In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Q: Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 15 times as heavy as water ? 
Options: a ) 3 : 2 , b ) 3 : 8 , c ) 5 : 7 , d ) 3 : 7 , e ) 3 : 6

A: a
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Q: Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of b - a ? 
Options: a ) - 10 , b ) 10 , c ) - 19 , d ) 20 , e ) 21

A: a
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Q: Problem: in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 3 ohms and y is 5 ohms ? 
Options: a ) 15 / 8 , b ) 3 / 8 , c ) 5 / 8 , d ) 7 / 15 , e ) 8 / 15

A:
a
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