Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
(a) 200 (b) 300 (c) 350 (4) 550
Tuesday, September 20, 2011
Monday, September 19, 2011
Problem of the Day 19 September 2011
Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 a.m. and 10 a.m., and stay for exactly 
mintues. The probability that either one arrives while the other is in the cafeteria is 
and 
where 
and 
are positive integers, and is not divisible by the square of any prime. Find 
mintues. The probability that either one arrives while the other is in the cafeteria is and where and are positive integers, and is not divisible by the square of any prime. Find Thursday, September 15, 2011
Problem of the day 15 sept 2011
Rachel and Brian are playing a game in a grid with 1 row of 2011 squares. Initially, there is one
white checker in each of the first two squares from the left, and one black checker in the third square
from the left. At each stage, Rachel can choose to either run or ght. If Rachel runs, she moves the
black checker 1 unit to the right, and Brian moves each of the white checkers one unit to the right. If
Rachel chooses to fight, she pushes the checker immediately to the left of the black checker 1 unit to
the left, the black checker is moved 1 unit to the right, and Brian places a new white checker in the
cell immediately to the left of the black one. The game ends when the black checker reaches the last
cell. How many diff erent final configurations are possible?
a) 2011 b) 2010 c) 2009 d) None
white checker in each of the first two squares from the left, and one black checker in the third square
from the left. At each stage, Rachel can choose to either run or ght. If Rachel runs, she moves the
black checker 1 unit to the right, and Brian moves each of the white checkers one unit to the right. If
Rachel chooses to fight, she pushes the checker immediately to the left of the black checker 1 unit to
the left, the black checker is moved 1 unit to the right, and Brian places a new white checker in the
cell immediately to the left of the black one. The game ends when the black checker reaches the last
cell. How many diff erent final configurations are possible?
a) 2011 b) 2010 c) 2009 d) None
Wednesday, September 14, 2011
Problem of the day 14 Sep 2011
3 men -A,B and C played a Dart game.
1.Each of the dart lodged in the game board scored 1,5,10,25,50, or 100 points.
2.Each man threw 9 darts that lodged in the board.
3.Each man's total score was the same as any other man's total score.
4.No number of points scored by a dart was scored by more than 1 man.
5.A scored all the 5s and B scored all the 10s.
Who scored all the 100's?
1) A 2) B 3) C 4) Cannot be determined
1.Each of the dart lodged in the game board scored 1,5,10,25,50, or 100 points.
2.Each man threw 9 darts that lodged in the board.
3.Each man's total score was the same as any other man's total score.
4.No number of points scored by a dart was scored by more than 1 man.
5.A scored all the 5s and B scored all the 10s.
Who scored all the 100's?
1) A 2) B 3) C 4) Cannot be determined
Tuesday, September 13, 2011
Problem of the Day 13 Sept 2011
Let X be the set of three digit prime numbers with the following properties:
1) Each digit of the elements of X are distinct.
2) Each digit of the elements of X are prime.
Let K be the sum of all the elements of X. Find the sum of the digits of K?
Tips: Tournament Problems
Tournament Problems
There are 16 teams and they are divided into 2 pools of 8 each. Each team in a group plays against one another on a round-robin basis. Draws in the competition are not allowed. The top four teams from each group will qualify for the next round i.e round 2. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead.
1. Minimum number of wins required to qualify for the next round _____?
2. Minimum number of wins required to guarantee qualification in the next round _____?
Now, i don't know how many of you are aware of the following method. But 1 thing I mention in advance that this should take only 30 seconds to solve
1.
1 group is consisting of 8 teams. So each team will play 7 match each. Suppose each of the 8 teams were seeded and we consider the case where a higher seeded team will always win.
So the number of wins for the 8 teams would be 7,6,5,4,3,2,1,0 with highest seeded team winning all and lowest seeded team losing all.
For minimum number of wins we allow 3 teams to win maximum number of matches. Of the remaining 5 teams just find out the mean of their number of wins.
In this case it would be (4+3+2+1+0)/5=2.
So 5 teams can end up with 2 wins each and a team with better run rate will qualify with 2 wins.
2.
In this case consider the mean of first 5 higher seeded teams (7+6+5+4+3)/5=5
So it may be the case that 5 teams can end up having 5 wins each. And hence 1 team will miss the second round birth. So minimum number of wins to guarantee a place would be 6.
The trick is to consider wording, qualify means best case scenario while guarantee qualify means worst case scenario.
There are 16 teams and they are divided into 2 pools of 8 each. Each team in a group plays against one another on a round-robin basis. Draws in the competition are not allowed. The top four teams from each group will qualify for the next round i.e round 2. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead.
1. Minimum number of wins required to qualify for the next round _____?
2. Minimum number of wins required to guarantee qualification in the next round _____?
Now, i don't know how many of you are aware of the following method. But 1 thing I mention in advance that this should take only 30 seconds to solve
1.
1 group is consisting of 8 teams. So each team will play 7 match each. Suppose each of the 8 teams were seeded and we consider the case where a higher seeded team will always win.
So the number of wins for the 8 teams would be 7,6,5,4,3,2,1,0 with highest seeded team winning all and lowest seeded team losing all.
For minimum number of wins we allow 3 teams to win maximum number of matches. Of the remaining 5 teams just find out the mean of their number of wins.
In this case it would be (4+3+2+1+0)/5=2.
So 5 teams can end up with 2 wins each and a team with better run rate will qualify with 2 wins.
2.
In this case consider the mean of first 5 higher seeded teams (7+6+5+4+3)/5=5
So it may be the case that 5 teams can end up having 5 wins each. And hence 1 team will miss the second round birth. So minimum number of wins to guarantee a place would be 6.
The trick is to consider wording, qualify means best case scenario while guarantee qualify means worst case scenario.
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