ATHENA FIRST ROUND

60 MINS

10 QUESTIONS

1) A pie is to be divided among 20 people. A man eats 3 pieces, a woman eats 2 pieces and a child eats ½ a piece of pie. What is the number of men, women children, so that 20 people in total and everyone get the same pie? There are 20 pieces of pie in all

2) Two planes take off at the same exact moment. They are flying across the Atlantic. One leaves New York and is flying to Paris at 500 miles per hour. The other leaves Paris and is flying to New York at only 450 miles per hour ( because of a strong head wind ). Which one will be closer to Paris when they meet?

3) Joey leaves his house in the morning to go to day camp.Just as he is leaving his house he looks at an analog clock reflected in the mirror. There are no numbers on the clock, so Joey makes an error in reading the time since it is a mirror image. Joey assumes there is something wrong with the clock and rides his bike to day camp. He gets there in 20 minutes and finds that just as he gets there the day camp clock has a time that is 2 1/2 hours (2 hours and 30 minutes) later than the time that he saw in the mirror image of his clock at home. What time was it when he got to day camp? The clock at camp and the clock at home were both set to the correct time.)

5) While house hunting in London, i came across a very good leasehold property Discussing the lease the landlady told me: 'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out yourself and see how many years are there to go!'

6) What is the smallest positive integer that leaves a remainder of 1 when divided by 2, remainder of 2 when divided by 3, a remainder of 3 when divided by 4, … and a remainder of 9 when divided by 10?

7) There r 1000 lockers and 1000 students in a school. the principal asks the 1st student to go to every locker and open it. then he has the 2nd student go to every 2nd locker and close it. the 3rd goes to every 3rd locker and, if it is closed he opens it, and if it is open, he closes it. the fourth student does this to every fourth locker and so on. the process is completed with the 1000th student. How many lockers are open?

8) Mr. Black, Mr. White and Mr. Grey were chatting in the Yahoo conference. They were wearing a black suit, a white suit and a grey suit, not necessarily in the same order. Mr. Grey sent message, "We all are wearing suit that are of the same color as our names but none of us is wearing a suit that is the same color as his name." On that a person wearing the white suit replied, "What difference does that make?" Can you tell what color suit each of the three persons had on?

10)There are five doors, one leads to the exit, the others lead to traps. They are in a line. The clues tell you which position the doors are in the line and where the door to freedom is. All the clues are true. Each door has a clue written on it. The clues read:

The blue door: This door is two spots away from the door to freedom.The red door: This door is at the far right, and is two spots away from the blue door.The purple door: This door is not next to the door to freedom.The green door: This door is left of the blue door.The orange door: This door is not next to the red or blue doors.

Which door leads to freedom?