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Source: Official Guide Revised GRE 1st Ed. Part 8; Section 5; #12


In a graduating class of 236 students

In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry.

4 Explanations


James Moore

Quick question, ... if the question were rephrased to say "the least amount" not the greatest amount, the answer would be 27, correct?

Nov 28, 2019 • Comment


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


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



Why not 142?

Dec 17, 2018 • Comment

David Recine

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


Lorenzo Peve

if you put 121 you cannot get 236 students

Aug 5, 2017 • Comment


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


Chris Lele

Oct 11, 2012 • Comment

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