Math Puzzles Questions

In the given puzzle, the logic behind is

9 = 72 => 9 x 8 = 72

8 = 56 => 8 x 7 = 56

7 = 42 => 7 x 6 = 42

6 = 30 => 6 x 5 = 30

5 = 20 => 5 x 4 = 20

Similarly,

4 = 12 => 4 x 3 = 12

3 = 6 => 3 x 2 = 6

Let that something be 'x'

From the given data,

x + x/5 = 21

5x + x/5 = 21

6x = 21 x 5

=> x = 17.5

Hence, that something is x = 17.5.

From the hints,

Only two options for 1st and 2nd digits => 4,2 and 9,3 since it is single digits

Sum of second and third digit  = 10 

If 2 => 3rd digit = 8

If 3 => 3rd digit = 7

4th digit = 2nd digit + 1 => (2+1 =3) or (3+1 = 4)

Sum of all digits = 30

Let 5th digit be x

=> 1st possibility = 4 + 2 + 8 + 3 + x = 30 => x = 13 (Not possible since it has 2 digits)

=> 2nd possibility = 9 + 3 + 7 + 4 + x = 30 => x = 7

Therefore, the PIN is 93747 

From the assumption and trial and error method,

last three digits sum must leave the same digit as the answer. It is possible only if the answer must be units digit number leaving tens digit as carry.

And the possible 3rd digit is 5. Since 5 + 5 + 5 = 15 

Now, 2nd step is  1 + x + x + x = 5

=> 3x = 4

It is possible with x = 8. 8 + 8 + 8 + 1 = 25 leaving 2 as carry. 

Now, 3rd step is 2 + x + x + x = 5 => x = 1

Hence, the three dgits are 1, 8, 5.

185 + 185 + 185 = 555. 

From the given equations,

(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
(6)2=14 + 2(ab + bc + ca)
36 - 14 = 2(ab + bc + ca)
22/2 = ab + bc + ca
ab + bc + ca = 11

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
= (6) (14 - 11)
=(6)(3)
=18

Since, a3 + b3 + c3 - 3abc = 18

36 - 3abc = 18

-3abc = 18 - 36

-3abc = -18

abc = 6.

Here in the given puzzle,

2 x (2 + 2) = 8

3 x (3 + 3) = 18

4 x (4 + 4) = 32

5 x (5 + 5) = 50

Similarly,

6 x (6 + 6) = 72.

The number of blueberries is equal to number of cups multiplied by 4 minus one left.

That is :

      B = 9(C - 2) -> (1)

Then the number of blueberries will be equal to the number of cups times three plus one left.

That is :

      B = 6C + 3 -> (2)

Now substitute the 1st and 2nd equations:

      B = 9(C - 2)

      B = 6C + 3

      C = 7, B = 45.

Therefore Blueberries = 45 and cups = 7.

From given data,

Rs. 1 = 40 strawberries => Rs. 2 = 80 strawberries

Rs. 5  = 1 apple => Rs. 95 = 19 apple.

Rs. 3 = 1 mango => Rs. 3 = 1, mango

Now, Total So 100 Rs = 100 Fruits.