UPSC Prelims PYQs – CSAT – Number System

1. A bill of Rs1840 is paid in denominations of Rs50, Rs20 and Rs10 notes. 50 notes are used in total. Consider the following statements (UPSC 2022)

1. 25 notes of Rs50 are used and the remaining are in the denominations of Rs20 and Rs10
2. 35 notes of Rs20 are used and the remaining are in denominations of Rs50 and Rs10
3. 20 notes of Rs10 are used and the remaining are in the denominations of Rs50 and Rs20

Which of the above statements are not correct

2. Consider the Question and two statements given below:

Question: Is x an integer?

   Statement 1: x/3 is not an integer

Statement 2: 3x is an integer

Which one of the following is correct in respect to the Question and the statements? (UPSC 2022)

3. Let A, B and C represent distinct non zero digits. Suppose x is the sum of all possible 3 digit numbers formed by A, B and C without repetition

Consider the following statements:

1. The 4 digit least value of x is 1332
2. The 3 digit greatest value of x is 888

Which of the statements is correct (UPSC 2022)

4. There is a numeric lock which has 3 digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty? (UPSC 2022)

5. Consider the following statements in respect to two natural numbers p and q such that p is a prime number and q is a composite number:

1. p x q can be an odd number
2. q/p can be a prime number
3. p + q can be a prime number

Which of the above statements are correct? (UPSC 2022)

6. Sum of three consecutive integers is equal to their product. How many possibilities are there? (UPSC 2022)

7. What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits? (UPSC 2022)

8. Integers are listed from 700 to 1000. In how many integers is the sum of digits 10? (UPSC 2021)

9. Consider the following multiplication problem: PQ X 3= RQQ, where P, Q and R are different digits and R≠0.

What is the value of (P+R) ÷ Q? (UPSC 2021)

10. Consider the following statements

1. The sum of 5 consecutive integers can be 100
2. The product of three consecutive natural numbers can be equal to their sum

Which of the above statements are correct? (UPSC 2021)

11. The difference between a 2 digit number and the number obtained by interchanging the positions of digits is 54. (UPSC 2021)

Consider the following statements:

1. The sum of the two digits of the number can be determined if the product of the two digits is known
2. The difference between the two digits of the number can be determined

12. A certain number is multiplied by 7, the product entirely comprises of ones only (1111…..). What is the smallest such number? (UPSC 2021)

13. How many zeroes are the end of the result 1X5X10X15X20X25X30X35X40X45X50X55X60 (UPSC 2020)

14. In the sum  + 1  + 5  +  + 1 = 1  , for which digit does the symbol  stand? (UPSC 2020)

15. A3BC and DE2F are two numbers such that each digit is distinct and greater than 3. If their sum is 15902, then difference between A and D is? (UPSC 2020)

16. The recurring decimal representation 1.272727.. is equivalent  (UPSC 2020)

17. Which one of the following will have minimum change in its value if 5 is added both to numerator and denominator of fractions? (UPSC 2020)

18. P-2016=Q+2017=R-2018=S+2019. Then which is the largest? (UPSC 2020)

19. How many numbers are there from 1 to 100 which has 4 has digit and not divisible by 4 (UPSC 2020)

20. A frog tries to come out of a dried well 4.5m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15cm. What is the number of jumps required by the frog to come out of the well? (UPSC 2020)

21. The number of times digit 5 will appear while writing the integers from 1 to 1000 is (UPSC 2019)

22. If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct? (UPSC 2019)

23. If a numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is. (UPSC 2019)

24. A printer numbers the pages of a book starting from 1 and uses 3089 digits in all. How many pages does the book have? (UPSC 2019)

25. Consider the two statements S1 and S2 followed by a question.

S1: p and q both are prime numbers

S2: p+q is an odd integer

Question: Is pq an odd integer?

Which one of the following is correct? (UPSC 2019)

26. How many triplets (x, y, z) satisfy the equation x+y+z=6, where x, y and z are natural numbers? (UPSC 2019)

27. Let p be a two digit number and q be the number consisting of same digits written in reverse order. If p x q = 2430, then what is the difference between p and q (UPSC 2019)

28. Choose the group which is different from others: (UPSC 2023)

29. If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p+q)(r+s)? (UPSC 2023)

30. 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? (UPSC 2023)

31. What is the sum of all digits which appear in all the integers from 10 to 100? (UPSC 2023)

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

1. p + q + r – s – t is definitely even
2. 2p + q + 2r – 2s + t is definitely odd

Which of the above statements is/are correct? (UPSC 2023)

33. Consider the following in respect of prime number p and composite number c

1. can be even
2. 2p + c can be odd
3. pc can be odd

Which of the statements given above are correct? (UPSC 2023)

34. A three digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non – zero digits. What is the value of A + B + C? (UPSC 2023)

35. If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that ABC+DEF = 1111, then what is the value of A + B + C + D + E + F? (UPSC 2023)

36. 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 between the digit at the hundred’s place and the digit at the unit’s place of D? (UPSC 2023)

37. AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E=0, F=8, then what is A + B + C equal to? (UPSC 2023)