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33 votes
33 votes
Consider the equation $(123)_5=(x8)_y$ with $x$ and $y$ as unknown. The number of possible solutions is _____ .

3 Answers

Best answer
51 votes
51 votes
Converting both sides to decimal,

$25+10+3=x$*$y+8$

So, $xy=30$

Possible pairs are $(1,30),(2,15),(3,10)$ as the minimum base should be greater than $8.$
edited by
8 votes
8 votes

Changing (123) base 5 into base 10= 1*25+2*5+3*1=38 Changing x8 base y in decimal= x*y+8 Equating both we get xy+8=38

  • xy=30
  • possible combinations =(1,30),(2,15),(3,10)

but we have ‘8’ present in x8 so base y>8 as all three are satisfying the conditions so total solutions =3 hence ans is ( C) part

3 votes
3 votes
here the equation is x*y=30 so the possible values for x and y is (5,6) other values like (6,5) (3,10)(10,3) etc are not valid.
Answer:

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