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Number System: Divisibility Test-2

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Question 1
If the divisor is 7 times the quotient and three times to the remainder .Then what will be the Dividend if the remainder is 28?
A
588
B
784
C
823
D
1036
Question 1 Explanation: 
Divisor = 7q
Divisor = 3r where q and r is the Quotient and Remainder respectively
Divisor = 3 x 28 = 84
So the value of q = 12
r = 28
q = 12
Divisor= 84
So the dividend = 12 x 84 + 28 = 1036
Question 2
A number when divided by 5 leaves 3 as remainder. What will be the remainder when 5 divide the square of the number?
A
0
B
1
C
2
D
4
Question 2 Explanation: 
Let us Assume the number is N
So N = 5q + 3
Therefore
N2 = (5q +3)2
So it will become 25q2 + 30q + 9
When 5 divides this number, we get 4 as the remainder
Question 3
What is the smallest five-digit number that which is divisible by 476?
A
10004
B
10472
C
10476
D
47600
Question 3 Explanation: 
Smallest number of 5 digits =10000
When this number divided by 476, 4 will be the remainder
So the required number is 10000 + (476 – 4) = 10472
Question 4
What is the largest five-digit number that which is divisible by 91?
A
99918
B
99921
C
99981
D
99971
Question 4 Explanation: 
Largest five-digit number = 99999
When this number divided by 91, 81 will be the remainder
So the required number is 99999 – 81 = 99918
Question 5
When N is divided by 4 the remainder is 3 , what will be the remainder when 2N is divisible by 4?
A
1
B
2
C
3
D
0
Question 5 Explanation: 
N = 4q + 3
Therefore 2N = 8q + 6 = 4(2q +1) + 2
Hence when this number is divided by 4,
the remainder will be 2.
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