Solution:

In such questions, the best thing is to assume each one of them as his sister till you can find all the conditions fulfilled. According to our assumptions, Megan is Alex's sister. We will discuss only this case therefore.

Assuming that Megan is Alex's sister, she has told a lie. This also means that Maggie is not Alex's girlfriend.
If Katie is the truth speaking girl, Megan is lying and it proves our assumption.
Now, if Charlize is Alex's girlfriend, she has also told a lie. This further tells that Katie is speaking the truth which also supports our assumption.
Maggie stated that Charlize is not his sister and that is also true because according to our assumption, Charlize is his girlfriend.

Taking that into account, we can conclude that Megan is Alex's sister and Charlize is his girlfriend.

In any other assumption, you will find the data conflicting with the conditions.

Solution:

Put one black rock in one sack and put all the rest in the other one. In such manner you will get about 3/4 probability of surviving.

Solution:

We now have a square of 3x3 size, 2 squares of 2x2 size and 5 squares of 1x1 size.

Solution:

It will take the man 58 minutes to reach the top.

Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.
Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.

Solution:

Flyball should pay Lavy $11 instead of accepting his counter offer as in that case the club will end up paying almost double the amount.

Solution:

LOTTO

Explanation:
Just flip the two rows 1 and 2 vertically, you will find the word "Lotto".

Solution:

If you are thinking to hold one chocolate from each box in hand and then balancing weight in bare hands, you are thinking all wrong.

Let us begin by labelling boxes as 1, 2, 3 and so on till 10.

Now pick one chocolate from box 1, two chocolates from box 2, three from box 3 and so on. In total, you will have 55 chocolates now. (1 + 2 + 3 + ..... + 10)

The ideal weight of the chocolates should be 55 * 20 = 1100. However, somewhere in there are the defected chocolate/s.

You can judge that clearly by noting down the result of 1100 - total weight of chocolates. If the weight is less than 1 gram, the defected box is box 1, if the weight is less than 2 grams, the defected box is box 2 and so on.

Solution:

100

Series of number that do not contain albhabet 'T'

Solution:

888 + 88 + 8 + 8 + 8 = 1000

Solution:

The girl was born on 29 February. Thus her birthday came once in four years only while her sister was born on a normal day and celebrated her birthday every year. Thus the girl had a chance of depositing money only 10 times in 4 years through which she collected $2500 while her sister took $50 from the piggy bank every year making the total amount to be $2000. Thus when the piggy bank was opened, it had just $500.

Solution:

28 =>1+2+4+7+14

cannot be 1 (as number cannot be included)