GMAT Tip of the Week

E-Venn Easier

(This is one of a series of GMAT tips that we offer on our blog.)

Some historical titles are more well-deserved than others. Louis Braille deserves far more credit than he gets, as many are probably unaware that the term “braille” derives from the name of the man who made it possible for the blind to read. On the flip side, Amerigo Vespucci, from whose name the geographical name “America” was created to describe the majority of the Western Hemisphere, was fairly lackluster as an explorer compared to others of his generation. Still, his name has become affiliated with some of the greatest businesses, halls of government, and other paragons of world culture throughout the modern world.

Similarly overrated, at least in this author’s opinion, is the work of John Venn, whose name strikes fear in the hearts of GMAT test-takers who dread the appearance of “Venn Diagram” problems. Not to slander Venn’s name, but his diagrams, while useful in many instances, tend to be more complicated than necessary in their application on most GMAT problems.

Venn’s contribution to mathematics is a device for remembering something that logic should dictate on its own:

If there are 200 people invited to a house party for Kid ‘n Play, and 150 were invited by Kid, while 100 were invited by Play, how many people received invitations from both Kid and Play?

Venn notes that this is an overlapping set, as the total number of invitations — 150 from Kid, 100 by Play — adds up to a larger sum (250) than the number of people invited. (Surely that house can’t fit 250 people!) Therefore, some people must have been double-counted. How can we determine how many?

Well, they’re “double-counted,” or counted twice — once as a Kid invite, and once as a Play invite. So, if we need to make sure that they’re only counted once, we need to subtract them once (twice – once = once). Accordingly, we reach our total of 200 by using the equation:

Kid invites + Play invites – invited by both = total
150 + 100 – both = 200
250 – both = 200
50 = both

Venn’s contribution to this problem would be to draw circles representing “Kid” and “Play,” with the two circles overlapping at “both,” to visually represent the fact that there is overlap. For this, Venn’s name is known around the world as the inventor of these required mathematical diagrams, when in this case the logic behind the diagram is hopefully intuitive and fairly quick to reason.

For your GMAT preparation, keep in mind that the sheer memorization of items like the “Venn Diagram” is much less important than your ability to use the logic behind them to solve problems. Before you succumb to Venn anxiety, remind yourself that Venn didn’t do much more than represent logic visually; you could create the same if necessary, but as Venn and Vespucci proved, timing in life is everything when it comes to name recognition…

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