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## Number System: Level 2 Test -3

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Question 1 |

9^6 + 7, when divided by 8, what would be the remainder by such operation

0 | |

6 | |

5 | |

None of these |

Question 1 Explanation:

According to the remainder theorem,Â

9^ 6 + 7/8 will have the same remainder Â as 1^6 + 7/8Â

and this will have the remainder as 0

9^ 6 + 7/8 will have the same remainder Â as 1^6 + 7/8Â

and this will have the remainder as 0

Question 2 |

What is the least fraction number which must be added to 29/12+ 15/16, will make the result a whole number

21/38 | |

31/38 | |

31/48 | |

17/48 |

Question 2 Explanation:

Now 29/12 + 15/16 = 116+ 45/48 = clearly,

the least fraction among options given is 31/ 48 161/48 + 31/48 = 192/48=4

which is a whole number

the least fraction among options given is 31/ 48 161/48 + 31/48 = 192/48=4

which is a whole number

Question 3 |

The highest power of 9 which completely divide 99!

20 | |

24 | |

22 | |

12 |

Question 3 Explanation:

99! = 99 x 98 x 97 x 96 x 95 x 94 xâ€¦â€¦â€¦â€¦â€¦. x 1

To find the highest power of 9 that divides the

above product, it is required to find the sum of powers of all

9s in the expansion. Â Sum of powers of 9 s

= 99/9^1 Â + Â 99/9^2 Â = 11 + 1 = 12 (ignoring the fractional part )

To find the highest power of 9 that divides the

above product, it is required to find the sum of powers of all

9s in the expansion. Â Sum of powers of 9 s

= 99/9^1 Â + Â 99/9^2 Â = 11 + 1 = 12 (ignoring the fractional part )

Question 4 |

In a community of 175 persons, 40 read the Times, 50 read the Samchar and 100 do not read any. How many persons read both the papers?

10 | |

15 | |

20 | |

25 |

Question 4 Explanation:

Number of persons, who read = 175-100 =75

Now, number of persons who read either and of the papers = (40 + 50) = 90

Hence, number of those who read both the papersÂ = (90 -75) = 15

Now, number of persons who read either and of the papers = (40 + 50) = 90

Hence, number of those who read both the papersÂ = (90 -75) = 15

Question 5 |

In a group of buffaloes and ducks, the number of legs of the group is 24 more than twice the number of heads of the group. Find the number of buffaloes in the group?

6 | |

12 | |

8 | |

None of these |

Question 5 Explanation:

Let the number of buffaloes be x and number of ducks be y.

Then, number of legs = 4x + 2y,

number of heads = x + y given, 4x + 2y = 2(x + y) + 24

2x = 24

x =12

Then, number of legs = 4x + 2y,

number of heads = x + y given, 4x + 2y = 2(x + y) + 24

2x = 24

x =12

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