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## Number System Basics: Test-5

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Question 1 |

If p x q x r = +ve where p ,q, r are integer then which of the following statements is correct ?

A | Either q or r must be positive |

B | At most two of them is negative |

C | At most two of them is positive |

D | none |

Question 1 Explanation:

Explanation for (B) – Since at most two of the numbers can be negative, so the no of negative no can be either 0 or 1 or 2. In case of 1 negative no, the answer comes out to be negative

Explanation for (C) – Since at most two of the numbers can be positive, so the no of positive no can be either 0 or 1 or 2. In case of 0 or 2 positive no, the answer comes out to be negative

Options A is self explanatory.so the right answer is option d

Explanation for (C) – Since at most two of the numbers can be positive, so the no of positive no can be either 0 or 1 or 2. In case of 0 or 2 positive no, the answer comes out to be negative

Options A is self explanatory.so the right answer is option d

Question 2 |

If P+Q+R= odd and P,Q,R are integers then which of the following are true

A | Either two of these three numbers must be odd numbers |

B | All of them must be odd |

C | Either 2 must be even |

D | Both 2, and 3 are correct |

Question 2 Explanation:

Since it is given that P + Q + R are odd ,

we have the following two cases:

Case 1: all of them are odd i.e.= 1+3+5= 9

Case 2: two of them are even = 4+5+6= 15

So the best answer is D, since both the statements are correct

we have the following two cases:

Case 1: all of them are odd i.e.= 1+3+5= 9

Case 2: two of them are even = 4+5+6= 15

So the best answer is D, since both the statements are correct

Question 3 |

Richa has a book which contains 445 pages but the book did not contain the page numbers, so she decided to write all the page numbers on the top of the book .Then how many digits she will use while writing all these page numbers

A | 1557 |

B | 1227 |

C | 1478 |

D | 1670 |

Question 3 Explanation:

Number of digits from 1 to 9 = 9

Number of digits from 10 to 99 = 90 x 2 = 180

Number of digits from 100 to 445= 346x3= 1038

Hence total number of digits = 1227,

so number of digits that Richa will use are 1227

Number of digits from 10 to 99 = 90 x 2 = 180

Number of digits from 100 to 445= 346x3= 1038

Hence total number of digits = 1227,

so number of digits that Richa will use are 1227

Question 4 |

What should be the value of n so that A= 9

^{1}+9^{2}+9^{3}+ .....................9^{n}is a perfect square?A | 23 |

B | 14 |

C | 25 |

D | none |

Question 4 Explanation:

The value of A = (9

^{n}- 1)}/8 can not be a perfect square by hit and trial.Question 5 |

What is the remainder when product of digits of 33333 x 3333366667 is divided by 5?

A | 1 |

B | 5 |

C | 6 |

D | 2 |

Question 5 Explanation:

The remainder when 33333 is divided by 5 is 3, and 2 when 3333366667 is divided by 5.

So now 3 x 2 = 6 when divided by 5 leaves remainder 1, so the answer is option a

So now 3 x 2 = 6 when divided by 5 leaves remainder 1, so the answer is option a

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