In this task, you need to provide the correct option for a given problem from the provided options.

Q: Problem: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30

A: d
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Q: Problem: the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 is ? 
Options: a ) 3 : 5 , b ) 2 : 7 , c ) 1 : 1 , d ) 1 : 4 , e ) none

A: c
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Q: Problem: the ratio of the incomes of uma and bala is 8 : 7 and the ratio of their expenditure is 7 : 6 . if at the end of the year , each saves $ 2000 then the income of uma is ? 
Options: a ) $ 16800 , b ) $ 16500 , c ) $ 16000 , d ) $ 16300 , e ) $ 16200

A:
c
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