Algebra
Aptitude

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Q.

A number of three digits in base 7, when expressed in base 9, has its digits reversed in the order. What is the sum of the digits of the number?

 A.

5

 B.

6

 C.

7

 D.

8

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Solution:
Option(D) is correct

Only (0,1,2,3,4,5,6) can be the digits as base 7.

\((pqr)_7=(rqp)_9\)

\(\Rightarrow 7^2p+7^1q+7^0r =9^2r+9^1q+9^0p\)

\(\Rightarrow 49p+7q+r=81r+9q+p\)

\(\Rightarrow 48p=80r+2q\)

\(\Rightarrow 24p=40r+q\)

After hit and trial,the number:

\(pqr=(503)_7=(305)_9\)

$\Rightarrow$  248 in the decimal system.


(1) Comment(s)


Salman
 ()

any approach without hit and trial.