Math Puzzles Questions

 It is a strange sequence. Each number describes the resemblance of the previous one, except the first one.

11 describes the previous '1' which contains one '1'

21 describes the previous '11' which contains two '1'

1211 describes the previous '21' which contains one '2' and one '1'

111221 describes the previous '1211' which contains one '1', one '2' and two '1'.

So the next sequence will be 312211, that is the previous '111221' contains three '1', two '2' and one '1'.

Let the required number be 'X'

Condition 1 :  

$$\begin{gathered} XX = 2X \\ => 2X2 = X \\ => X = 12 \end{gathered}$$

Condition 2 :

$$\begin{gathered} X × X = X2 \\ => X = 12 \end{gathered}$$

Therefore, 12 is the number which becomes double when it is divided by itself and becomes half when it is multiplied by itself.

Let the two digits be x & y

From given data in the question, we get

x + y = 3(x - y)

x + y = 3x - 3y

=> 2x = 4y

x/y = 2/1

For having the 2:1, numbers satisfying are

12, 21, 24, 42, 36, 63, 48, 84

From this 36 is eleminated because it is a perfect square and no others are prime or perfect squares.

Hence, there exists 7 such 2-digit numbers => 12, 21, 24, 42, 63, 48, 84.

In the given puzzle, the logic is

2 + 3 = 10 => (2 + 3) * 2 = 10

6 + 3 = 54 => (6 + 3) * 6 = 54

8 + 3 = 88 =>  (8 + 3) * 8 = 88

Similarly,

9 + 7  => (9 + 7) * 9 = 16 x 9 = 144.

Given two trains of length = 180 mts + 180 mts 

The distance is = Length of trains = 360 mts 

Speed = 58 - 50 = 8 kmph x 5/18 m/s

Then, Time = dis/speed = (360x18) / (8x5) = 162 sec.

In the given puzzle, the logic is the product of the number and its preceeding number gives the result.

9 = 9 x 8 = 72

8 = 8 x 7 = 56

7 = 7 x 6 = 42

6 = 6 x 5 = 30

5 = 5 x 4 = 20

Similarly,

3 = 3 x 2 = 6.

1113122110

In given series 2nd number gives number of  which digits present in the 1st number and so on continues for 3rd ,4th,...

Here 1st no. has only one zero, so  2nd no. is 10 and 2nd no. has one 1 and one 0,so 3rd no. is 1110, so like that 5th no. has one 1,one 3,one 2,two 1's and one 0.So the next no. is 1113122110. 

In the given puzzle,

The logic is in the format of lets say, a/b

In that case b doesn't matter, because

2/2 = 1,

6/5 = 6/2 = 3,

10/11 = 10/2 = 5

This means that equation is a/2

So 16/19 is equal 16/2 = 8.