“We- Aaron, Brian, and Clyde- each have some children.
[1] Aaron has at least one girl and twice as many boys as girls.
[2] Brian has at least one girl and three times as many boys as girls.
[3] Clyde has at least one girl and three more boys than girls.
[4] When I tell you the number of children we have altogether- a number less than 25- you will know how many children I have, but not how many children each of the others has. Altogether we have…”
Starting with the 2 in the centre, the number 2005 can be formed by moving from circle to circle only if the two circles are touching. How many different paths can be followed to form 2005?
How many integer solutions (x, y) are there for the equation (x – 5)(x – 23) = 3y?
a) 0
b) 1
c) 2
d) 3
e) More than 3
A king wanted to marry off his daughter. Many suitors wanted to marry the princess. So, the king devised a competition to find the most worthy of them all. He put 27 identical looking diamonds in a box. He then announced that one of the 27 diamonds was a fake. The fake diamond was identical to the other diamonds in all respects except that it had a slightly different weight. The challenge was to find the fake diamond using only a simple pan balance. What is the minimum number of weighings required to find the fake? Provide a detailed explanation with your answer.
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?
A. 5
B. 20
C. 25
D. 36
E. 30
Find positive integral solutions for the equation: a! + b! + c! = 3d, where a ≤ b ≤ c.
Mr. and Mrs. Aye and Mr. and Mrs. Bee competed in a chess tournament. Of the three games played:
[1]In only the first game were the two players married to each other.
[2]The men won two games and the women won one game.
[3]The Ayes won more games than the Bees.
[4]Anyone who lost game did not play the subsequent game.
Who did not lose a game?
The number of positive integer valued pairs (x,y) satisfying 13x – 5y = 14 and x ≤ 500 is
A. 50
B. 100
C. 200
D. More than 300
