# Number System Practice Problems 3 | Hamaraguru

21. A number is formed by writing the 1st 35 natural numbers side by side. Find the remainder when same number is divided by 4.
a) 1
b) 2
c) 3
d) none

22. A fifty digit number is formed by writing natural numbers side by side starting from 1. Find the remainder when same number is divided by 8.
a) 3
b) 4
c) 5
d) 6

23. A 6 digit number is formed by repeating a three-digit number for example 369369 is formed by repeating 369. Any number which is in the same form is divisible by which of the following:
a) 7 only
b) 11 only
c) 13 only
d) 1001

24. 4^100 + 4^101 + 4^102 + 4^103 is divisible by
a) 3
b) 10
c) 11
d) 13

25. 3^20 + 3^21 + 3^22 + 3^23 is divisible by
a) 11
b) 16
c) 25
d) 30

26. 5^90 + 5^91 + 5^92 is divisible by
a) 150
b) 160
c) 155
d) 30

27. 49^21 − 1 is exactly divisible by
a) 50
b) 51
c) 29
d) 8

28. Find the unit digit of 9!.
a) 9
b) 0
c) 2
d) 8

29. What will be unit digit of 7^309?
a) 1
b) 3
c) 9
d) 7

30. The unit of 133^99 is
a) 3
b) 9
c) 7
d) 1