ISRO2008-20

Question

If $(12x)_3 = (123)_x$, then the value of $x$ is

• A. $3$
• B. $3$ or $4$
• C. $2$
• D. None of these

Comments

Base x uses digits 1,2,3.

=> Base is at least 4. Which directly eliminates Options A, B and C.

Answer 1

we know radix>digit

so  in lhs 3>x

and in rhs x>3

there is no such number exist which satisfies the conditions

D is the ans

Comments

Very correct.

Answer 2

x+2*3+1*3^2=3+2*x+1*x^2

=>x+6+9 =3+2x+x^2

=>x^2+2x-x+3-15=0

=>x^2+x-12=0

=>(x+4)(x-3)=0

x-3=0; x=3

x+4=0;x=-4

so option should be A

Comments

for example if we take any number in decimal no system(where base is 10) we can use only 0,1,2,3,4,5,6,7,8,9  ...it is like 123,123459,45699 etc we can never use 10 as a digit in decimal number system.so as like that in  number system is of base 3 and we can use only 0,1,2 as digit for number representation. thats why option A is wrong.

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Got it ...Thanks buddy

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@pinku ur eq are wrong