Set Theory

[sarathsasikumar]

Question from www.thegmatcoach.com

Of the Diplomats attending a conference, 20 speak
German, 32 do not speak Spanish, 20% speak neither German nor
Spanish, and 10% speak both German and Spanish. How many
diplomats came to the conference?

[jssaggu.tico]

By Venn Diagram we have :

(Not.Spanish+Not.German)+German-(German+Spanish)=Not.Spanish
You must draw a Venn diagram of Spanish & German speaking diplomats having intersection enclosed in rectangular block which represents total number of diplomats. Then only you may understand the above statement.

Lets total people be x, then we have:
0.2x+20-0.1x=32
=>x=120
So, total number of diplomats are 120.

[RonPurewal]

Question from http://www.thegmatcoach.com

Of the Diplomats attending a conference, 20 speak
German, 32 do not speak Spanish, 20% speak neither German nor
Spanish, and 10% speak both German and Spanish. How many
diplomats came to the conference?

you don't want to use venn diagrams here - venn diagrams are awful for problems with only two criteria.

instead, use the DOUBLE SET MATRIX: (if you don't know what this is, and don't have our materials, it's the same thing as a "two-way table with marginal distribution". you can google that.)

for this problem, the COLUMNS are GERMAN / NO GERMAN / TOTAL
and the ROWS are
SPANISH
NO SPANISH
TOTAL

here you get:


0.1X / blank / blank
blank / 0.2X / 32
20 / blank / X

since all the rows and columns are additive, you can subtract to get:

0.1X / blank / blank
20 - 0.1X / 0.2X / 32
20 / blank / X

then, add up the middle row:

20 - 0.1X + 0.2X = 32
X = 120

totally routine.