**To Venn or not to Venn**

Your faithful GURU remembers the first time he solved a complex looking GMAT set problem with an oh-so-simple Venn diagram. He felt warm and fuzzy and powerful all over.

Venn diagrams are definitely useful for 2 or 3 sets of elements with overlaps... kids who like hot dogs, kids who like hamburgers, kids who like both. But what about problems involving kids who are vegetarian? What about those set problems where the elements fall into categories that are mutually exclusive? These come up occasionally, and, though we all love our Venn diagrams, they are best solved with a table or a matrix. For example,

**Q.** Of 30 students who took the GMAT, 14 had been out of school for at least 3 years, 18 had business degree, 3 had been out of school for less than 3 years and did not have business degrees. How many students had been out of school for at least 3 years and had degrees in business

(A) 14

(B) 13

(C) 9

(D) 7

(E) 5

**Soln.** Either you have a business degree or you don't. Either you've been out of school for at least 3 years or you haven't. Either you've got green eyes or blue eyes or brown eyes. This problems involves mutually exclusive categories, so we should use a table:

Out at least 3 | Out less than 3 | Total | |
---|---|---|---|

Business degree | X | 18 | |

Non-Bussiness degree | 3 | ||

Total | 14 | 30 |

As you can see the table provides an easy way to classify all the information. GURU is careful, so he has labeled what he is looking for with an X. This is a good idea with all story problems - always make a note of what you're looking for so you don't get sidetracked.

Now we can fill out the table using some simple arithmetic:

Out at least 3 | Out less than 3 | Total | |
---|---|---|---|

Business degree | X = 18 - 13 = 5 |
16 - 3 = 13 |
18 |

Non-Business degree | 3 | ||

Total | 14 | 30 - 14 = 16 |
30 |

First we find the stuff in red, then blue, then green. The green calculation is our answer: 5 or E.

Note: we could have found the answer a different way - we could have started with the total number of non-business degrees. Try it yourself.

Note: We don't have to fill in the entire table to get the answer we're looking for. The GMAT is time intensive, and avoiding unnecessary calculation is imperative.

You can learn more nifty techniques like this using BenchPrep's GMAT prep package.