instruction:
In this task, you need to provide the correct option for a given problem from the provided options.
question:
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is 
Options: a ) 276 , b ) 299 , c ) 312 , d ) 322 , e ) none
answer:
d


question:
Problem: there are two positive numbers in the ratio 3 : 11 . if the larger number exceeds the smaller by 32 , then what is the smaller number ? 
Options: a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 17
answer:
c


question:
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 16 th highest price and the 23 rd lowest price among the prices of the items sold , how many items were sold at the garage sale ? 
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
answer:

d