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Number System: Remainders Test-2

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Your answers are highlighted below.
Question 1
When n is divided by 6 then it leaves a remainder of 5 what will be the remainder when n+4 is divided by 6?
A
3
B
4
C
5
D
6
Question 1 Explanation: 
When n is divided by 6 it gives remainder 5
Hence the n is the form of 6k+ 5 , the smallest positive values of n is when k=0 i.e = 5
Hence the number n+4 = is the form of 6k+5 +4 = 6k+9
So on dividing 6k+9 by 6 we will get 3 as the remainder.
Hence option (a) is the right answer.
Question 2
When p+4 is divided by 7 the remainder left was 5 then what will be remainder when p is divided by 7
A
1
B
2
C
3
D
4
Question 2 Explanation: 
The number p+4 is divided by 7 gives remainder 5 ; 
hence the number p+4 is in form of 7k + 5
P + 4 = 7k+5
p – 1 = 7k

p = 7k+1
Hence number p is in the form of 7k + 1  ,
which means when number p is divided by 7 , the remainder will be 1.
Question 3
When p+7 is divided by 5 the remainder left was 4 then what will be the remainder when p-3 is divided by 5?
A
-4
B
6
C
5
D
4
Question 3 Explanation: 
p+7 when divided by 5, 4 will be the remainder as given ;
hence number will be in form of
p +7 = 5k+4
So the possible values for p = 2,7,12, 17for value of k = 1,2,3,4
We can take any value of p, taking p = 7 and p-3 = 4 when divided by 5 ,
remainder should be 4 ,Hence the answer should be option number (d)
Question 4
What will be the remainder when 60 x 62 x 64 x 66 is divided by 7?
A
240
B
8
C
6
D
2
Question 4 Explanation: 
(60 x 62 x 64 x 66)/7 , The number 63 when divided by 7  will give remainder 0 ,
when number 62 divided by 7 it gives remainder 6 or -1 
similarly we can write remainder by 60 = -3 , 62=-1 , 64 = 1 , 66 = 3
so when we divide the multiplication of all remainders with 7 we will get the remainder as 2,
so the right answer for the question is option (d)
Question 5
What will be the remainder when 567 + 786 + 879 + 980 + 986  is divided by 9  
A
2
B
4
C
6
D
8
Question 5 Explanation: 
576 /9 = 0 remainder
786 /9 = 3 as the remainder
879/9 = 6 as the remainder
980/9 = 8 as the remainder
986/9 = 5 as the remainder
Now add all the remainders 22 since 22 is greater than the 9
so it be further divided by 9 so the remainder for the question is 4 option (b)
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