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## Few Questions on Number Theory and Counting (combined)

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• HI all, 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
Message 1 of 2 , Jun 2, 2011
HI all,

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?

Cheers,
Rajesh
99626 48484
CAT 2011 Weekend batches starting @ Chennai, June 3rd @ Anna Nagar, June 4th@ Velachery
• Sir,  is the answer of 1st question is  54 ? --- On Fri, 3/6/11, Rajesh Balasubramanian wrote: From: Rajesh Balasubramanian
Message 2 of 2 , Jun 2, 2011
 Sir,  is the answer of 1st question is  54 ? --- On Fri, 3/6/11, Rajesh Balasubramanian wrote:From: Rajesh Balasubramanian Subject: [2IIM CAT Prep] Few Questions on Number Theory and Counting (combined)To: ascent4cat@yahoogroups.comDate: Friday, 3 June, 2011, 8:02 AM HI all, 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? Cheers,Rajesh99626 48484CAT 2011 Weekend batches starting @ Chennai, June 3rd @ Anna Nagar, June 4th@ Velachery
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