Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 150 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from  Choose the correct choice from the following answers:
A) 30 to 70
B) 70 to 100
C) 110 to 130
D) 130 to 150
E) 150 to 170
if there are 150 students majoring in electrical then there must be 70 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 20.   if there are 150 students majoring in mechanical there must be 50 students who are not majoring mechanical at all, since the number of the student who are not majoring electrical but majoring mechanical will be at least 20, hence the number of students both majoring mechanical and electrical will be at least 70   so there must be at least 70 students who major in both   see the answers option the only possible answer is 70 to 100 !
<result>B</result>
Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 150 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from