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

Adam Lyons, Magoosh Tutor

That's exactly right!

Dec 1, 2019 • Reply



Why not 142?

Dec 17, 2018 • Comment

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


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


Gravatar Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

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