why (5,6) and (6,5) are not the possible pair n why ? the minimum base should be greater than 8 ? can someone expain ?

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+17 votes

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

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why (5,6) and (6,5) are not the possible pair n why ? the minimum base should be greater than 8 ? can someone expain ?

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the minimum base should be greater than 8 ? can someone expain ? n why (5,6) (6,5) are not possible pairs

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@priyanka gautam 1

here (x8)y means** y>8 **means from 9 onwards..

also** x<y**

therefore,(5,6) is not possible because y is not >8

and (6,5) is not possible because x is not <y...

+28 votes

Best answer

+6 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

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