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## Number System: Level 1 Test - 3

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Question 1 |

1. The LCM and HCF of two numbers are 4641 and 21 respectively. If one of the numbers lies between 200 and 300, find the numbers which satisfy the condition

A | 273, 357 |

B | 273, 361 |

C | 273, 359 |

D | 273, 363 |

Question 1 Explanation:

Product of the numbers = HCF x LCM

= 21 x 4641 = 21 x3x7 x13x17

= 3x7 x3x7 x13x17 The numbers can be 3x7 x13 and 3x7 x17,

= 21 x 4641 = 21 x3x7 x13x17

= 3x7 x3x7 x13x17 The numbers can be 3x7 x13 and 3x7 x17,

*ie,*273 and 357.Question 2 |

Members of a club have their ages are in AP, the common difference being 3 months. If the youngest member of the club is just 7 years old and the sum of the ages of all the members is 250 yr, Find the number of members in the club is

A | 15 |

B | 20 |

C | 25 |

D | 30 |

Question 2 Explanation:

Let

Then 250 =n/2[2x7+(n-1)3/12]

250= n/2[14+1/4n-1/4]

250= 7n +n^2/8-n/8

n= 25

*n*be the number of members in the club.Then 250 =n/2[2x7+(n-1)3/12]

250= n/2[14+1/4n-1/4]

250= 7n +n^2/8-n/8

n= 25

Question 3 |

6 identical machines can produce a total of 270 bottles per min by running at constant speed. At this rate, how many bottles could 10 such machines produce in 4 min?

A | 1800 |

B | 648 |

C | 2700 |

D | 10800 |

Question 3 Explanation:

Answer a) Number of machines =270x10x4/6=1800

Question 4 |

There are two examination rooms A and B. If 10 candidates from A are sent to

*B,*the number of students in each room is the same. If 20 candidates from B are sent to A, the number of students in A is double the number of students in B. Find the number of students in each room.A | (a) 100 in A and 80 in B |

B | (b) 80 in A and 100 in B |

C | (e) 120 in A and 100 in B |

D | (d) 100 in A and 120 in B |

Question 4 Explanation:

A -10 = B + 10

A - B = 20 ... 1)

and A + 20 = 2 (B - 20)

A - 2B = - 60 ... 2

From Eqs. (i) And (ii), A = 100, B = 80

A - B = 20 ... 1)

and A + 20 = 2 (B - 20)

A - 2B = - 60 ... 2

From Eqs. (i) And (ii), A = 100, B = 80

Question 5 |

The LCM of two numbers is 4800 and their HCF is 160. One of the numbers is 480, Find the other number is

A | 16 |

B | 16000 |

C | 160 |

D | 1600 |

Question 5 Explanation:

Product of two numbers=LCM*HCF

4800*160=480*x

x=1600

4800*160=480*x

x=1600

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