# Numbers Questions

51 + 52 + 53 + ...........+ 100

= (1 + 2 + 3 + .... + 100) - (1 + 2 + 3 + ...... + 50)

= **It is in the form of $\frac{n(n+1)}{2}seriessummation$**

= n1 = 100 , n2 = 50

=$\left[\frac{{\displaystyle 100\left(100+1\right)}}{{\displaystyle 2}}\right]-\left[\frac{50\left(50+1\right)}{2}\right]$

= **(5050 - 1275) = 3775**

A) 23 | B) 31 |

C) 29 | D) 37 |

Explanation:

87)13601(156

87

-----

490

435

-----

551

522

-----

29

-----

Required number is 29.

A) 945 | B) 678 |

C) 439 | D) 568 |

Explanation:

Required numbers are 10,15,20,25,...,95

This is an A.P. in which a=10,d=5 and l=95.

Let the number of terms in it be n.Then t=95

So a+(n-1)d=95.

10+(n-1)*5=95,then n=18.

Required sum=n/2(a+l)=18/2(10+95)=945.

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) 6393 | B) 5831 |

C) 6993 | D) 6339 |

Explanation:

(Place value of 7)-(face value of 7)

=7000-7=6993.

A) 1 | B) 3 |

C) 5 | D) 2 |

Explanation:

Let the Number be Y.

Then Y = 296 q + 75

= (37 x 8)q +( 37 x 2) + 1

= 37 (8q + 2) + 1

Thus, when the number is divided by 37, the remainder is 1

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) 13 | B) 12 |

C) 11 | D) 10 |

Explanation:

(2272-875) = 1397, is exactly divisible by N.

Now , 1397 = 11 x 127

The required 3-digit number is 127,the sum of digits is 10.