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## Number System: Level 1 Test -9

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Question 1 |

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

12 | |

48 | |

84 | |

108 |

Question 1 Explanation:

Let the numbers by 21x and 84x.

The LCM is 84 and the larger number is 84x.

Thus the largest number is 84.

Correct option is (c)

The LCM is 84 and the larger number is 84x.

Thus the largest number is 84.

Correct option is (c)

Question 2 |

The unitâ€™s digit in the product of 7

^{35}x3^{71}x 11^{55}1 | |

3 | |

7 | |

9 |

Question 2 Explanation:

We can easily observe that 11

has the last digit as 1

Now 3

Thus the last digit of (3

So the correct option is a

^{11}is divisible by 7^{35}3^{35}has the last digit as 1

Now 3

^{36}is left,Thus the last digit of (3

^{4})^{9}=1So the correct option is a

Question 3 |

Which of the following pairs of fractions adds up to a number greater than 5?

$ \displaystyle \frac{13}{5},\frac{11}{6}$ | |

$ \displaystyle \frac{11}{4},\frac{8}{3}$ | |

$ \displaystyle \frac{7}{3},\frac{11}{5}$ | |

$ \displaystyle \frac{5}{3},\frac{3}{4}$ |

Question 3 Explanation:

Let us evaluate the options,

Option a $ \frac{133}{30}$

Option b $ \frac{65}{12}>5$

By observation, we can find that correct option is (b)

Option a $ \frac{133}{30}$

Option b $ \frac{65}{12}>5$

By observation, we can find that correct option is (b)

Question 4 |

The remainder when 7

^{1987}is divided by 5 is1 | |

2 | |

3
| |

4 |

Question 4 Explanation:

7

Hence, unitâ€™s digit repeats after index 4.

Remainder when 1987 is divided by 4= 3

Unitâ€™s digit = 3

Hence, remainder non division by 5 = 3

^{1}= 7, 7^{2}= 49; 7^{3}= 343; 7^{4}= 2401; 7^{5}= 16807Hence, unitâ€™s digit repeats after index 4.

Remainder when 1987 is divided by 4= 3

Unitâ€™s digit = 3

Hence, remainder non division by 5 = 3

Question 5 |

Unitâ€™s digit in 13

^{2003}is1 | |

3
| |

7 | |

9 |

Question 5 Explanation:

The question is same as finding unitâ€™s digit of ${{3}^{2003}}={{3}^{3}}=\_7$

Thus correct option is (c)

Thus correct option is (c)

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