GATE 2015 CS (CS3) – Question 59
For unknown number bases x and y, (43)ₓ=(y3)₈. How many integer solutions (x,y) are possible?
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Correct answer: 5
Explanation
Converting both sides to decimal gives 4x+3=8y+3, hence x=2y. A valid base x must exceed the largest digit four, so x≥5. The octal digit y lies between one and seven. Therefore y can be three,four,five,six,seven, giving x=6,8,10,12,14. There are five solutions.