instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
Problem: at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 5 : 5 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ? 
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 2 , e ) 1
answer:
d


question:
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 19 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ? 
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 10 , e ) 29 / 100
answer:
e


question:
Problem: in a class of 210 students , 70 did not opt for math . 55 did not opt for science and 42 did not opt for either . how many students of the class opted for both math and science ? 
Options: a ) 123 , b ) 125 , c ) 127 , d ) 137 , e ) 148
answer:

c