Have given below a few questions on Counting that also include a bit of Number Theory. These types of questions are commonly tested.
1. a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)
2. A seven-digit number comprises of only 2’s and 3’s. How many of these are multiples of 12?
3. How many factors of 2^5 * 3^6 * 5^2 are perfect squares?
4. How many factors of 2^4 * 5^3 * 7^4 are odd numbers?
5. A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?
- August 21, 2011 Solutions to questions on permutations and combinations Have given below solutions to the questions on permutations and combinations
1. a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. […] 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
- May 23, 2013 CAT Counting: Question with digits
This is an interesting question from Counting. Simple framework, but one needs to be very careful with the enumeration. One can get wrong answers in a number of […] Posted in Combinatorics
- November 11, 2010 Number Theory questions – LCM HCF Few more questions on LCM and HCF on Number Theory
1. How many pairs of integers (x,y) exist such that the product of x, y and HCF (x,y) = 1080?
2. Find the smallest number that […] Posted in Number Theory