this is just my empirical observation, but i have found that EVERY SINGLE ONE of the official gmat problems involving three sets are specifically written in such a way as to make them extremely venn-friendly.
in particular, a randomly written problem would be, in all likelihood, extremely ugly from the standpoint of a venn diagram. for instance, an innocent-sounding statement such as "40 members speak english" would actually span FOUR regions of the venn diagram (eng only, eng/span, eng/germ, all 3). throw together a couple of statements like that, and you've got a disaster just waiting to happen.
however, the gmat writers apparently take pains to ensure that this sort of thing won't happen on their 3-set problems. note all the convenient restrictions in this problem:
* the 60 and the 20 in the statements both go into single well-defined regions of the venn diagram (english only for (1), outside the circles for (2))
* 0 for german only
* 0 for spanish and german (this takes some thought)
* 70 for spanish only
* 0 for all three
notably, there is not a single figure given in the problem statement that spans two or more regions of the venn diagram. compared to random venn problems in math textbooks, which go out of their way to make you create ugly simultaneous equations, this is a nice treat.
lesson: use a venn diagram for 3-set problems. the problem is going to roll out the proverbial red carpet with its restrictions.
Ron has been teaching various standardized tests for 20 years.
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Yves Saint-Laurent
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