# Numbers Questions

A) 4 | B) 2 |

C) 0 | D) 6 |

Explanation:

When we divide 1234 by 8, remainder is 2

When we divide 1235 by 8, remainder is 3

When we divide 1237 by 8, remainder is 5

As 30 will not be the remainder because it is greater than 8,

when 30 divided by 8, remainder = 6.

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) 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) 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) 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