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## Number System: Level 1 Test - 7

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Question 1 |

The sum of two numbers is 462 and the HCF of these two numbers is 22. Find the maximum number of pairs that satisfy these conditions?

1 | |

3 | |

2 | |

6 |

Question 1 Explanation:

Since 22 is the HCF, the two numbers are
22x and 22y (x and y are prime to each other).

Also, we know

22x+22y=462

x+ y=21

Now 21 can be written as a sum of two co-prime numbers in the following ways:

(1,20) (2,19) (4,17) (5,16) (8,13) (10,11).

Therefore option d is the right answer.

Also, we know

22x+22y=462

x+ y=21

Now 21 can be written as a sum of two co-prime numbers in the following ways:

(1,20) (2,19) (4,17) (5,16) (8,13) (10,11).

Therefore option d is the right answer.

Question 2 |

The LCM of two numbers is 280 and their ratio isÂ 7 : 8. Find the two numbers which satisfy this criterion

70, 80 | |

42, 48 | |

35, 40 | |

28, 32 |

Question 2 Explanation:

Let the number be 7

LCM x HCF = Product of numbers

so

*x*and*8x. Â*HCF=x,LCM x HCF = Product of numbers

so

*280 *x**=**56x*

x=5 Â:. Numbers are 35, 40.^{2},x=5 Â

Question 3 |

If the age of Ram is one-third the age of his father Sham now, and was one-fourth the age of his father 5 yr ago, then how old will his father Sham be 5 yr from now?

20 | |

25 | |

50 | |

45 |

Question 3 Explanation:

Let the present age of Ram and his father be x and y respectively.

Then x=1/3y Â and

From Eqs. (i) and (ii), y = 45 yr and

Hence, required age = (y + 5) = 50 yr

Then x=1/3y Â and

*(x*- 5) = Â¼ Â (y - 5)From Eqs. (i) and (ii), y = 45 yr and

*x*= 15 yrHence, required age = (y + 5) = 50 yr

Question 4 |

Find the number which leave remainder of 1, 2 and 3 when divided by 2, 3 and 4 respectively?

11 | |

17 | |

19 | |

36 |

Question 4 Explanation:

The number which leave remainder 1, 2 , 3 when divided by 2,

3 ,4 respectivelyÂ is LCM of ( 2, 3 , 4)- 1

Â i.e. = 12-1= 11

3 ,4 respectivelyÂ is LCM of ( 2, 3 , 4)- 1

Â i.e. = 12-1= 11

Question 5 |

If

*x*+*y*> 5 and*x*-*y*> 3, then which of the following gives all possible values of*x?*x> 3 | |

x> 4 | |

x > 5 | |

x < 5 |

Question 5 Explanation:

*x*+ y > 5 Â and

*x-y>3*

Solving Eqs. (i) and (ii), we get Â

*2x*> 8 so Â

*x>*4

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