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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?

3 | |

4 | |

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

1 | |

2 | |

3 | |

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.

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?

-4
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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 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)

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

2
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4 | |

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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