# Numbers Questions

A) 6 and 2 | B) 8 and 2 |

C) 6 and 5 | D) 8 and 5 |

Explanation:

Let the number be 476ab0

476ab0 is divisible by 3

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

if a=6 and b=2,

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

if a=8 and b=2,

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

if a=6 and b=5,

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

if a=8 and b=5,

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer

A) 1 | B) 2 |

C) 3 | D) 4 |

Explanation:

clearly 4864 is divisible by 4

So 9 P 2 must be divisible by 3.So(9+P+2) must be divisible by 3.

so P=1.

A) 3/5 | B) 3/10 |

C) 4/5 | D) 5/4 |

Explanation:

Let the required fraction be x. Then, (1 / x )- x = 9/20

1 - x^(2) / x = 9 / 20 => 20 - 20 * x^(2) = 9 * x.

20 * x^(2) + 9 *x - 20 = 0.

=> (4 * x + 5) (5 * x - 4) = 0.

=> x = 4 / 5.

A) 553681 | B) 555181 |

C) 555681 | D) 556581 |

Explanation:

987 = 3 * 7 * 47.

So, the required number must be divisible by each one of 3, 7, 47

553681 => (Sum of digits = 28, not divisible by 3)

555181 => (Sum of digits = 25, not divisible by 3)

555681 is divisible by each one of 3, 7, 47.

A) 8 | B) 9 |

C) 10 | D) 11 |

Explanation:

Here a = 3 and r = 6/3 = 2. Let the number of terms be n.

Then, t = 384 => a * r^(n-1) = 384

=> 3 * 2^(n-1) = 384 => 2^(n-1) = 128 = 2^(7)

=> n-1 = 7 => n = 8.