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'.

Problem: a large field of 900 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 435 hectares . , b ) 425 hectares . , c ) 445 hectares . , d ) 415 hectares . , e ) 405 hectares .
e

Problem: the mean of 40 observations was 100 . it was found later that an observation 50 was wrongly taken as 75 the corrected new mean is
Options: a ) 125.8 , b ) 102.8 , c ) 99.375 , d ) 100.52 , e ) 122
c

Problem: how many different values of positive integer x , for which | x + 7 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
b