New Batches at TathaGat Delhi & Noida!               Directions to CP centre
some questions of number system
by somarani patnaik - Tuesday, 13 October 2009, 11:30 AM
 

hello everyone..i've some doubts regarding the following questions..

1--M is a two digit number which has the property tht:the product of factorials of it's digits>sum of factorials of its digits

how many values of M exist?

2--how mnay two-digit numbers less than or equal to 50 have the product of the factorials of their digits less than or equal to the sum of the factorials of their digits?

3--define K such that it is the sum of the squares of the first M natural numbers(ie,k=1^2+2^2+3^2+.....M^2)where M<55.How many values of M exist such that k is divisble by 4?

Re: some questions of number system
by WitHouT FiLTeR - Tuesday, 13 October 2009, 01:39 PM
  1) The cases where "sum of factorials of its digits">"the product of factorials of it's digits" are 10,12,13,14,15,16,17,18,19,20,21,30,31,40,41,50,51,60,61,70,71,80,81,90,91.

Rest other cases will satisfy the condition as given in the question.smile
Re: some questions of number system
by WitHouT FiLTeR - Tuesday, 13 October 2009, 01:55 PM
  3) If u observe then all the squares of odd numbers are type of 4K + 1. So for the given series the no's will be like

2^2,4^2,6^2,7^2 (4th odd no),8^2, 10^2,12^2,14^2,15^2 (4th odd no)...like that it will be upto 55...

Total no will be 54/2 + 54 mod 8= 27+6=33
Re: some questions of number system
by somarani patnaik - Tuesday, 13 October 2009, 10:11 PM
  hey thanks for ur reply.bt u dint find it for divisibility by 4
Re: some questions of number system
by WitHouT FiLTeR - Tuesday, 13 October 2009, 11:33 PM
    3) If u observe then all the squares of odd numbers are type of 4N + 1. So for the given series the no's will be like

2^2,4^2,6^2,7^2 (4th odd no),8^2, 10^2,12^2,14^2,15^2 (4th odd no)...like that it will be upto 55...

In that I wanted to explain that the 1st number which will be divisible by 4 is
=1^2+2^2+3^2....7^2
as all the even squares will be divisible by 4 so we need to take the sum upto 7^2.

The next will be
=1^2+2^2+3^2......15^2

Like that the total no of possible K can be 54 mod 8=6

Let me know whether I am able to make u understand or not.
Re: some questions of number system
by somarani patnaik - Wednesday, 14 October 2009, 10:50 AM
  thanks a lot.i understood the concept.this question i got frm arun sharma book.the answer they have given is 12
Re: some questions of number system
by hsvsguptha p polisetty - Friday, 12 February 2016, 01:18 PM
  where is 22? 22 also doesnt satisfy the condition