UPSC basic numeracy Previous Year Questions

Q5. What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35^n ?...

Number System (Divisibility, Prime Factorization)

Q7. P and Q walk along a circular track. They start at 5:00 am. from the same point in opposite directions. P walks at an av...

Time, Speed and Distance (Circular Tracks)

Q9. A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and complete...

Time, Speed and Distance (Trains/Overtaking)

Q10. If N^2 = 12345678987654321, then how many digits does the number N have?...

Number System (Squares and Patterns)

Q15. Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?...

Number System (Divisibility, Primes)

Q16. If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?...

Inequalities

Q17. Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible...

Number System (Prime Numbers)

Q18. There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is ...

Number System (LCM and HCF)

Q27. The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹90...

Percentage, Ratio and Proportion (Applications)

Q28. A 4-digit number N is such that when divided by 3, 5, 6, 9 it leaves a remainder of 1, 3, 4, 7 respectively. What is the...

Number System (Remainders, LCM)

Q30. What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × … × 999?...

Number System (Unit Digit)

Q45. What is the number of fives used in numbering a 260-page book?...

Number System - Counting Digits

Q46. What 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,.........

Series and Sequences

Q47. A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what i...

Ratio and Proportion - Percentage

Q48. If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote dist...

Number System - Digits

Q49. Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such ...

Number System - Inequalities

Q50. The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples...

Algebra - Linear Equations

Q54. 32^5 + 2^27 is divisible by...

Number System - Divisibility

Q55. Let p and q be positive integers satisfying p<q and p+q=k. What is the smallest value of k that does not determine p and...

Number System - Properties

Q64. 40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1pass...

Number Series & Patterns

Q65. What is the middle terms of the sequence Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W,…….,A?...

Sequence & Series

Q69. Consider a 3-digit number. Question: What is the number? Statement-1: The sum of the digits of the number is equal to th...

Data Sufficiency - Number Properties

Q70. For five children with ages a < b < c < d < e; any two successive ages differs by 2 years. Question: What is the age of ...

Data Sufficiency - Arithmetic Progression

Q74. A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P b...

Compound Interest

Q75. How many natural numbers are there which given a remainder of 31 when 1186 is divided by these natural numbers?...

Number Theory - Divisibility

Q76. Let pp, qq and rr be 2 digit numbers where p < q < r. If pp + qq + rr =tt0, where tt0 is a 3-digit number ending with ze...

Number Properties & Data Sufficiency

Q77. What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is re...

Permutations & Combinations - Number Formation

Q78. What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction?...

Permutations & Combinations - Circular Arrangements

Q80. There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first sign...

LCM & HCF - Time & Work