Find value of M

@rengaraj-89Rrct • Oct 21, 2024

Oct 21, 2024

1.1K

Sir / Madam,
My questions is,

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

Advance Thanks,
R.Rengaraj
{InfosysTrain-Q109 Pg27}

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sherya mathur

@sherya-mathur-cI63wY • Apr 12, 2010

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

@rengaraj-89Rrct • Apr 13, 2010

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

@saandeep-sreerambatla-hWHU1M • Apr 14, 2010

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

@sherya-mathur-cI63wY • Apr 18, 2010

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