In a graduating class of 236 students

Adam Lyons, Magoosh Tutor

That's exactly right!

Dec 1, 2019 • Reply

Hi Adam, quick question. At first I tried to solve this problem using the two items formula (group A + group B - both + neither = total). I made neither 0 to maximize the both value. This gave me 27, which is the wrong answer. I then solved this problem using the double matrix method and that gave me the right answer, 121. Two questions, what is the difference between these two methods? Are they used for different types of problems? And secondly, why didn’t the two items formula yield the right answer? Thank you in advance.

Apr 10, 2020 • Reply

Adam Lyons, Magoosh Tutor

Hello there,
I've seen this formula before (group A + group B - both + neither = total), and I don't like it. It can be confusing to students, and generally I think it's best to use logic when you can and avoid formulas. The error you've made is to assume that everyone in the 236 student graduating class is taking either algebra or chemistry (i.e., neither = 0). But that's not necessarily true. If neither = 94, then the equation becomes 142 + 121 - 121 + 94 = 236. And that gets us our "both" value of 121.
To maximize the overlap between chemistry and algebra, we simply assume that all 121 chemistry students also take algebra. The answer is as simple as that!

Apr 24, 2020 • Reply

David Recine, Magoosh Tutor

We can't have 142 taking both algebra and chemistry, because only 121 students took chemistry. An only the students who took chemistry could have conceivably taken both chemistry and algebra. So the smaller number-- 121-- must be the maximum.

Dec 18, 2018 • Reply

Adam

Hi Lorenzo,

As Chris notes in the video, the numbers in the Venn diagram do not need to add up to 236. The 236 number includes students who did not take algebra or chemistry.

Sep 2, 2017 • Reply