instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ? 
Options: a ) 424 . , b ) 428 . , c ) 430 . , d ) 432 . , e ) 436
answer:
d


question:
Problem: 20 balls are numbered 1 to 20 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ? 
Options: a ) 7 / 30 , b ) 3 / 14 , c ) 9 / 38 , d ) 4 / 21 , e ) 5 / 26
answer:
c


question:
Problem: the ratio of the number of females to males at a party was 1 : 2 but when 7 females and 7 males left , the ratio became 1 : 3 . how many people were at the party originally ? 
Options: a ) 28 , b ) 32 , c ) 36 , d ) 42 , e ) 50
answer:

d