Solution:

nineteen

Explanation:
worstcase (7purple+11yellow+1blue)

Solution:

10 Bulbs

For this tricky puzzle, you must check how many light bulbs in the row are having an odd number of factors. The first one surely has odd number of factors, the second has even, four has odd. Thus the bulb four and one will remain lit. The bulbs that are going to remain lit are perfect squares as they have an odd number of factors - 1, 4, 9, 16.

Since there are 100 passes, you can go up to 10 times 10 i.e. the square of 10. There are 10 perfect squares available to you - one, two, three, four, five, six, seven, eight, nine and ten. They corresponds to the bulb number 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. All of them will remain lit and thus total ten bulbs will remain lit after 100 passes.

Solution:

It is one of those problems which will keep you thinking for much time. But did you consider the fact that that the number of pennies are not told and the question asks if the stack will fit the room or not.

Also the size of the room is not mentioned and it is left to your intuition. Now consider the Empire State Building which is 102 stories tall or say 100 story tall on a rough note. Now that is hundred times more than an ordinary room measured on the inside. Now you will have to break the skyscraper-high column of pennies into about a hundred floor-to-ceiling-high columns. Now the question becomes if you can fit approximately hundred floor-to-ceiling penny columns in a room?

Surely! It will be just a ten by ten array of penny columns. Of course, every room will have enough space to set hundred pennies flat on the floor.

Solution:

This is quite a famous interview puzzle and is usually asked as a warm up question. While you can figure out endless possibilities, the answer is quite simple. Detective Hoffman will just have to wait till the night. When there is no sun, he can simply walk out of the door that leads to the chamber built with magnifying glass.

Solution:

This puzzle is also known as Monty Hall Puzzle. If Michael choose the box on the table, the probability of finding the pearl inside will be 2/3.

Let us consider the same thing with more boxes. If Sarah placed 100 boxes on the table with one box that contains the pearl and Michael is allowed to pick random, 99 boxes will remain on the table. Now at least 98 boxes in the table will be empty. Sarah will remove these 98 boxes and now Michael will have to choose from the box on table or the box in his hand. If he chooses the box below, the probability of finding the pearl in the box will be 99/100.

Now you must be convinced why he should pick the box on the table.

Solution:

Keep one coin from the first set and place it on the scale along with the two from the second set etc. If the weight is off by one hundredth of an ounce, then you will know that it is the first set that is faulty and if the weight is off by two hundred of an ounce, then the second set is faulty and so on.

Solution:

Let us assume that the initial price was Rs.100
Then after reducing it 30% the price will be Rs.70

To make it back to Rs.100, the price must be increased by
100*30/70 = 300/7 % = 42.86%

Solution:

4 Kg

Explanation:
2% of 100kg = (100 - 50)% of x
2kg = x/2

=> x = 4kg (answer)

Solution:

1/5*8 + 1/8*11 + 1/11*14

= sum (1/n (n+3)) = Sum [1/3*(1/n - 1/n+3)]

= 1/3(1/5 -1/8+ 1/8 - 1/11+ 1/11 + .... - 1/245) = 1/3*(1/5-1/245)

= 1/3 * 48/245 = 16/245

Thus the sum of the series is 16/245

Solution:

This is quite a common interview question.
Let us begin counting.

There are 61 1x1 squares
39 2x2 squares
20 3x3 squares
5 4x4 squares

Thus the total number of squares = 61 + 39 + 20 + 5 = 125