Solution:

The first number divisible by 7 is 105 and the last is 994 (we have to find the sum of only three digit numbers)

The divisible numbers are 105, 112, 119, ..., 994
Sum of digits = 105 + 112 + 119, ..., + 994

Now if you see the above series it is an arithmetic progression
Where a = 105, d = 7, I = 994

Thus
994 = 105 + (n - 1)*7
or 889 = (n-1)*7
or 127 = n - 1
or n = 128
so sum = (n/2)*(a + l)
= (128/2)*(105 + 994)
= 70336

Solution:

There is a simple logic for magnet. It has maximum strength at ends and strength is weaker in the center.

You will have to mark the items as A, B and C.

Now bring the end of A near the middle of B then near the middle of C.
If B is attracted towards A, then B is a magnetic material and A is the magnet. C is not attracted, so it is non-magnetic.

If neither B nor C is attracted towards A, the take A closer to the end of B and then to the end of C.
If B attracts A, then B is magnet and C is a non-magnetic material. Also then, A is a magnetic material.

If none of them attracts A or is attracted by A, the A is nonmagnetic material.

Solution:

Let the number be x
As per the data given in the question
x/3 = x/6 + 3
x = 18

The problem is so simple that you can even calculate it in your head too.

Solution:

It his son.
'My father’s son is father of man.'

Solution:

One thing which you must keep in mind is that we must convert everything to one unit.
The speed of dog = 13 km/h i.e. 8.125 miles/h

Time I will take to catch the thief = 13/1/5 hours = 8.67 hours

Total distance that my dog will travel = 8.125 * 8.67 = 70.44 miles.

Solution:

This is a bit tricky series problem. Let us break that down for you

23 is the first term
25 = 21*1 + 2
53 = 25*2 + 3
163 = 53*3 + 4
657 = 163*4 + 5
3291 = 657*5 + 6

Thus the next term will be 3291 * 6 + 7 = 19753

Solution:

The clock ticks 6 times at 6'o clock.

Thus there must be 5 intervals in between the ticks.

According to the data in the question, the time between the first and the last tick = 30 seconds

Thus by unitary method, one interval = 6 seconds.

At 6'o clock
5*6 = 30 seconds

In the similar fashion,
At 7'o clock
6*6 = 36 seconds

Progressing with the same thing
At 12'o clock
11*6 = 66 seconds

Thus it will take 66 seconds at 12'o clock.

Solution:

Hermione's age = 64

Let us break down the calculations for you
Suppose that Hermione has 'N' children.
And each child have (N-1) children. (Grandsons for Hermione).

In that case, total children = N + (N*(N - 1))

Now we will put in the values of 6
Putting N = 6, we obtain 6 + (6*(6 - 1)) = 36 childrens.
Putting N = 7, we obtain 7 + (7*(7 - 1)) = 49 childrens.
Putting N = 8, we obtain 8 + (8*(8 - 1)) = 64 childrens.
Putting N = 9, we obtain 9 + (9*(9 - 1)) = 81 childrens.

Now we have already read in the question that the age of Hermione is between 50 and 70.

Thus out of the above results, the answer that fits is 64.

Thus her age is 64 years as the sum of sons and grandsons is equal to her age.

Solution:

Ironically, there is no possible combination that is divisible by 36 that can be framed using the digits 6, 2, 7 and 5.

For a number to be divisible by 36, it must be divisible by 2, 3, 4, 6 and 9.
Now the sum of the given digits = 6 + 2 + 7 + 5 = 20 which is not divisible by 3. Thus there can be no combination that is divisible by 3.

In such case, there can be no combination that is divisible by 36.

Solution:

The passenger will occupy three seats, per head payable amount will be 26.89.

80.67 rupees cannot be divided by 3.

Thus the number of occupied seats will be 3.
And unoccupied seats = 40-3 = 37.