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## Number System: Level 2 Test - 7

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Question 1 |

If the difference between one-third of a number and one-fourth of the number is 3, then find the value of the number?

18 | |

24 | |

30 | |

36 |

Question 1 Explanation:

Let the number be

Then x/3 – x/4 =3

x/12 = 3 so

*x*Then x/3 – x/4 =3

x/12 = 3 so

*x*= 36Question 2 |

If one-eighth of length of pencil is black, half of the remaining length is yellow, while the remaining 7/2 cm is blue, find the total length of the pencil is

6 cm | |

7 cm | |

8 cm | |

11 cm |

Question 2 Explanation:

1/8 part of pencil is black. Half of remaining,

Now, the part left = 7 / 16 , which

*ie, ½ x 7/8 = 7/16*is yellow.Now, the part left = 7 / 16 , which

*is equal to**7/2 = 3.5**Therefore, total length of the pencil 3.5/7/16=8cm*Question 3 |

In a certain shop, cost of 9 oranges is equal to 5 apples, cost of 5 apples is equal to 3 mangoes, cost of 4 mangoes is equal to 9 lemons. If 3 lemons cost 48 paise, find the price of an orange is

12 paise | |

14 paise | |

13 paise | |

15 paise |

Question 3 Explanation:

9 lemons = 144 paise = 4 mangoes

So, 3 mangoes = 144/4x 3 = 108 paise = 5 apples =>

9 oranges = 108 paise 108.

Therefore, One orange = 109/9 = 12 paIse

So, 3 mangoes = 144/4x 3 = 108 paise = 5 apples =>

9 oranges = 108 paise 108.

Therefore, One orange = 109/9 = 12 paIse

Question 4 |

Find the unit's digit of the product 7

^{35}x 3^{71}X 11^{55}1 | |

3 | |

7 | |

9 |

Question 4 Explanation:

Unit digit in (7)4 = 1, therefore unit digit in (74)8

Hence, unit digit in

Again, unit digit in (3) ^ 4 = 1

Therefore, unit digit in the expansion of

(3) ^68 = 1: Unit digit in the expansion of (3) ^71 =1 x3x3x3=7

and unit digit in the expansion of (11) ^55 = 1:

Unit digit in the expansion of 7^35 x 3^71

*^32 will be l.*

i.e., 7i.e., 7

Hence, unit digit in

*(7) ^35*= 1 x 7 x 7 x 7 = 3Again, unit digit in (3) ^ 4 = 1

Therefore, unit digit in the expansion of

*(3^4) ^17 =*(3) ^68 = 1: Unit digit in the expansion of (3) ^71 =1 x3x3x3=7

and unit digit in the expansion of (11) ^55 = 1:

Unit digit in the expansion of 7^35 x 3^71

^{ }X 11^55 =3x7x1=1Question 5 |

The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4, Find the largest number of these two numbers

12 | |

48 | |

84 | |

108 |

Question 5 Explanation:

Let the numbers be

=>

=>

=>

Hence, the larger number is 4x = 84

*x*and*4x.*

Then, 84 x 21 =*x***4x*=>

*4x^2*= 1764=>

*x^2*= 441=>

*x*= 21Hence, the larger number is 4x = 84

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