is the answer of 1st question is 54 ?
--- On Fri, 3/6/11, Rajesh Balasubramanian <rajesh@...> wrote:
From: Rajesh Balasubramanian <rajesh@...>
Subject: [2IIM CAT Prep] Few Questions on Number Theory and Counting (combined)
Date: Friday, 3 June, 2011, 8:02 AM
CAT has been consistently asking questions combining basic number theory and counting. So, it is probably good practice to have a go at these. As always, the questions can also be found at our blog http://iimcat.blogspot.com/2011/06/few-questions-on-number-theory-and.html
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?
CAT 2011 Weekend batches starting @ Chennai, June 3rd @ Anna Nagar, June 4th@ Velachery