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Number System: Remainders Test-1

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Question 1
The sum of digits of a even number is 36. Then that number is always divisible by
A
9
B
18
C
987
D
Both A or B
Question 1 Explanation: 
We know that the number whose sum of digits is 36 always divisible by 9
And the number is even so the number is also divisible by 2
therefore the number is always divisible by 18,
because 18 is a factor of both 9 and 2
So the right option is D
Question 2
When a natural number is divided by 4, the remainder is 3. What is the remainder when the 2n is divided by 4?
A
1
B
2
C
3
D
6
Question 2 Explanation: 
Let us assume the number is 7
On dividing 7 by 4, the remainder is 3
Now the number 2n = 14
14 / 4 = 3 as quotient and 2 as the remainder
So the right  option is option B
Question 3
A number is when divided by 56, the remainder is 29. What will be the remainder when the number is divided by 8
A
4
B
5
C
3
D
7
Question 3 Explanation: 
If any number is divided by 56 and leaves remainder 29
then that number will be = 56n + 29
(Where n is any natural number)
Now 56 is factor of 8 i.e. every value of 56n would be divisible by 8
but 29 = 8 x 3 + 5 i.e. 5 is the remainder when 29 is divided by 8
So in every value of 56n + 29 ,
5 will be the remainder so the right answer is option b
Question 4
A number when divided by 119 leaves remainder 19. Then what will be the remainder when same number is divided by 17
A
2
B
7
C
10
D
12
Question 4 Explanation: 
If the dividend is same for both the cases then there will be a condition for that
i.e. both the divisors must be multiple of each other i.e.
119 is multiple of 17 Now the remainder will obtained by dividing 19 by 17
so the remainder is 2, and the right option is A
Question 5
What is the remainder when 7343  is divided by 9?
A
3
B
7
C
2
D
none
Question 5 Explanation: 
7343   is divided by 9
The cyclicity of 9 is 2 i.e. after 2 the cycle is changes
So on dividing
7 / 9  remainder is 7
72 / 9  remainder is 4
73 / 9  remainder is 2
So here cycle changed
Now we will divide the power of 7 with the cycle number i.e. 343 by 2 the remainder is 1 so,
71/9 the remainder is 7
So when we divide 7343 by 9 we get 7 as the reminder
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