GMAT Graphics Interpretation: How to Interpret a Venn Diagram:

by on February 7th, 2012

The Graphics Interpretation section will present you with a piece of data in the form of a graph, Venn diagram, scatter plot, etc. Below will be two statements, each with a missing portion. You will be asked to answer by choosing one of four choices presented in a drop-down menu.

The mock questions released from GMAC have shown that Venn diagrams will appear in Graphics Interpretation questions. So, what is a Venn diagram? And how can we apply our knowledge of set theory to the new Integrated Reasoning section? Let’s take a look at how Venn diagrams are currently tested on the GMAT first. This is a classic, challenging GMAT question involving a Venn:

In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

(A) 11N/12
(B) 7N/12
(C) 5N/12
(D) 6N/7
(E) N/7

We can quickly make sense of this word problem by creating our own Venn diagram:

Notice how the number at the top is the total for ALL PARTS of the Venn. The number above each circle “N/3” and “?” represent the total number WITHIN that circle (both the overlap and non-overlap sections). To solve, the key to understanding this question lies in the last sentence: who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

We have two categories to sum: the people who ONLY received a science degree but NOT from one of the 6 schools, and the people who ONLY went to the 6 schools but did NOT receive a science degree. I made up variables for these categories (x and y).

If N = 12, there are 4 applied science students, 1 of which is both. That means x = 3. If 4 students are applied science, then 12 – 4 = 8 are from one of the six states but NOT applied science. y = 8. 3 + 8 = 11. Therefore, we are looking for an answer choice that gives us 11 when N = 12; the answer is A.

The key to a Venn is being able to apply information from one part of the diagram to another part. If you are rusty on these, you may want to memorize some of the formulas in this article.

1 comment

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