Saturday 2 February 2013

Analytical Questions

Analytical Questions:

1.Why is a manhole cover round?

2. If you had an infinite supply of water and a 5 quart and 3 quart pail, how would you
measure exactly 4 quarts?

3. You have 5 jars of pills. Each pill weighs 10 gram, except for contaminated pills
contained in one jar, where each pill weighs 9 gm. Given a scale, how could you tell
which jar had the contaminated pills in just one measurement?

4. If you are on a boat and you throw out a suitcase, will the level of water increase or
decrease?

5. How many times a day a clock's hands overlap?

6. One train leaves Los Angeles at 15mph heading for New York. Another train leaves
from New York at 20mph heading for Los Angeles on the same track. If a bird, flying
at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth
between the two trains until they collide, how far will the bird have traveled?

7. There are 3 ants at 3 corners of a triangle; they randomly start moving towards another
corner. What is the probability that they don't collide?

8. If you look at a clock and the time is 3:15, what is the angle between the hour and the
minute hands? (The answer to this is not zero!)

9. How would you weigh a plane without using scales

10. Why are beer cans tapered at the top and bottom?

11.You have 8 balls. One of them is defective and weighs less than others. You have
a balance to measure balls against each other. In 2 weightings how do you find the
defective one?

12. There are 3 baskets. One of them have apples, one has oranges only and the other has
mixture of apples and oranges. The labels on their baskets always lie. (i.e. if the label
says oranges, you are sure that it doesn’t have oranges only, it could be a mixture) The
task is to pick one basket and pick only one fruit from it and then correctly label all the
three baskets.

13. Given a rectangular (cubical for the puritans) cake with a rectangular piece removed (any
size or orientation), how would you cut the remainder of the cake into two equal halves
with one straight cut of a knife?

14. If you have two buckets, one with red paint and the other with blue paint, and you take
one cup from the blue bucket and poor it into the red bucket. Then you take one cup
from the red bucket and poor it into the blue bucket. Which bucket has the highest ratio
between red and blue? Prove it mathematically.

15. You have a bucket of jelly beans. Some are red, some are blue, and some green. With
your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you
have 2 of the same?

16. You are given a scale which you are to use to measure eight balls. Seven of these balls
have the same weight: the eight ball is heavier than the rest. What is the minimum
number of weighs you could perform to find the heaviest of the eight balls?

17. Pairs of primes separated by a single number are called prime pairs. Examples are 17 and
19. Prove that the number between a prime pair is always divisible by 6 (assuming both
numbers in the pair are greater than 6). Now prove that there are no 'prime triples.'

18. There is a room with a door (closed) and three light bulbs. Outside the room there are
three switches, connected to the bulbs. You may manipulate the switches as you wish, but
once you open the door you can't change them. Identify each switch with its bulb.

19. There are 4 women who want to cross a bridge. They all begin on the same side. You
have 17 minutes to get all of them across to the other side. It is night. There is one
flashlight. A maximum of two people can cross at one time. Any party, who crosses,either 1 or 2 people, must have the flashlight with them. The flashlight must be walked
back and forth; it cannot be thrown, etc. Each woman walks at a different speed. A pair
must walk together at the rate of the slower woman's pace.

Woman 1: 1 minute to cross
Woman 2: 2 minutes to cross
Woman 3: 5 minutes to cross
Woman 4: 10 minutes to cross

For example: if Woman 1 and Woman 4 walk across first, 10 minutes have elapsed When they get to the other side of the bridge. If Woman 4 then returns with the flashlight,
a total of 20 minutes have passed and you have failed the mission. What is the order
required to get all women across in 17 minutes? Now, what's the other way?

No comments:

Post a Comment