Asurvey of 392 children given at a local elementary school showed that 175 like chocolate ice cream 200 like pistachio ice cream, and 142 do not like chocolate or pistachio ice cream. how many children like at most one kind of ice cream mentioned in the survey?

Assuming that the students were not asked about any other type of ice cream, there are 392 students and 142 do not like either of ther flavors. That means that there are 392-142=250 students who like one or both of the flavors listed.

However, when we add the number for chocolate (175) to the number for pistachio (200) we get 375. Since there are only 250 students that like the ice cream it must mean that there are some students who like both chocolate and pistachio. 

Specifically there are 375-250=125 students who like both flavors of ice cream. That leaves 250-125 = 125 students who like one or the other but not both.

There are 125 students who like one flavor and 142 who like no flavors so 125 + 142 = 267 who like at most one flavor (0 or 1).