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

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

=

= (5050 - 1275) = 3775

A) 4 | B) 6 |

C) 3 | D) 1 |

Explanation:

Number = quotient x divisor + remainder;

so, here

number = 138 k + 26

=> (23 x 6k) + (23+3)

=> 23(6k+1)+3

so, remainder is 3.

A) 2893 | B) 4528 |

C) 6587 | D) 4875 |

Explanation:

For solving this problem first we would break the whole range in 5 sections

1) From 1 to 9

Total number of zero in this range = 0

2) From 10 to 99

Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)

3) From 100 to 999 - three type of numbers are there in this range

a) x00 b) x0x c) xx0 (here x represents a non zero number)

Total possibilities

for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18

for x0x = 9*1*9 = 81, hence total zeros = 81

similarly for xx0 = 81

total zeros in three digit numbers = 18 + 81 +81 = 180

4) From 1000 to 9999 - seven type of numbers are there in this range

a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx

Total possibilities

for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27

for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162

for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162

for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162

for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729

for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729

for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729

total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700

thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)

= 2893

A) 4 | B) 1 |

C) 5 | D) 3 |

Explanation:

(3x + 2) (2x - 5) = ...............(1)

But (3x + 2)(2x - 5) = ........(2)

so by comparing (1) & (2),

we get a= 6, k= -11 , n= -10

(a - n + k) = 6 + 10 - 11 = 5.

A) 2 | B) 3 |

C) 4 | D) 5 |

Explanation:

By trial and error method, we get

2880/3 = 960 is not a perfect square

2880/4 = 720 is not a perfect square

2880/5 = 576 which is perfect square of 24

Hence, 5 is the least number by which 2880 must be divided in order to make it into a perfect square.

A) L / (k-3) | B) k / (L-3) |

C) 2K / 3L-K | D) 3L / K(K-3) |

Explanation:

Intial contribution = L/K

After 3 men drop, then contribution =L/K-3

The amount more to pay in contribution =

=