Math Puzzles Questions

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. 

Let the integer be x. Then,

 x2-20x = 156

(x + 6)(x - 26) = 0

x = 26

The integer is 26.

The given math puzzle follows a logic that,

1 + 4 = 5 => 1 x 4 + 1 = 5

2 + 5 = 12 => 2 x 5 + 2 = 12

3 + 6 = 21 => 3 x 6 + 3 = 21

Similarly,

8 + 11 = > 8 x 11 + 8 = 96.

Here given that 9 = 63, 8 = 48, 7=35, ... 

The given question follows a pattern that

9 x (9 - 2) = 9 x 7 = 63

8 x (8 - 2) = 8 x 6 = 48

7 x (7 - 2) = 7 x 5 = 35

Similarly, 4 x (4 - 2) = 4 x 2 = 8.

Let the given be resembled in letters like R, G & B.

Here given,

1) R + R + R = 30

=> 3R = 30 => R = 30/3 = 10

2) R + G + G = 18 => R + 2G = 18 => 10 + 2G = 18 => 2G = 8 => G = 4

3) G - B = 2 => B = G - 2 => B = 4 - 2 => B = 2

Hence, R + G + B = 10 + 4 + 2 => 16.

394  is the code to unlock the key.

If you take the second statement, 7 is incorrect from the first statement and 1 is incorrect from the fourth statement. Hence 4 is correct, but not on the second place. From the third statement, 4 is not on the first place. Hence 4 is on the third place.

From the fifth statement either 6 or 9 is correct. But combining it with the third statement, 6 is incorrect. Hence along with the first statement, 9 is correct and on the second place.

From the third statement, 3 is correct and on the remaining first place.

From the given data, 

if 60% = 45 minutes

100% =  ?

=> 45 × 100/60

= 75 min

i.e, = 1hr 15 min.

By trial and error method,

P=0, Q=9, R=0 satisfies the values.