number system

Question

consider the number:

   5324+2342=(7666) of base r

what is the value of r:

a.8

b.10

c.16

d.>=8

Comments

by using hit and trial no any option is correct.

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Actually, I correct the question. Now check it.

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Radix 8 works now.

Answer 1

Let's check one by one option,

${\color{Blue} {(a)}}$   r=8,when we add LSB bits of both (4+4=8) should be zero and one carry but at RHS, LSB bit is 6 .so option a is wrong.

${\color{blue}{(b)}}$   r=10,it is simply when we add LSB bits of both then answer should be 8 but at RHS, LSB bit is 6 so option B is also wrong.

${\color{blue}{(c)}}$. r=16,in this also when we will add LSB bits then LSB bit will be 8,same reason as above option ,,so this is also wrong.

${\color{blue}{(D)}}$,  when at r=8,10,16 is not satisfied then r>=8 is also false (only one condition is enough to make false)

So none of these option is true.

Answer 2

r must be greater than 7

(5324)base r +(2324) base r=(7666) base r

(5*r^3+3*r^2+2*r+4)+(2*r^3+3*r^2+2*r+4)=(7*r^3+6*r^2+6r+6)

2r=2

r=1(rejected)

hence no value of r for which it is satisfied

Answer 3

I am not getting whats wrong with u people

Its direct base 10  ..