There are 93 students in the class; 42 like Math, while 41 like English. If 30 students don't like either subject, how many students like both?




D. The answer cannot be determined from the data given.

  • 1
    $\begingroup$ use venn diagram $\endgroup$ – NewGuy Mar 18 '18 at 19:18
  • $\begingroup$ You have some idea of set theory? $\endgroup$ – ab123 Mar 18 '18 at 19:18
  • $\begingroup$ actually not too too much. $\endgroup$ – Ian Simons Mar 18 '18 at 19:25


The principle of inclusion-exclusion tells us that

$$|A\cup B|=|A|+|B|-|A\cap B|$$

Let $M$ represent the set of students in the class who like math and $E$ who like english.

The problem tells you $|M|$ and $|E|$ directly and gives you enough information to find $|M\cup E|$ (the amount of people who like at least one of math or english)

People who like at least one of math or english are those people who aren't a part of the people who don't like either.

The problem is now to use this information to find $|M\cap E|$, the amount of students who like both.

It may help to draw yourself a Venn Diagram to help visualize the information.


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