - Pigeonhole Principle

Q14. If 7  9  10 = 8, 9  11  30 = 5, 11  17  21 = 13, what is the value of 23  4  15 ?...

Number Series / Mathematical Operations

Q15. Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?...

Number System - Divisibility

Q16. If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q) (r + s) ?...

Number System - Maximization

Q17. A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13 ?...

Number System - Remainder Theorem

Q18. Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?...

Number System - Properties of Numbers

Q19. What is the sum of all digits which appear in all the integers from 10 to 100 ?...

Number System - Sum of Digits

Q20. ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many dist...

Permutations and Combinations - Geometry

Q24. Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider ...

Number System - Parity (Even/Odd)

Q25. Consider the following in respect of prime number p and composite number c. 1. 𝑝+𝑐 / 𝑝−𝑐 can be even. 2. 2p+c can be...

Number System - Prime and Composite Numbers

Q26. A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the...

Number System - Digit Problems

Q27. For any choices of values of X, Y and Z, the 6 digit number of the form XYZXYZ is divisible by:...

Number System - Divisibility Rules

Q28. 125 identical cubes are arranged in the form of cubical block. How many cubes are surrounded by other cubes from each si...

Cubes and Cuboids

Q29. How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits oc...

Permutations and Combinations

Q30. A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone...

Time and Work

Q35. In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the s...

Number Theory (Combinatorics)

Q37. What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?...

Number System (Remainders)

Q38. What is the unit digit in the expansion of (57242) 9×7×5×3×1 ?...

Number System (Unit Digit)

Q40. D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference betwee...

Number Properties

Q44. What is the remainder if 2^192 is divided by 6?...

Number System (Remainders)

Q49. A cuboid of dimensions 7cm × 5cm × 3cm is painted red, green and blue colour on each pair of opposite faces of dimension...

Mensuration (Cubes and Cuboids)

Q55. In an examination, the maximum marks for each of the four papers namely P, Q, R and S are 100. Marks scored by the stude...

Combinatorics (Stars and Bars)

Q56. A flag has to be designed with 4 horizontal strips using some or all of the colours red, green and yellow. What is the n...

Permutations and Combinations

Q57. A rectangular floor measures 4 m in length and 2.2m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that ...

Mensuration (Area and Tiling)

Q59. There are large number of silver coins weighing 2gm, 5gm, 10gm, 25gm, 50gm each. Consider the following statements: 1. T...

Number Theory (Optimization)