1. One of Mr. Bajaj, his wife, their son and Mr. Bajaj's mother is an Engineer and another is a Doctor.

If the Doctor is a male, then the Engineer is a male.

If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives.

If the Engineer is a female, then she and the Doctor are blood relatives.

Can you tell who is the Doctor and the Engineer?

Answer :

Mr. Bajaj is the Engineer and either his wife or his son is the Doctor.

Mr. Bajaj's wife and mother are not blood relatives. So from 3, if the Engineer is a female, the Doctor is a male. But from 1, if the Doctor is a male, then the Engineer is a male. Thus, there is a contradiction, if the Engineer is a female. Hence, either Mr. Bajaj or his son is the Engineer.

Mr. Bajaj's son is the youngest of all four and is blood relative of each of them. So from 2, Mr. Bajaj's son is not the Engineer. Hence, Mr. Bajaj is the Engineer.

Now from 2, Mr. Bajaj's mother can not be the Doctor. So the Doctor is either his wife or his son . It is not possible to determine anything further.

2. Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number.

Answer :    285714.

If its rightmost digit is placed at its left end, then new number is 428571 which is 50% larger than the original number 285714

The simplest way is to write a small program. And the other way is trial and error !!!

3. An emergency vehicle travels 10 miles at a speed of 50 miles per hour. How fast must the vehicle travel on the return trip if the round-trip travel time is to be 20 minutes?

Answer :    75 miles per hour

While going to the destination, the vehicle travels 10 mils at the speed of 50 miles per hour. So the time taken to travel 10 miles is
= (60 * 10) / 50
= 12 minutes

Now it's given that round-trip travel time is 20 minutes. So the vehicle should complete its return trip of 10 miles in 8 minutes. So the speed of the vehicle must
= (60 * 10) / 8
= 75 miles per hour

4. At University of Probability, there are 375 freshmen, 293 sophomores, 187 juniors, & 126 seniors. One student will randomly be chosen to receive an award. What percent chance is there that it will be a junior? Round to the nearest whole percent.

Answer : 7

5. A mule and a donkey were carrying full sacks on their backs.

The mule started complaining that his load was too heavy. The donkey said to him "Why are you complaining? If you gave me one of your sacks I'd have double what you have and if I give you one of my sacks we'd have an even amount."

How many sacks were each of them carrying? Give the minimal possible answer

Answer :    The mule was carrying 5 sacks and the donkey was carrying 7 sacks.

Let's assume that the mule was carrying M sacks and the donkey was carrying D sacks.

As the donkey told the mule, "If you gave me one of your sacks I'd have double what you have."
D + 1 = 2 * (M-1)
D + 1 = 2M - 2
D = 2M - 3

The donkey also said, "If I give you one of my sacks we'd have an even amount."
D - 1 = M + 1
D = M + 2

Comparing both the equations,
2M - 3 = M + 2
M = 5

Substituting M=5 in any of above equation, we get D=7

Hence, the mule was carrying 5 sacks and the donkey was carrying 7 sacks.

6. Substitute digits for the letters to make the following relation true.

N E V E R

L E A V E

+ M E

-----------

A L O N E

Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be 3.

Answer :

Since R + E + E = 10 + E, it is clear that R + E = 10 and neither R nor E is equal to 0 or 5. This is the only entry point to

solve it. Now use trial-n-error method.

N E V E R 2 1 4 1 9

L E A V E 3 1 5 4 1

+ M E + 6 1

-------- --------

A L O N E 5 3 0 2 1

7. A man is stranded on a desert island. All he has to drink is a 20oz bottle of sprite.

To conserve his drink he decides that on the first day he will drink one oz and the refill the bottle back up with water. On the 2nd day he will drink 2oz and refill the bottle. On the 3rd day he will drink 3oz and so on...

By the time all the sprite is gone, how much water has he drunk?

Answer :  The man drunk 190oz of water.

It is given that the man has 20oz bottle of sprite. Also, he will drink 1oz on the first day and refill the bottle with water, will drink 2oz on the second day and refill the bottle, will drink 3oz on the third day and refill the bottle, and so on till 20th day. Thus at the end of 20 days, he must have drunk (1 + 2 + 3 + 4 + ..... +18 + 19 + 20) = 210oz of liquid.

Out of that 210oz, 20oz is the sprite which he had initially. Hence, he must have drunk 190oz of water

8. Karan bought a little box of midget matches, each one inch in length. He found that he could arrange them all in the form of a triangle whose area was just as many square inches as there were matches.

He then used up six of the matches, and found that with the remainder he could again construct another triangle whose area was just as many square inches as there were matches.

And using another six matches he could again do precisely the same. How many matches were there in the box originally? Note that the match-box can hold maximum of 50 matches.

Answer :

Initially, there were 42 or 36 matches in the match-box.

There are 42 matches in the box with which he could form a triangle 20, 15, 7, with an area of 42 square inches. After 6 matches had been used, the remaining 36 matches would form a triangle 17, 10, 9, with an area of 36 square inches. After using another 6 matches, the remaining 30 matches would form a triangle 13, 12, 5, with an area of 30 square inches. After using another 6, the 24 remaining would form a triangle 10, 8, 6, with an area of 24 square inches.

Thus, there are two possible answers. There were either 42 or 36 matches in the match-box.

9. There are 4 mugs placed upturned on the table. Each mug have the same number of marbles and a statement about the number of marbles in it. The statements are: Two or Three, One or Four, Three or One, One or Two. Only one of the statement is correct. How many marbles are there under each mug?

Answer :

As it is given that only one of the four statement is correct, the correct number can not appear in more than one statement. If it appears in more than one statement, then more than one statement will be correct.

Hence, there are 4 marbles under each mug.

10. Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.

Answer :

Assume that initial there were 3*X bullets.

So they got X bullets each after division.

All of them shot 4 bullets. So now they have (X - 4) bullets each.

But it is given that, after they shot 4 bullets each, total number of bullets remaining is equal to the bullets each had after division i.e. X

Therefore, the equation is
3 * (X - 4) = X
3 * X - 12 = X
2 * X = 12
X = 6

Therefore the total bullets before division is = 3 * X = 18