Bunuel wrote:
How many of the 350 students at Glendale High School took math?
(1) All students must take math, science, or both.
(2) The number of students taking math is one-third the number of students taking science and two times the number of students taking both.
This question asks us to find how many of the 350 students at Glendale High School took math; in order to solve this question it necessary to know it some students took neither, both, or perhaps only one or the other- in knowing the answers to those questions we can apply set theory.
Statement (1) tells us the all students must take math, science or both- therefore there are three categories and no student can take neither. Yet we have no restrictions such as twice as many students took math therefore there are infinite possibilities. Insufficient.
Statement (2) tells us the relative frequency of students taking math, science, or both; however, again, if we do not know that no student can take neither then there are infinite possibilities ( e.x 60 students could be taking science, 20 could be taking math, 10 could be taking both and the rest could be taking neither. Insufficient.
Statement (1) and Statement (2) allows us to synthesize restrictions and are therefore sufficient together.