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Number System: Remainders Test-2
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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?
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5 | |
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.
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
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2 | |
3 | |
4 |
Question 2 Explanation:
The number p+4 is divided by 7 gives remainder 5 ;Â
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 + 1Â ,
which means when number p is divided by 7 , the remainder will be 1.
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 + 1Â ,
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?
-4 | |
6 | |
5 | |
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)
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?
240 | |
8 | |
6 | |
2 |
Question 4 Explanation:
(60 x 62 x 64 x 66)/7 , The number 63 when divided by 7Â will give remainder 0 ,
when number 62 divided by 7 it gives remainder 6 or -1Â
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)
when number 62 divided by 7 it gives remainder 6 or -1Â
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 + 986Â is divided by 9
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6 | |
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)
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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