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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?

588 | |

784 | |

823 | |

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

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?

0 | |

1 | |

2 | |

4 |

Question 2 Explanation:

Let us Assume the number is N

So N = 5q + 3

Therefore

N

So it will become 25q

When 5 divides this number, we get 4 as the remainder

So N = 5q + 3

Therefore

N

^{2}= (5q +3)^{2}So it will become 25q

^{2}+ 30q + 9When 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?

10004 | |

10472 | |

10476 | |

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 â€“ 4) = 10472

When this number divided by 476, 4 will be the remainder

So the required number is 10000 + (476 â€“ 4) = 10472

Question 4 |

What is the largest five-digit number that which is divisible by 91?

99918 | |

99921 | |

99981 | |

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 â€“ 81 = 99918

When this number divided by 91, 81 will be the remainder

So the required number is 99999 â€“ 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?

1 | |

2 | |

3 | |

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.

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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