Venn Diagram: Goops, Gorps, Gorgs

Date: 09/19/2002 at 00:03:47
From: Regina
Subject: Brain teaser

Every Goop is a Gorp. Half of all Gorgs are Gorps. Half of all Gorps 
are Goops. There are 40 Gorgs and 30 Goops. No Gorg is a Goop. How 
many Gorps are neither Goops nor Gorgs?

Is the answer zero?

Date: 09/19/2002 at 12:25:28
From: Doctor Peterson
Subject: Re: Brain teaser

Hi, Regina.

Draw a circle representing the Goops. Draw another circle around this 
for the Gorps; we put the Goops entirely inside the Gorps because all 
Goops are Gorps.

Now notice that no Gorgs are Goops. Where should we draw the circle 
for the Gorgs?

Now you have a Venn diagram for the problem, and can start filling in 
numbers, using the given numbers and ratios.

For fun, here's my version:

    +---------------------+
    | gorps               |
    | +-------+   +-------|-------+
    | | goops |   |     gorgs     | 40
    | |  30   |   | 20    |    20 |
    | +-------+   +-------|-------+
    |           10        |
    +---------------------+

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/