Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This is an overlapping set question that is testing our ability to solve for maximum and minimum values. We know this because the answer choices each provide a range of values. The best way to solve this problem would be to set up a table with two categories: chemistry and biology. More specifically, our table will be labeled as follows:
1) Majored in chemistry (Chemistry)
2) Did not major in chemistry (No Chemistry)
3) Majored in biology (Biology)
4) Did not major in biology (No Biology)
We are given:
Total = 200
Chemistry = 130
Biology = 150
No Chemistry and No Biology = at least 30
We can fill all this into our table. Remember, all the columns and rows sum together.
Now that we have our chart initially filled in, we can determine the greatest and least number of students who majored in biology and chemistry.
Because we are given that at least 30 students majored in neither biology or chemistry, let’s assume that this number is exactly 30 students. Using the value 30 as the “No Chemistry-No Bio” entry, we can solve for the remaining entries in the table by subtraction.
We see that there are 110 students who majored in both biology and chemistry. Even though at this point we don’t know whether this is the maximum or the minimum number of students who could major in both sciences, we can guess it’s a minimum by looking at the answer choices given. Furthermore, if that is the case, the answer must be either choice D or E.
Now, if 110 is indeed the minimum, how can we find the maximum? Recall that we used 30 as the number of students who majored in neither science, and 30 is the smallest number we can use for the “No Chemistry-No Bio” entry. So, now let’s find the largest number we can use for that entry. Recall that there are a total of 50 students who did not major in Bio, so the “No Chemistry-No Bio” entry can be at most 50. That is, the largest number we can use for that entry is 50. Now let’s fill in the rest of the table.
We see that there are now 130 students who majored in both biology and chemistry, which is also the maximum number of students who could major in both sciences.
Answer: D
Note: If you (incorrectly) think there are a total of 70 students who did not major in Chemistry, the “No Chemistry-No Bio” entry can be at most 70, and subsequently pick choice E as your answer, then your table might look as follows:
But this is incorrect because you haven’t filled in the entire table. If you were to finish, you would see that the “Chemistry” and “No Bio” entry would yield a negative number, which is an impossibility.
It’s always safest to fill out the entire table, which will let you know whether it makes sense or not. By doing so, you won’t fall into the trap the test makers have set up for you.
