Find value of M

Replies

• 

  sherya mathur

  Q.A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals?
  ans:
  I think the m equals to 91
  am I right?
• 

  rengaraj

  i am not sure of answer but can you give me the working ?
  R.Rengaraj
• 

  Saandeep Sreerambatla

  Generally if we talk about the base systems 2 ,3 and 5 here. The provided condition is the last digit is 1.
  So it is sure that the last digit of the original number will be 1 and the number when divided by 2 ,3 and 5 will leave a reminder 1.
  So the list of numbers satisfying this criteria are.
  31 ,61 and 91 and 1 too. SInce given the number is less than 100.
  One more condition is the leading digit is also 1 in that case 1 is ruled out , now lets look for other numbers.
  
  31 in base 5 system = (111)[sub]5[/sub]
  31 in base 3 = (1011)[sub]3[/sub]
  
  In base 2 system all the numbers are represented as 0's or 1's so 31 is not the right choice.
  
  Next we have 91, in base 2 it will be represented in 0's and 1's with 1 as a leading digit so we need to check for base 3 and base 5.
  
  In base 3 system = 91 is represented as (10101)[sub]3[/sub]
  In base 5 system = 91 is represented as (331)[sub]5[/sub]
  
  So in this case only 2 out of 3 cases 1 is the leading digit , so 91 is the answer.
  
  To get the base system value of any number Synthesize that number with the base number of your need.
  
  I hope this answer is fine.
• 

  sherya mathur

  English-Scared

  Generally if we talk about the base systems 2 ,3 and 5 here. The provided condition is the last digit is 1.
  So it is sure that the last digit of the original number will be 1 and the number when divided by 2 ,3 and 5 will leave a reminder 1.
  So the list of numbers satisfying this criteria are.
  31 ,61 and 91 and 1 too. SInce given the number is less than 100.
  One more condition is the leading digit is also 1 in that case 1 is ruled out , now lets look for other numbers.
  
  31 in base 5 system = (111)[sub]5[/sub]
  31 in base 3 = (1011)[sub]3[/sub]
  
  In base 2 system all the numbers are represented as 0's or 1's so 31 is not the right choice.
  
  Next we have 91, in base 2 it will be represented in 0's and 1's with 1 as a leading digit so we need to check for base 3 and base 5.
  
  In base 3 system = 91 is represented as (10101)[sub]3[/sub]
  In base 5 system = 91 is represented as (331)[sub]5[/sub]
  
  So in this case only 2 out of 3 cases 1 is the leading digit , so 91 is the answer.
  
  To get the base system value of any number Synthesize that number with the base number of your need.
  
  I hope this answer is fine.

  thanks for explaining the answer in such a great way
  I hope now it will be undrstood for all