# Numbers Questions

A) n is odd | B) n + 1 cannot be a prime number |

C) (n + 2) divided by 7 has remainder 2 | D) n + 3 is divisible by 5 |

Explanation:

You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5. So we have n = 7 , 12, 17, 22 etc.

From this series we can see that n does not have to be odd.

Also n + 1 can be a prime because, for example, 12 + 1 = 13

And (n + 2) / 7 has a remainder 2 in some cases but not all.

Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases. However, adding 3 to any of the values of n will always give a multiple of 5.

A) 961 x 861 | B) 961 x 961 |

C) 961 x 2 | D) 29791 |

Explanation:

We know that ${a}^{m}\times {a}^{n}={a}^{m+n}$

$\therefore {\left(31\right)}^{31-27}$ = ${31}^{4}$ = 961 x 961**.**

A) decrease | B) stay the same |

C) increase four fold | D) increase to more than double |

Explanation:

The best approach is to pick a number that satisfies the rules that x and y are greater than 0. So for example you could choose 25 for y.

The value of x before doubling is then 25 - 50/25 = 23

The value after doubling y will be 50 - 50/50 = 49, which is more than double.

A) 144 | B) 72 |

C) 36 | D) 24 |

A) 5 | B) 15 |

C) -5 | D) 10 |

Explanation:

The pattern is -45, -35, -25, -15

The next number = 20-15= 5

A) 17 | B) 18 |

C) `19 | D) 20 |

Explanation:

The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P).

Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17

A) 3 | B) 2 |

C) 1 | D) 0 |

Explanation:

Given that, ${4}^{198}+{6}^{12345}+{348}^{66}+{24}^{11}+1$

Now Power Cycle of

4 is 4, 6

6 is 6

8 is 8, 4, 2, 6

1 is 1

${4}^{198}$- 198 is even number , So the unit digit value is 6

${6}^{12345}$ - It is always 6

${348}^{66}$- 66/4 the remainder is 2 , So the second value is 4

${24}^{11}$- 11 is odd number, So the unit digit value is 4

1 - It is always 1

Total = 21

Therefore, The unit digit is 1

A) 4981 | B) 6481 |

C) 4964 | D) 6449 |

Explanation:

The pattern is ${1}^{2}{2}^{2},{3}^{2}{4}^{2},{5}^{2}{6}^{2}$,

$\therefore $The next number= ${7}^{2}{8}^{2}$= 4964