Puzzles Questions

PRINCE.

Sum of numbers in the outer circle in before Arc should come in inner circle patterns in the clock wise direction next Arc.

i.e, 9+6 = 15 comes in next arc of inner circle

7+3 = 10 comes in next arc of inner circle

In the same way, 4+2 = 6 comes in place of '?'.

Answer:  K

Explanation:  In each row, the product of the left and right hand numbers equals the sum of the numerical values of the three letters.

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 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 

Given 

1 = 1 => 1 x 11 = 11

2 = 22 => 2 x 11 = 22

3 = 33 => 3 x 11 = 33

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Similarly,

11 => 11 x 11 = 121.

The total angle traced by the hour hand is the angle traced in 7 hours and 10 minutes.
We know that the angle traced by the hour hand in one hour is 30º and in one minute is 1/2º.
Therefore, (30º x 7) + (10 x 1/2º) = 215º is the angle traced by the hour hand.