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# Ambigiuous Question

Hi all,

Recently I came across this question.

33/11=3 is true in which base?

a)10 b)2 c)both d)none

The answer given to this was both which is satisfactory when we use the equation which relates the number with place values and coefficients. But then can base 2 have '3' as its symbol? and even if it has, would the arithmatic be the same and valid as in base 2. First of all can 3 be a part of binary system as a symbol.

What are your views on this?

Recently I came across this question.

33/11=3 is true in which base?

a)10 b)2 c)both d)none

The answer given to this was both which is satisfactory when we use the equation which relates the number with place values and coefficients. But then can base 2 have '3' as its symbol? and even if it has, would the arithmatic be the same and valid as in base 2. First of all can 3 be a part of binary system as a symbol.

What are your views on this?

(C) is the correct answer.

Explanation:

33 in binary code is 100001

11 in binary code is 1011

Let's perform the division of 100001 by 1011

..........________

1011 ) 100001 ( 11

.............1011

...........______

.............01011

...............1011

...........______

...............0000

Here we get quotient as 11 which is 3 in decimal and 0000 as the remainder.

So 33 / 11 = 3 both in decimal and binary.

Explanation:

33 in binary code is 100001

11 in binary code is 1011

Let's perform the division of 100001 by 1011

**Binary Division:**..........________

1011 ) 100001 ( 11

.............1011

...........______

.............01011

...............1011

...........______

...............0000

Here we get quotient as 11 which is 3 in decimal and 0000 as the remainder.

So 33 / 11 = 3 both in decimal and binary.

I don't think 3 can be part of binary system, it can be represented in binary code.simplycoderBut then can base 2 have '3' as its symbol? and even if it has, would the arithmatic be the same and valid as in base 2. First of all can 3 be a part of binary system as a symbol.

What are your views on this?

33/11 is 3 in any number system, if we convert them to that system first.

33 in base 5 is 113, and

11 in base 5 is 21

115/21 in base 5 will be

So, regardless of what base we use, it will always hold true. But the question does not ask that, I think. If anything, it might be a mistake and the choice should have been some other number instead of 2.. like 6 or 7, for example. In that case, we should convert both 33 and 11 to the appropriate base and see if it is indeed correct.

33 in base 5 is 113, and

11 in base 5 is 21

115/21 in base 5 will be

_____

21) 113 ( 3113

_____

0

So, regardless of what base we use, it will always hold true. But the question does not ask that, I think. If anything, it might be a mistake and the choice should have been some other number instead of 2.. like 6 or 7, for example. In that case, we should convert both 33 and 11 to the appropriate base and see if it is indeed correct.