UPPCL AE 2018:82

Question

If $703_{x}$ (in base-$x$ number system) equals $504_{y}$ (in base-$y$ number system), then possible values of $x, y$ are:

• A. $17, 18$
• B. None of these
• C. $8, 11$
• D. $12, 13$

Answer 1

$x^{0}*3+x^{1}*0+x^{2}*7=y^{0}*4+y^{1}*0+y^{2}*5 \\ 3+7x^{2}=4+5y^{2}\\ 7x^{2}=5y^{2}+1$
Now put x,y values in the equation

None of the option satisfies the above condition

Comments

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I will take care next time