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 many 5-digit numbers can be formed that have distinct digits and are multiples of 12?
2. All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?
3. All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will not contain any zero?
4. How many factors of 1080 are perfect squares?
Solutions to these questions can be found here.
- 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
- October 31, 2014 CAT Preparation Online – Permutation and Combination
Product of the distinct digits of a natural number is 60. How many such numbers are possible?
60 = 2^2 * 3 * 5
60 cannot be written as a product of […] Posted in Combinatorics
- 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
- April 22, 2011 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. […] Posted in Number Theory