subject problem

Hi All,

This question has a lot of details to keep track of, but since the answers are NUMBERS, we can use them to our advantage. With a bit of logic and some notes, we can TEST THE ANSWERS and find the two values that will "fit" the given "restrictions" in the prompt.

We're told that there are 3 science classes: Chemistry, Physics and Biology. The following facts are also included:
1) Each student in school takes AT LEAST 1 science class.
2) Each class contains 20 students.
3) Take any 2 classes, and they have the SAME NUMBER of COMMON students
4) 5 students take ALL 3 classes.

We're asked to find two numbers that are consistent with each other (meaning they occur in the SAME solution) for:
A) The number of students who could take JUST 1 class
B) The number that are COMMON to any 2 classes.

Here's how we can use the answers to our advantage. Since the classes contain just 20 students each, there can't be a situation in which 24, 33 or 39 have a class in common. Thus, the answer to the second question is either 7 or 9. We can now TEST those values to see how many students take 1, 2 or 3 of the classes.

Let's start with 7. We know that the 5 students who take ALL 3 classes will be COMMON to any 2, so with 7 total who fit that description, we'd have to account for 2 more students who are COMMON to any pair of classes...

Chemistry & Physics: 2 students
Chemistry & Biology: 2 students
Physics & Biology: 2 students

So, we have the 5 students who are in ALL 3 classes and the 6 students described above (who appear in 2 classes each). So far, that gives us....

Chemistry: 5 + 2 + 2 = 9 students
Physics: 5 + 2 + 2 = 9 students
Biology: 5 + 2 + 2 = 9 students

Since each class has a TOTAL of 20 students, that means that each class has ANOTHER 11 students who take JUST that 1 CLASS.

11 + 11 + 11 = 33

These values: 7 and 33 match two of the numbers in the options, so they MUST be the respective answers to the two questions.

Final Answer: 33 and 7

GMAT assassins aren't born, they're made,
Rich