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?
- December 10, 2010 Percentages – Solutions Have given below solutions to the first three questions on Percentages
1. a is x % of b, b is x% more than a. Find x?
a = bx,
b = a (1+x), substituting this in the previous […] Posted in Percentages
- November 23, 2016 CAT Online Coaching – Partial Fractions We get a lot of questions on partial fractions, on how to simplify them and how to solve questions that involve a summation of a series of fractional terms. In this post, I will solve 3 […] Posted in Number Theory
- June 3, 2011 Few Questions on Number Theory and Counting (combined) CAT has been consistently asking questions combining basic number theory and counting. So, it is probably good practice to have a go at these.
1. From the digits 2,3,4,5,6 and 7, how […] Posted in Combinatorics
- June 4, 2011 Solutions to Number Theory and Counting questions Given below are the solutions to these Number theory questions.
1. From the digits 2,3,4,5,6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of […] Posted in Combinatorics