13. Practice Question Set A — Basic Level (20 MCQs)

Q1. [Divisibility by 4] Which of the following numbers is divisible by 4? (a) 4,58,722 (b) 3,25,764 (c) 7,89,326 (d) 6,12,345

Q2. [Divisibility by 8] Which of the following numbers is divisible by 8? (a) 45,326 (b) 78,904 (c) 63,412 (d) 91,238

Q3. [Missing digit, div by 9] What least value must be given to x so that the number 63x2 is divisible by 9? (a) 2 (b) 3 (c) 4 (d) 7

Q4. [Divisibility by 11] Find the value of x if 5x4832 is divisible by 11 (given digits from the number 5 x 4 8 3 2). (a) 0 (b) 1 (c) 2 (d) 3

Q5. [Divisibility by 6] Which number is divisible by 6? (a) 3,542 (b) 4,326 (c) 5,671 (d) 2,213

Q6. [Divisibility by 3] What is the remainder when 8,42,917 is divided by 3? (a) 0 (b) 1 (c) 2 (d) 3

Q7. [Missing digit, div by 9] Find x so that 27x4 is divisible by 9. (a) 3 (b) 4 (c) 5 (d) 6

Q8. [Missing digit, div by 11] Find x so that 92x389 is divisible by 11. (a) 6 (b) 7 (c) 8 (d) 9

Q9. [Divisibility by 7] Which of the following is divisible by 7? (a) 5,431 (b) 5,432 (c) 5,433 (d) 5,434

Q10. [Divisibility by 13] Which of the following is divisible by 13? (a) 1,001 (b) 1,002 (c) 1,003 (d) 1,004

Q11. [Trailing zeros] How many zeros are at the end of 50!? (a) 10 (b) 11 (c) 12 (d) 13

Q12. [Highest power of prime] Find the highest power of 2 that divides 20! exactly. (a) 16 (b) 17 (c) 18 (d) 19

Q13. [Algebraic divisibility] x^(12) - y^(12) is always divisible by: (a) x-y only (b) x+y only (c) both x-y and x+y (d) neither

Q14. [Consecutive integers] The product of any 3 consecutive positive integers is always divisible by: (a) 4 (b) 5 (c) 6 (d) 8

Q15. [Remainder shortcut] What is the remainder when 71,364 is divided by 9? (a) 1 (b) 2 (c) 3 (d) 4

Q16. [Divisibility by 15] Which of the following numbers is divisible by 15? (a) 4,275 (b) 3,812 (c) 5,288 (d) 7,295

Q17. [Missing digit, div by 9] Find x so that 3x74 is divisible by 9. (a) 2 (b) 3 (c) 4 (d) 5

Q18. [Remainder shortcut, div by 11] What is the remainder when 8,192 is divided by 11? (a) 6 (b) 7 (c) 8 (d) 9

Q19. [Trailing zeros] How many zeros are at the end of 40!? (a) 7 (b) 8 (c) 9 (d) 10

Q20. [Algebraic divisibility] x^(8) - y^(8) is always divisible by: (a) x-y only (b) x+y only (c) both x-y and x+y (d) neither