Numbers Questions

A multiple of a number is the number multiplied by an integer.

The first four multiples of 9 are given by multiying the first 4 integers with number 9.

That is,

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

Hence, first four multiples of 9 are 9, 18, 27, 36.

Let the original number is 82 i.e 8 + 2 = 10 and when the digits are reversed i.e 28
The difference is 82 - 28 = 54 i.e, the number is decreased by 54.

Screws weight = 90x100 = 9000gms
bolts weight = 100 x 150 = 15000gms
weight = screws + bolts => 24000 gms =>24 kg
Given entire box weight = 35.5kg
empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg
so the empty box is 11.5kg.

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

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

---> 2 x 3 x 5 = 30 

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

when 30 divided by 8, remainder = 6.

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.