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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

9 | |

18 | |

987 | |

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

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?

1 | |

2 | |

3 | |

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 Â option is option B

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 Â 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

4 | |

5 | |

3 | |

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

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

2 | |

7 | |

10 | |

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

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 7

^{343}Â is divided by 9?3 | |

7 | |

2 | |

none |

Question 5 Explanation:

7

The cyclicity of 9 is 2 i.e. after 2 the cycle is changes

So on dividing

7 / 9Â remainder is 7

7

7

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,

7

So when we divide 7

^{343}Â Â is divided by 9The cyclicity of 9 is 2 i.e. after 2 the cycle is changes

So on dividing

7 / 9Â remainder is 7

7

^{2}/ 9Â remainder is 47

^{3}/ 9Â remainder is 2So 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,

7

^{1}/9 the remainder is 7So when we divide 7

^{343 }by 9 we get 7 as the reminder
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