# Numbers Questions

A) 4 | B) 8 |

C) 12 | D) None |

Explanation:

we can do this by trial and error method.

Putting x = 2,we get 2²(2² - 1) = 12.

checking with other integers, the above equation always gives a value which is a multiple of 12,

So, x²(x² - 1) is always divisible by 12.

A) 12 | B) 8 |

C) 6 | D) 4 |

Explanation:

Two digit numbers: The two digits can be 2 and 9: Two possibilities 29 and 92.

Three-digit numbers: The three digits can be 1, 2 and 9 3! Or 6 possibilities.

We cannot have three digits as (3, 3, 2) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

A) 8 | B) 2 |

C) 6 | D) 4 |

Explanation:

Let the two consecutive odd integers be (2x + 1) and (2x + 3)

Then,

(2x + 3)^{2} - (2x + 1)^{2}

= (2x + 3 + 2x + 1) (2x + 3 - 2x - 1)

= (4x + 4)(2)

= 8 (x + 1), which is always divisible by 8

A) 4 | B) 1 |

C) 5 | D) 7 |

Explanation:

1 1

8 A 9

+ 4__ C 6 __

- 6__ B 2 __

__ 7 2 3 __

We may represent the given sum, as shown below:

1 + A + C - B = 12

A + C - B = 11

Now,giving the maximum values to A and C, i.e.

A = 9 and C = 9, we get B = 7.

A) 147 | B) 168 |

C) 162 | D) 182 |

Explanation:

The pattern is -4, +9,-16, +25, -36

The next number=119+49=168