CAT Number Theory

1. The six faces of a cube have 6 distinct natural numbers written on them. Each vertex of a cube is assigned a number that is the product of the three faces passing through the vertex. The sum of all the numbers assigned to the vertices is equal to 385. What is the sum of the numbers written on the 6 faces of the cube?

 

2. Six men engaged in a game. Whenever a player won a game he doubled the money of each of the players. That is, he gave each player as much money as he/she originally had in his/her pocket. They played six games and each player won one game. In the end all of them had Rs. 256 each. What was the difference between the money the person with the highest amount had and the person with the smallest amount had to start off with?

 

3. X and y are two distinct natural numbers such that x, y range from 1 to 15 (both inclusive). If the probability that x/y is a terminating decimal is n/420, what is the value of n?

 

4. How many positive integers exist such that they divide 1011 but not 10 10?

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