Numbers Questions

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = ( 22 + x ), which must be divisible by 3.

When x=2. [(22 + 2) = 24 is divisible by 3]

So, the answer is 2

The pattern is 32+42=52,  52+122=132, 72+242=252 

The next number = 82+152=172

 i.e. 17

Number = ( 779 x a) + 47, where "a" is the quotient

           = (19 x 41 x a) + (19 x 2) + 9

           = 19 x (41a + 2) + 9

           = 19 x (New quotient) + 9

  Required remainder = 9

Since 653xy is divisible by 5 as well as 2, so y = 0.
Now, 653x0 must be divisible by 8.
So, 3x0 must be divisible by 8. This happens when x = 2
x + y = (2 + 0) = 2.

6)4456(742
42
--------
25
24
-------
16
12
-----
4
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Required number = (6-4) = 2.

Given that, 4198+612345+34866+2411+1

Now Power Cycle of

4 is 4, 6 

6 is 6 

8 is 8, 4, 2, 6

1 is 1

4198- 198 is even number , So the unit digit value is 6 

612345 - It is always 6

34866-  66/4 the remainder is 2 , So the second value is 4

2411- 11 is odd number, So the unit digit value is 4

1 - It is always 1 

Total = 21

Therefore, The unit digit is 1

Let,

no. of rice bowl = x
no. of dal bowl = y
no. of meat bowl = z

Then, x + y + z = 65 ....(1)

Also given that, 2x = 3y = 4z

substituting value of y & z in terms of x i.e. y = 2x/3 and z = x/2 in eq (1),
We get x = 30.

As 1 rice bowl is shared between 2 guests,
Therefore, there are 60 guests.

The maximum number of bows will be 4 yards (= 4 x 36 inches) divided by 15 inches.

This gives 9.6. But as a fraction of a bow is no use, we can only make 9 bows.