There are two boxes, one containing 32 red balls and the other containing 31 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is

A man has some socks in his drawer: 14 identical blue, 20 identical red, and 28 identical black. The lights are out and it is totally dark. How many socks must he take out to make sure he has a pair of each colour?

A cyclist buys a cycle for 29 pounds paying with a 50 pound cheque. The seller changes the cheque next door and gives the cyclist change. The cheque bounces so the seller paid his neighbor back. The cycle cost the seller 12 pounds. How much did the seller lose?

The original price of a car was $23600. Because the car owner thought he could get more money for the car, he increased the price of the car to 160% of its original price. After a week, the car had not sold, so the owner then discounted the price by 20%, the car was finally sold. What price was the car sold for?

The chairman of Tata Motors, Ratan Tata, had 300 engineers work for 5 years designing the world's lowest-cost car, convinced that cost-conscious Indian drivers could live without air-conditioning and cup holders. However, after the booking started they found that only 23 percent of initial 253850 orders for the car - the Nano - were for the no frills $2600 model. How much time (in days) would it have taken if there were 500 employees working for double the time?

Earl can stuff advertising circulars into envelops at the rate of 36 envelopes per minute and Ellen requires a minute and a half to stuff the same number of envelopes. Working together, how long will it take Earl and Ellen to stuff 360 envelopes?

In 1911, a French physicist Paul Langevin, devised a thought experiment based on Einstien's Special Relativity. In the experiment, a person makes a journey into space at nearly the speed of light and comes back to earth. He finds that he has aged five times less than his twin who stayed back on earth for 40 years. This is popularly known as the Twin Paradox. Now, consider the case of Hansel and Gretel, who are not twins. 9 years ago, Hansel was twice as old as Gretel. If they journey into space, an atomic clock assists in logging the start time of their journey accurately. If they do not journey into space, 9 years hence, Hansel's age will be 4/3 times the age of Greters. Find Hansel's age today in binary numbers.

Recent reports have suggested that sportsmen with decreased metabolic rates perform better in certain sports. After reading one such report, Jordan, a sportsperson from Arlington decides to undergo a rigorous physical training program for 3 months, where he performs Yoga for 3 hours, walks for 2 hours and swims for 1 hour each day. He says: I began my training on a Wednesday in a prime number month of 2008. I lost 1% of my original weight within the first 30 days. In the next two months combined, I lost 1 Kg. If he walks at 5 mph over a certain journey and walks back over the same route at 7 mph at an altitude of 200 meters, what is his average speed for the journey?

Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is

Alok and Bhanu play the following min-max game. Given the expression N=46+X+Y-Z, where X,Y and Z are variables representing single digits (0 to 9) Alok woul like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitues this for a variable of her choice (X, Y or Z) Alok then chooses the next value and Bhanu the Variab le to substitute the value. Finallyu Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies the value of N at the end of the game would be

The number of bacteria in a colony was growing exponentially. At 4 pm yesterday the number of bacteria was 400 and at 6 pm yesterday it was 3600. How many bacteria were there in the colony at 7 pm yesterday?

A multiple choice question has 4 options. Choosing the correct option earns the student 3 marks. However choosing the wrong option incurs negative marks so that if a student chooses an option randomly, his expected score is 0. Suppose a student has successfully eliminated 2 incorrect options. His expected score if he chooses randomly among the remaining options is.

On the planet Oz, there are 8 days in a week - Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 minutes while each minute has 60 seconds. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 12:40 am.

You're going to get grounded for a week if you don't get at least 80% in your science class. So far you have 237 of the total 300 points. The final test is worth 100 points. What is the minimum score you need to get on the final test? Assume the teacher rounds properly.

Middle earth is fictional land inhabited by hobbits elves dwarves and men. The hobbits and the elves are peaceful creatures who prefer slow silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournoi is one where out of the two teams that play a match the one that loses get eliminated the matches are played in different rounds where in every round; half of the teams get eliminated from the tournament. If there are 6 rounds played in a knock out tournoi how many matches were played?

Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (for some i between 0 and 100). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2- move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coin is the third coin from the top. Then

The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate. Suppose 14 such programmers = take 14 minutes to write 14 lines of code in total. How long will in take 5 programmers to write 5 lines of code in total ?

Achilles was the son of the nymph Thetis and Peleus, the king of the Myrmidons. Zeus and Poseidon had been rivals for the hand of Thetis until Prometheus, the fire-bringer, warned Zeus of a prophecy that Thetis would bear a son greater than his father. For this reason, the two gods withdrew their pursuit, and had her wed Peleus. The following statement is another interesting prophecy about the ages of two childen of Zeus that would hold true at some time during the lifetime of the children. 4 years ago, Athena's age was twice Helen's age. 4 years hence, Athena's age will be 4/3 times the age of Helen. Find Athena's present age in binary numbers during the time that the statement holds true.

36 people (a1, a2, ……, a36) meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, (a1, a2), (a2, a3),………., (a35, a36), (a36, a1). Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

Let exp(m,n) = m to the power n. If exp(10, m) = n exp(2, 2) where to and n are integers then n = ………………?